Guessing the game: An individual's awareness and assessment of a game's existence

Kostelic, Katarina Article Guessing the game: An individual's awareness and assessment of a game's existence Games Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Kostelic, Katarina (2020) : Guessing the game: An individual's awareness and assessment of a game's existence, Games, ISSN 2073-4336, MDPI, Basel, Vol. 11, Iss. 2, pp. 1-28, https://doi.org/10.3390/g11020017 This Version is available at: https://hdl.handle.net/10419/257436 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ games Article Guessing the Game: An Individual’s Awareness and Assessment of a Game’s Existence Katarina Kostelic Faculty of Economics and Tourism “Dr. Mijo Mirkovic”, Juraj Dobrila University of Pula, 52100 Pula, Croatia; [email protected] Received: 21 December 2019; Accepted: 20 March 2020; Published: 26 March 2020   Abstract: In everyday life, games begin inconspicuously, leaving an individual to stumble upon their assessment of a situation. An unaware individual is unlikely to exhibit strategic behavior in a given situation, which highlights the importance of awareness examination. The purpose of this exploratory analysis is to examine awareness and assessment of a game’s existence at the individual level. That requires examination of respondents’ detection (as an indication of their awareness) and identification (as an indication of their assessment) of game elements in game-like situations and their relation to awareness of the game existence. The empirical data is collected using a scenario technique and is statistically analyzed. The results show that the respondents are, on average, at least partially aware of possibility for strategic interaction (even in vague situations). The revealed regularities point out to the relation of the game elements to game existence belief, but also indicate the presence of psychological biases and information utilization issues. For example, the respondents assign different levels of belief to game existence regarding possible losses or gains. Research limitations involve the use of a small convenience sample and lead to suggestions for results validation in future research. Possible implications of the results are discussed. Keywords: game awareness; behavioral game theory; individual; belief 1. Introduction In everyday life, games do not follow standard game theory procedure, with all assumptions predefined; instead, they begin covertly, leaving an individual to assess what is happening. This leads to the very important game theory assumption, which is implicitly assumed and often not particularly isolated—awareness of the game. Halpern and Rego [ 1 ] argue that the flaw of standard game representation is that it implicitly assumes that the modeler and the players all understand the game the same way, that is, the game elements are common knowledge. In order to play a strategic game, players ought to be aware that they are playing a game. Such a necessity, as well as lack of awareness, is narrowly tied to another game theory assumption: interaction. Interaction requires communication, which can be intended and unintended [ 2 ] and can have intended and unintended consequences as well. In addition, individuals can make mistakes in perceiving and interpreting the communication signals received from others. This means that individuals can be part of a game without knowing it, as well as believe that there is a game in process when there is none. Such situations can occur for an individual in everyday life, regarding interactions with partners, friends, coworkers, or in business, economic and law interactions, etc. Many of those examples can be observed as game-like situations. Insights into individuals’ awareness in everyday game-like situations can be used to enhance modeling of individual assessment of the situations, and consequently, their strategic behavior. Individual awareness and assessment of a game’s existence relate to the fields of situational awareness, unawareness, and a ‘pre-game’ theory. Salmon et al. [ 3 ] examine definitions of situational Games 2020,11, 17; doi:10.3390/g11020017 www.mdpi.com/journal/games Games 2020,11, 17 2 of 28 awareness, Bazerman and Chugh [ 4 ] and Chugh and Bazerman [ 5 ] offer definitions of bounded awareness, and Blasch et al. [ 6 ] review situation awareness in game theory, while most of the empirical research in the area focuses on threat awareness, in-game assessment, and prediction, with an emphasis on the application in the security field and the gaming industry [ 7 – 10 ]. Halpern and Rego [1,11–13] examine modeling unawareness regarding the language, knowledge, probabilities assignment, extensive games, action choice, and solutions. Most of the existing research focuses on the (un)awareness and outcome prediction in an ongoing game and not the player’s belief about a game’s existence. It is important to notice the distinction: once the individual is aware of an ongoing game, s/he might focus their efforts on recognizing and perceiving game elements and potential threats; while awareness of the game represents an individual’s ability to determine whether a game or game elements exist in the first place. To explore the awareness and assessment of the game-like situations at an individual level, a scenario technique is employed. For example, an individual is going to the shop to buy their usual groceries. Besides the usual shopping list, s/he intends to buy a favorite chocolate. When s/he arrives to the shell with the chocolates, they learn that the chocolate’s price increased. In this situation, a price increase can be detected as an action. While the party that initiated this activity is not explicitly stated, an individual could guess based on common knowledge that it could be the shop manager, supplier, manufacturer, or government (through taxes). Most scenarios are open-ended, meaning that the actions of the respondent are not offered in the scenario. The reason for this is that the awareness and assessment of the game’s existence precede the individual’s assessment of their own possible and feasible actions. Possible immediate outcomes for the individual are the loss in case of a purchase or the lack of satisfaction from chocolate in the case of a non-purchase. That is merely a purchase decision, without any observable strategic implications. So, based on the respondent’s awareness and assessment of a situation, it can be perceived as a game or as not being a game. Only if an individual assesses that there is a possibility of strategic interaction it would make sense to put effort into examination of their own set of possible and feasible strategies/actions. In this example, if an individual believes it is a strategic interaction, they may decide to play the game and to choose their own action that would lead to a preferable outcome. Besides the immediate purchase action choice, the individual might choose not to purchase that brand of chocolate until the price drops. The underlying strategy of such a choice is a presumed decline in demand, which would force the other player to reduce the price. If taken to an extreme, individual may, for example, choose to form or join an association for consumer protections and bargain for a reduction in the price of the chocolate. But that is possible only if an individual previously assessed the situation as strategic, like a game. If an individual is not aware of the game-like situation, then it is not likely that s/he will employ a strategy. A game-unaware individual is almost like a passive player in a dictator-like game. The “player” unaware of the game will most likely not exhibit strategic behavior, while a partially aware “player” might exhibit a skewed assessment and strategic behavior that deviates from optimal behavior. Therefore, an exploratory empirical research of awareness is necessary. The purpose of this research is to examine individual awareness of a game’s existence and assessment of game elements. The empirical data, gathered using a scenario technique, is used to provide insights into an individual’s use of awareness and assessment of game elements and assigned beliefs to obtain answers about game elements regarding contextually different (everyday) situations. The analysis is focused on the quantification of self-reported detection, identification, and beliefs in game elements and the game’s existence. Insights into individual awareness in everyday game-like situations enable deeper understanding of an individual’s awareness and assessment of interaction situations, which can influence their outcomes/payoffs. The theoretical framework section examines awareness and the formation of a belief assigned to a game’s existence and offers an assessment of game presumptions on a personal level under incomplete information and uncertainty. The next section examines game existence awareness using a scenario technique and offers results and interpretation of statistical analysis. The conclusion section summarizes the results, discusses the implications, and offers proposals for further research. Games 2020,11, 17 3 of 28 2. Theoretical Framework 2.1. Awareness and Forming a Belief Assigned to a Game’s Existence: A Literature Review According to Camerer, Ho, and Chong [ 14 ], in a standard equilibrium analysis, every player forms his or her belief based on the analysis of what the other players can do; players choose the best responses given their beliefs, adapt their responses, and update beliefs until they achieve equilibrium. To form a game theory model, there must be: a strategic interaction; at least two players for which the choice of actions of least one of them should imply the presence of a strategy; and there must exist two or more possible outcomes shaped by players’ choices. Basic game elements and presumptions must be satisfied for a game to exist. Hence, the existence of those elements and presumptions should be a threshold for determining whether the game exists. The individuals may misinterpret a situation: individuals can either be a part of a game without knowing it, or there is no game, but one believes there is. The first option has strategic importance regarding the outcome. To paraphrase Harsanyi [ 15 ], the lack of action is also an action in itself, and the probability that an unaware player’s lack of actions will result in a preferable outcome is very small. In order to assess individual awareness and assessment of a game existence, it is necessary to examine the (un)awareness framework. Salmon et al. [ 3 ] systematize the most frequently used models of awareness. Smith and Hancocks’ Perceptual cycle model of situation awareness is general enough to be used prior to the game, and reflects the information retrieved from the environment and the influence of cognitive features, and has an action as a result. Chen et al. [ 16 ]’s approach to defining unawareness as “a real-life phenomenon associated with an unconscious mental state directed toward, or lacking positive knowledge about, a definite event”. Chugh and Bazerman examine the aspects of bounded awareness. They define bounded awareness as individual’s “failure to see and use accessible and perceivable information, while seeing and using other accessible and perceivable information” [ 4 ] and “a phenomenon that encompasses a variety of psychological processes, all of which lead to the same error: a failure to see, seek, use, or share important and relevant information that is easily seen, sought, used, or shared” [ 5 ]. This approach to unawareness sets a broad framework, allowing a wide range of possibilities for individual differences. This can be related to previous extensive research regarding perception flaws, cognitive illusions and heuristics, and bounded rationality [ 17 – 20 ]. The awareness and assessment of a game’s existence can vary over individual assessments given perceptions, common knowledge, memory retention, information interpretation, and the ability to conduct outcome calculation. Blasch et al. [ 6 ] provide an extensive review of situation awareness in game theory, while defining a game situation as “economic effort to extract either a real or virtual monetary payoff”. As a systematization of their review, they offer an explanatory figure. They distinguish awareness and assessment, which can be related to the Perceptual cycle model of situation awareness. Awareness consists of entity awareness, situation awareness, cyber awareness, and knowledge awareness. The assessment is consisted of object assessment, situation assessment, network assessment, and social assessment. Application of this approach to basic game theory elements would refer to awareness and assessment of the other player(s), interaction (action), and the outcome. Additional elements that an individual may be aware of and assess are the rules and game context, as well as possible and feasible strategies. However, Halpern and Piermont [ 21 ]’s approach to (un)awareness does not have a distinction between the awareness and the assessment. The authors propose partial awareness, where the player: values different objects (or different states of the objects) the same, if their properties are the same; can value objects differently if they can be distinguished in some way that individual is aware of; can base their own preferences only on the properties that they are aware of. Such an approach implicates that an individual must be able to assess (evaluate) some properties to be aware of them. The difference in approaches indicates that the relationship of the awareness and assessment requires further investigation. Whether the awareness precedes the assessment, or the assessment is a part of the awareness, those constructs are interlinked and often used interchangeably. Games 2020,11, 17 4 of 28 Von Thadden and Zhao [ 22 ] find that unawareness requires modeling restricted decision making by agents. Chen et al. [ 16 ] argue that plausibility says that “player’s unawareness arises if the agent does not know that the event is true, and that the player does not know that he or she does not know it”. Authors offer a concept of player’s introspections, which allows the player not to know about their own unawareness or to be unaware of their own unawareness. Heifetz, Meier, and Schipper [ 23 ] examine dynamic interactions where the player has unawareness of their available actions. Action availability is relevant because of its strategic implications: unawareness of the action is distinct from the unavailability of the action. They suggest that players can become aware of new aspects of the dynamic interaction through the game, where the player’s evolving belief must be represented by a belief system as a part of the definition of the game (and cannot be defined as an initial probabilistic belief about nature). This provokes a thought about a possible extension—can the same findings be applied to the distinction between the availability, existence, and awareness of the action(s) of other players? Ozbay [ 24 ] finds that players can extend their awareness if they come to a node in the game that they were not aware of before. The author discusses the problem of assigning zero probabilities to actions/outcomes, which can be applied if a player receives information through the in-game communication that can be perceived as cheap talk. Much of the previous research considers uncertainty and beliefs about game elements, such as: other players’ preferences, information, available actions, and possible outcomes [ 9 , 25 – 27 ]. The findings from the epistemic logic approach provide context and relevant influencing factors for the theoretical consideration of awareness. Halpern and Rego [ 11 ] use primitive prepositions to generate awareness. They find that knowledge represents a relevant part of modeling unawareness, and distinct implicit knowledge (“truth in all worlds the agent considers possible”) and explicit knowledge (“conjunction of implicit knowledge and awareness”). They find that there exists a subjective view of the objective situation and that view can result from the limited agent’s vocabulary. Same authors [ 13 ] examine a general solution concept where some possible game histories are removed, while others may be augmented. In such a game representation, a player may reach a certain node in the game and not be aware that he is experiencing a subjective representation of the game, which may include a “virtual” move for another player. That implies that players’ payoffbeliefs include moves that have no relationship to the underlying game or actual payoffs. Halpern and Rego [ 1 ] examined the lack of common knowledge in games. These authors’ approach allowed “the augmented games to be based on different underlying games”, where players reveal the underlying game through a game, while also revealing a lack of common knowledge. Rabin [ 28 ] forms a model of pre-game communication and examines its impact on the game equilibrium. Neuberg [ 29 ] examines how the influence of information perceived outside of conscious awareness influences social behavior. This author observes that the strategies players use differ given the subliminal information that they were exposed to. Even though the experiment was conducted during the game, and not prior to it, it reveals the intuition of individuals grasping signals about strategic interaction from their surroundings. According to Camerer [ 17 ], the most useful research regarding a behavioral ‘pre-game’ theory are unstructured games derived by Neale and Bazerman, a series of negotiation experiments, designed to resemble realistic negotiation situations (and not a game). Afterwards, the results of such experiments can be used to verify whether results confirm game theory presumptions and axioms. This served as an inspiration for the scenario approach, which will be used in this paper. The existing research mostly focuses on (un)awareness definitions, resulting strategies, and outcomes prediction in an ongoing game, rather than assessing the perception and the belief about the game’s and game elements’ existence. It is important to notice the distinction: once the individual is aware that he or she is part of a game, it is likely that he or she will focus his or her efforts on recognizing and perceiving game elements; meanwhile, awareness of a game existence represents an individual’s ability to detect whether game elements and a game exist in the first place. Moreover, Games 2020,11, 17 5 of 28 the unawareness of the game elements and game existence leads to an individual’s failure to act and to strategically influence the interaction outcomes. The research in the fields of security and gaming raised the question of empirical assessment of situational awareness [ 7 , 8 , 30 – 32 ]. This empirical research of (un)awareness represents a motivation for an empirical approach to determine an individual’s awareness of game elements and game existence in everyday game-like situations. 2.2. Assessing Game Presumptions on a Personal Level, Under Incomplete Information And Uncertainty If an individual wants to figure out whether a game exists, he or she might stumble upon an ambiguous situation. The beginning of the analysis requires a descriptive approach. If the individual can identify game elements, then he is probably in a game. However, a distinction must be made regarding the intentions of any other player: actions can have deliberate or unintended effects an individual’s payoffs. Consequently, the game’s existence might not be determined if an individual believes that the other player’s action is not related to him, and if presumed effects on his payoffs are unintended. Assuming that individuals differ given common knowledge (or lack thereof), perception flaws, information interpretation, and their ability to calculate probabilities and outcomes, their detection and identification of game elements (GEE) and a game’s existence (GE) will vary. To figure out whether there is a game, the individual should start by answering the following set of questions: •Are someone’s actions and strategies influencing my possible outcomes? •Who are the players who choose those actions and strategies? •Which actions and strategies have already been played? • What are the possible outcomes and how do other players’ actions influence the set of possible outcomes? •What are the other players’ preferences given the actions and strategies employed? Also, it is necessary to make a distinction about game element detection (awareness about the GEE) and game element identification/description (assessment of the GEE). Usually, the individual cannot answer these questions with certainty due to their lack of complete information, but they can assign a certainty or belief (probability) to each answer, respectively: • certainty or belief assigned to awareness that someone’s actions influence individual’s possible outcomes βA •certainty or belief assigned to awareness that players exist βB • certainty or belief assigned to assessment that actions and strategies exist that have already been employed βC •certainty or belief assigned to assessment of players βD •certainty or belief assigned to assessment of possible outcomes βE •certainty or belief assigned to the assessment of their own possible payoffβF The probabilities denote the level of certainty, confidence, or belief that the provided answer to a question about GEE detection/description is true. Questions differentiate awareness and assessment according to Blasch et al. [ 6 ]. Those efforts, which an individual should make before modeling a game are systematized in Table 1. Games 2020,11, 17 6 of 28 Table 1. Game elements detection and identification with associated beliefs. Element Individual’s Answer Belief Action detection Yes/No/Not sure βA Player detection Yes/No/Not sure βB Action identification Description βC Player identification Description βD Defining set of possible outcomes Yes/No/Not sure, description βE Defining own possible payoffYes/No/Not sure, description βF Game existence belief /β Source: Author. Every further assessment requires time and information search and as such, exceeds the scope of this research. The answers about game elements can be coded (for example as a binomial variable, where occurrence of detection or description is coded as 1, else 0). Additional quantitative information is derived from the assigned beliefs. There is some other information relevant for belief asignment. The set of reasoning, computation, information interpretation and memory retrieval of the common knowledge could, but does not have to be done at the conscious level, as Salehnejad [ 33 ] finds that learning through continuous belief updates makes the homo economicus an intuitive Bayesian statistician—where some of the reasoning does not occur at the conscious level. 3. Examining Game Existence Awareness Using a Scenario Technique 3.1. Scenario Technique and the Data To assess an individual’s ability to recognize a game-like situation, exploratory research is conducted to gain initial insights. The survey was conducted in 2020 on a convenient sample of 87 first year students of economics and business economics 1 . After removing the incomplete answers and answers whose respondents had game theory knowledge, 48 responses per scenario were used in analysis, with total of 432 observations. The average age of the respondents is 19.48 with standard deviation of 0.13. Each respondent answered questions about nine scenarios. The examination was conducted without any instructions that would involve game theory elements. The first seven scenarios are unstructured (or semi-structured) game-like situations describing several everyday situations, while the last two present structured game-like situations (an adapted prisoner dilemma and adapted extended-dictator-trust game). The first seven scenarios are vague on their purposes, as everyday situations usually do not occur as structured games with the predefined rules, but require individuals’ awareness and assessment under circumstances of incomplete information and uncertainty, followed by an the information search and in-game assessment (the latter two extend the scope of this paper). Only the last two scenarios state possible actions for the respondents. The overview of the scenarios and provided information is presented in Table 2. 1 No incentive in the terms of material reward was provided, but the students could choose this task instead of the regular practice assignment (and would receive points; if they provided thoughtless answers, they would receive no points). Games 2020,11, 17 7 of 28 Table 2. Scenarios and provided information. Scenario 1 You are going to the shop to do your usual grocery shopping. Besides the items on your usual shopping list, you intend to buy your favorite chocolate. When you arrive to the shelf with the chocolates, you learn that your favorite chocolate’s price increased by 10 HRK (approx. $1.57). Information regarding action The price increase Information regarding player(s) Not stated explicitly (it can be recognized as a shop/shop manager, manufacturer, distributor, etc.) Information regarding payoffLoss of 10 HRK in the case of a purchase/lack of chocolate in case of a non-purchase Scenario 2 You are at a usual cafe hanging out with a friend. You notice that your friend is behaving slightly different and is somewhat restrained. Moreover, you notice an unusual look that can be interpreted as playful or mischievous. You are trying to figure out what that would mean: maybe it is a secret about preparations for your upcoming birthday, maybe the friend knows something you do not know (e.g., some gossip or some footage that has appeared on YouTube), maybe the friend is about to announce something important, maybe he or she is conducting a scheme, maybe . . . There may be a lot of options and maybe they have nothing to do with you. Information regarding action Non-verbal signals Information regarding player(s) Not stated explicitly (a friend with whom an individual is drinking coffee, or a third party) Information regarding payoffNot stated explicitly (the payoffcould be both positive and negative) Scenario 3 You arrive to work. You expect the usual tense working pace, and in addition to all your existing obligations, you get another one. Lately you have caught a few glances and greetings from other colleagues, and the reasons for these changes are not quite clear to you. You figure that you may be promoted to a better position. During the break, you meet a colleague and you mention the amount of work you need to do. With understanding and good intent, your colleague admits to you that one of your colleagues spoke badly about you. Moreover, it was the person who assigns you your tasks. Information regarding action Two separate actions are stated: workload and a rumor Information regarding player(s) Two players are stated: colleague and task assignor Information regarding payoffNot stated explicitly, but both positive and negative payoffs indicated Scenario 4 A month ago, you started a seasonal job. This season is better than the last one for the company’s turnover. There is a rumor amongst your colleagues that all the employees could get a raise. Information regarding action A rumor Information regarding player(s) Not stated explicitly (the rumor’s source is the colleagues, but the payer is the company) Information regarding payoffNot stated explicitly (a raise is stated as a possible payoff, but without the information about the amount) Games 2020,11, 17 8 of 28 Table 2. Cont. Scenario 5 You have received a team assignment to conduct some research and to report the results in a written form. There are four of you in the team. Your part of the assignment is to create a questionnaire. You are unfamiliar with designing questionnaires, so you contact one of the team members to help you. At that time, you learn that one of the team members already assembled the questionnaire. Information regarding action Activities within a team assignment Information regarding player(s) Team members Information regarding payoffA grade Scenario 6 You are a manager of a department for consulting clients in a leading consulting company. The company is well known for its large number of clients and for the lowest prices of its services. You meet a client and, in an informal conversation at the beginning of the meeting, he/she reveals that he/she has been contacted by a newly opened consultant company that offered their services at a lower price. Information regarding action New competitor that offers a service at a lower price and/or a client’s attempt to negotiate lower price Information regarding player(s) Newly opened consultant company and/or a client Information regarding payoff Not stated explicitly, but indicates loss (implicitly, it can be the loss of market share to competitor and/or a diminished price charged to a client) Scenario 7 You have come up with an idea to start your own business. Even though all the people who hear about the idea agree that it is an excellent idea, you do not have the capital to start the company. You consider giving up the idea, given that you cannot finance it. At that time, you receive an invitation to pitch your idea in front of five investors. If you impress the investors, they could decide to invest. Information regarding action Invitation to pitch the idea Information regarding player(s) Five investors Information regarding payoffNot stated explicitly (the possibility of investment—positive payoff—of an unknown amount is indicated) Scenario 8 Your colleague and you have been accused for cheating in an exam using unallowed electronical devices and are taken in front of the faculty’s ethical committee for interrogation. You and your colleague are placed in separate rooms and cannot know what the other one is saying during interrogation. The ethical committee member who conducts the interrogation makes the following offer to each of you: ”You may choose to confess or remain silent. If you confess and your accomplice remains silent, you will not be punished, and your testimony will be used to ensure that your accomplice gets a year of suspension. Likewise, if your accomplice confesses while you remain silent, s(he) will go free while you get a year of the suspension. If you both confess there will be two punishments, but I’ll see to it that you both get only 6 months of the suspension. If you both remain silent, I’ll have to settle for a token punishment for having unallowed devices during the exam and you will get 1 month of suspension.” Games 2020,11, 17 15 of 28 Table 4. Descriptive statistics of the beliefs. Action Detection βA Action Identification βB Player Detection βC Player Identification βD Possible Outcomes Identification βE Expected Payoff βF Game Existence Belief βGE Derived Game Elements Existence Belief βGEE Difference (βGEE −βGE) Scenario 1 β1i 0.6896 0.6906 0.7375 0.6406 0.6402 −0.4056 0.3756 0.2966 −0.0790 s1i 0.0498 0.0553 0.0541 0.0530 0.0554 0.1161 0.0231 0.3499 0.3374 95% conf. level 0.1003 0.1113 0.1088 0.1066 0.1114 0.2336 0.0465 0.1016 0.0980 Scenario 2 β2i 0.8235 0.6563 0.7296 0.5510 0.3585 −0.1367 0.3725 0.1678 −0.2047 s2i 0.0386 0.0568 0.0546 0.0639 0.0642 0.1219 0.0234 0.3475 0.3342 95% conf. level 0.0777 0.1143 0.1098 0.1286 0.1292 0.2452 0.0470 0.1009 0.0971 Scenario 3 β3i 0.8831 0.7133 0.8329 0.7513 0.5317 −0.5065 0.3869 0.2949 −0.0920 s3i 0.0323 0.0564 0.0415 0.0505 0.0654 0.1013 0.0234 0.4107 0.3992 95% conf. level 0.0650 0.1134 0.0835 0.1016 0.1315 0.2038 0.0470 0.1192 0.1159 Scenario 4 β4i 0.7273 0.5992 0.6842 0.6223 0.6365 0.7402 0.3690 0.2476 −0.1213 s4i 0.0541 0.0615 0.0566 0.0593 0.0597 0.0695 0.0261 0.3729 0.3697 95% conf. level 0.1089 0.1238 0.1138 0.1193 0.1201 0.1397 0.0525 0.1083 0.1074 Scenario 5 β5i 0.8781 0.7019 0.7860 0.7023 0.5260 −0.1102 0.3582 0.2140 −0.1442 s5i 0.0374 0.0541 0.0479 0.0600 0.0669 0.1288 0.0265 0.3645 0.3524 95% conf. level 0.0753 0.1088 0.0963 0.1207 0.1347 0.2592 0.0533 0.1058 0.1023 Games 2020,11, 17 16 of 28 Table 4. Cont. Action Detection βA Action Identification βB Player Detection βC Player Identification βD Possible Outcomes Identification βE Expected Payoff βF Game Existence Belief βGE Derived Game Elements Existence Belief βGEE Difference (βGEE −βGE) Scenario 6 β6i 0.8263 0.7206 0.7473 0.6256 0.6925 −0.5848 0.3738 0.3350 −0.0388 s6i 0.0452 0.0550 0.0539 0.0628 0.0587 0.0949 0.0264 0.4254 0.3753 95% conf. level 0.0909 0.1106 0.1085 0.1263 0.1180 0.1908 0.0532 0.1235 0.1090 Scenario 7 β7i 0.9379 0.7758 0.8102 0.6288 0.8660 0.8502 0.3869 0.4319 0.0450 s7i 0.0180 0.0537 0.0425 0.0645 0.0338 0.0554 0.0237 0.4415 0.4204 95% conf. level 0.0361 0.1081 0.0855 0.1298 0.0680 0.1114 0.0476 0.1282 0.1221 Scenario 8 β8i 0.7519 0.6779 0.6860 0.6510 0.6446 −0.4023 0.3940 0.2758 −0.1182 s8i 0.0547 0.0544 0.0599 0.0604 0.0610 0.1127 0.0225 0.3740 0.3367 95% conf. level 0.1101 0.1094 0.1206 0.1215 0.1227 0.2267 0.0453 0.1086 0.0978 Scenario 9 β9i 0.8450 0.7356 0.7688 0.7058 0.8446 0.5190 0.3616 0.4670 0.1054 s9i 0.0424 0.0528 0.0493 0.0575 0.0454 0.1063 0.0275 0.4363 0.4440 95% conf. level 0.0854 0.1062 0.0992 0.1156 0.0913 0.2138 0.0553 0.1267 0.1289 Source: Author’s computation. Games 2020,11, 17 17 of 28 Scenario 3 represents a more serious interaction framework, which can explain why average beliefs are higher. The player(s) are hinted at, and the workload can be interpreted as a negative payoff. While some of the respondents focused on the workload as an action and the boss as the other player, others perceived the gossip itself as an action and all colleagues participating in the gossip as other players. In addition, 87.5% of the respondents assessed the action as being deliberate. The expected payoffis negative, as predicted. A total of 37.5% respondents viewed the superior or the boss as the other player, while 41.67% of the respondents stated that the colleagues are the other players, and 6.25% indicated both the superior and colleagues as players. The outcome identification reveals a series of outcomes that vary given the gravity and the time-frame: getting fired, thinking about quitting, the further increase of the workload, diminishing productivity and the work dissatisfaction, hurt feelings because of the rumors, stopping the rumors, working even harder, and earning a promotion. This scenario offers the widest variety of the outcome descriptions. There was one description that explicitly stated an inability to assess the situation because of the lack of previous experience and one respondent related the descriptions to their own situation at a previous or current job. However, the GE belief is quite low, which might be the result of presumed future uncertainty. The only solid information in Scenario 4 is that the company’s turnover has increased, while the information about the raise is stated as a rumor. The overall average beliefs are moderate (in comparison to other scenarios), and 60.42% of the respondents assessed the action/signal as being deliberate. There were 20.83% of respondents that identified a raise as the action, 16.67% of the respondents stated that the action is the increase in company’s turnover, while the rest of the respondents who provided the action identification saw the activity to be a rumor about a raise among the colleagues. By the time the respondents answered about their own outcome identification (expected payoff), it seems that some of the respondents started to ‘believe’ the rumor, as 62.5% stated an increase in the salary as the payoff(some of them even offered a plan on how to spend the raise). Also, 12.5% of the respondents stated that their motivation would rise, as well as the effort put in the work, and suggested that this should lead to the expected raise. The remaining respondents who offered a description remained cautious and used terms such as ‘expecting’ or ‘hoping’, usually in combination with positive emotions related to that expectation or consideration of trust issues regarding the rumor. Scenario 5 indicates a multi-player situation with an assignment division, while the payoffis a grade. A total of 58.33% of the respondents found the activity to be deliberate. Given the provided information, the average GE belief is rather low (the lowest in comparison to other scenarios). The belief of the expected payoffis negative, as expected, but also low. While most of the respondents assessed the action and the player(s) as expected, the responses differed given the payoffidentification. A total of 43.75% of the respondents expected the outcome to be positive, as they do not have to do the job. However, the rest of the respondents assessed their outcome as being negative and offered descriptions that indicate that they expect to do another, heavier part of the workload. They also expressed worry because they could get a lower grade, or were hurt and felt left out. Scenario 6 can describe a market competition situation, with a statement from the other players and an indication of their strategy, or can be interpreted as a cheap-talk game with a client. A total of 62.5% of the respondents saw the other company as a player, while only 8.33% viewed the client as a player. A total of 75% of the respondents believed that the action described in the scenario is deliberate. While a negative payoffwas expected, the average GE belief is quite low, which in combination with the descriptive answers indicates that the respondents did not fully recognize the threat of the competition or perceived the situation as bluffing by the client. Scenario 7 describes a situation of a person who has a business idea and was offered a chance to pitch the idea in front of the investors. The provided action/signal was interpreted as deliberate by 81.25% of the respondents. While the invitation (to pitch the idea with the possibility of investment), observed as an action is only a signal without a real payoff, the average belief assigned to action detection assessment was the highest in comparison to other scenarios. The expected payoffbelief was also unexpectedly high, suggesting respondents’ (over)confidence and optimism towards winning Games 2020,11, 17 18 of 28 over the investors. The descriptive responses support that statement, but also indicate that some of the respondents treat the game as sequential, focusing on the payoffthat will result from their (excellent) presentation. One descriptive answer stated the inability of the assessment, because of the lack of any previous experience. Scenario 8 is an adaptation of the prisoner’s dilemma and represents a structured game theory example. Only 62.5% of the respondents found the activity to be deliberate (the same percentage as in the first and second scenario). It is surprising that respondents, on average, detected activity with a 0.7519 assigned belief rate, and identified the activity with a 0.6779 assigned belief rate. The average player detection and identification beliefs are low, given that all included parties are clearly stated in the scenario. In addition, 20.83% of the respondents who provided an answer for player identification (75%, Table 3), identified the person who conducts the interrogation as the other player, suggesting that they perceived the situation as a cheap talk game with the interrogator. A total of 6.25% of the respondents offered a long-term outcome identification that extends the game framework (would never cheat again/it is bad for society that cheaters finish college). Nevertheless, the most unexpected outcome was the low GE belief value, given that it is a scenario with complete information. This suggest that some individuals fail to assess the situation as strategic and include additional information or disregard provided information. Scenario 9 is an adaptation of the extended dictator trust game. Table 4shows that this scenario has the second lowest GE belief, and that the other awareness and assessment beliefs are lower than expected. Some of the responses regarding individuals’ own payoffindicate that some of the respondents recognized the trust issue (14.58%), other respondents stated that they cannot identify their outcome (14.58%), while some respondents referred to an altruistic approach and a positive payofffrom the satisfaction of doing a good deed (8.33%). Given the responses of the majority of the respondents (that can be classified as trust issue, tradeoff, or not-sharing) it seems that the homo economicus is still very much alive. On the other hand, all the respondents whose answers could be classified as focusing on the trust issue and a tradeoffstated that they would give/trade ‘half’ of the sandwich (although the scenario states “a piece”), presuming a fair trade. In addition, there were only 2.08% of the respondents that perceived the game as sequential, stating that they would first wait for the fulfillment of the colleague’s promise before sharing. Given these insights, there is a clear indication that some of the respondents did not understand the game in the same way as the modeler does [ 1 ]. The best example of this is Scenario 8, which qualifies as a structured game with all information provided. It was unexpected that almost a fifth of the respondents perceived the game as involving bluffing. It seems that the respondents systematically show deviation from the provided information (whether by including information from their previous experience or disregarding the provided information), which is also in line with the critique of the standard game representation [ 1 ]. Also, the respondents occasionally extended the given framework and offered solutions that turned an assumed one-stage game into a sequential one. That indicates a different respondents’ perception of the framework based on the time. The implications of such behavior can relate to inclusion of the ‘virtual’ moves and players’ payoffbeliefs that include moves that have no relation to the actual game and payoff[ 13 ]. The additional argument for this given observation is the average difference between the derived GEE belief and GE belief. While those differences show the deviation from the presumed underlying assessment process, they may also indicate the presence of psychological biases [ 4 , 5 ], intuitive probabilities weighting [ 33 ], or the use of different assessment functions. It can be noticed that the average detection and assessment beliefs are lower than expected, especially for Scenarios 1, 8, and 9, with an exception for Scenario 7. The insights from the identification answers reveal that many of the respondents recognize the game elements and decision-making situation, but only some of the answers indicate consideration of strategic behavior and their own role in the outcome. That could explain the low average GE belief. However, the individuals’ own outcomes (payoff) identification answers reveal that most respondents intuitively include their own Games 2020,11, 17 19 of 28 choice or possible actions while assessing their payoff. Given that the Scenarios 1, 3, 4, 6, 7, and 9 present a simple, everyday situation with economic significance, the lack of awareness about the GE also suggests that in most of simple real-life game-like economic situations, some individuals will not practice strategic behavior, and will only make decisions regarding the immediate choice (disregarding strategic implications) or passively accept the changes. Although the average beliefs of GE over scenarios are small, they do exist and indicate that, on average, the individuals are at least partially aware of strategic interactions, which opens the possibility for future empirical examination of augmented games, as presented by Halpern and Rego [ 1 ]. The comparison of the average deviation of GE belief from the derived GEE belief ( βGEE −βGE ) shows small deviations over the scenarios. It is expected for the GE estimation to be close to the derived estimation of the GEE. The deviations point to underlying patterns in forming the GE belief that take in account the beliefs assigned to GEE detection and identification. However, some of those deviations are positive, while others are negative (Scenarios 1, 2, 3, 4, 5, 6, and 8), indicating an overestimation or underestimation of the GE belief, given the respondents’ own awareness and assessment of GEE. Also, it seems that there is a relationship between the expected payoffand the difference (Table 4). As some of the previous research suggests, the awareness precedes assessment. The identification could intensify the awareness, which is in line with the Halpern and Piermont model [ 21 ]. The awareness in terms of “something is going on”, without the assessment, might be significant for the alertness, but could only have implications for strategic behavior when combined with the assessment. However, the empirical data (aside from Scenario 1) does not suggest the same conclusion about that relationship. Provided data insights reveal the inconsistencies in the awareness and assessments over the scenarios, indicating that variations of the information amount and type may influence provided answers, and as such, require further investigation. The following section will examine the differences in responses regarding the scenarios, provided information level, payofftype, action type, and the perceived deliberation. 3.3. Game Elements and Game Existence Beliefs To confirm the first insights, it is necessary to provide statistical analysis of differences in responses regarding the provided information in scenarios, payoff(positive/negative), and type of action. Table 5 presents the results of a Kruskal Wallis test. The Kruskal Wallis test compares mean ranks between the groups and is appropriate for the analysis of the data with compromised normality. The Monte Carlo method is applied because of the relatively small number of observations and to enable an unbiased estimate of the exact significance level. The tested hypotheses are that there are no statistically significant differences in mean rank of responses about game elements given the scenario, information, payoff, type of action, and deliberation. Scenarios differ given the provided information and context. Given the individual responses, there are differences in responses within a scenario, which are revealed in standard deviations (Table 4). However, the variations between the scenarios should indicate respondents’ sensitivity to the context and the amount and the type of information provided. There are statistically significant differences in responses about action detection, possible outcomes identification, expected payoff, derived GEE belief, and the difference between GE belief and derived GEE belief, given the Scenario (Table 5). The revealed statistically significant differences affirm the variations of responses regarding the scenarios and confirm the grasp of the contextually different situations while forming the belief about the game elements. Nevertheless, the lack of statistically significant differences between the GE responses regarding the scenario reveals that the contextual approach does not reveal relevant factors for awareness and assessment of GE belief. It seems that some other factors, like the information amount, payoff, action type, and perceived deliberation may be the key for determining the differences in responses regarding the rest of the game elements and GE belief. Games 2020,11, 17 20 of 28 Table 5. Differences between game elements’ existence estimates given the scenario, provided information, payoff, action type, and deliberation. Grouping Variable Parametar Action Detection βA Action Identification βB Player Detection βC Player Identification βD Possible Outcomes Identification βE Expected Payoff βF Game Existence Belief βGE Derived Game Elements Existence Belief βGEE Difference/(βGEE −βGE) Scenario Chi-Square 32.211 9.936 5.671 10.615 49.497 144.943 1.938 25.440 21.047 df 8 8 8 8 8 8 8 8 8 Asymp. Sig. 0.000 *** 0.270 0.684 0.224 0.000 *** 0.000*** 0.983 0.001*** 0.007*** MC Sig. 0.000*** 0.239 0.681 0.2 0.000*** 0.000*** 0.984 0.001*** 0.002*** Information Chi-Square 5.748 5.116 2.901 5.761 13.430 15.268 0.436 9.006 6.699 df 2 2 2 2 2 2 2 2 2 Asymp. Sig. 0.056 0.077 0.234 0.056 0.001*** 0.000*** 0.804 0.011** 0.035** MC Sig. 0.057 0.078 0.238 0.045** 0.000*** 0.001*** 0.818 0.012** 0.036** Payoff Chi-Square 4.195 2.253 9.778 0.183 3.457 334.761 6.528 0.685 2.199 df 1 1 1 1 1 1 1 1 1 Asymp. Sig. 0.041** 0.133 0.002*** 0.668 0.063 0.000*** 0.011** 0.408 0.138 MC Sig. 0.041** 0.143 0.001*** 0.676 0.065 0.000*** 0.013** 0.425 0.121 Action type Chi-Square 1.912 0.314 0.031 0.110 0.748 64.113 0.183 0.130 0.359 df 2 2 2 2 2 2 2 2 2 Asymp. Sig. 0.384 0.855 0.985 0.947 0.688 0.000*** 0.912 0.937 0.836 MC Sig. 0.417 0.85 0.987 0.953 0.698 0.000*** 0.9 0.94 0.816 Deliberation Chi-Square 11.203 1.111 10.573 9.672 26.796 1.390 14.138 12.710 3.149 df 1 1 1 1 1 1 1 1 1 Asymp. Sig. 0.001*** 0.292 0.001*** 0.002*** 0.000*** 0.238 0.000*** 0.000*** 0.076 MC Sig. 0.001*** 0.298 0.001*** 0.004*** 0.000*** 0.234 0.000*** 0.000*** 0.069 Notes: statistical significance at 5% and 1% level are denoted ** and ***, respectively; M. C. stands for Monte Carlo; the Monte Carlo method is based on 1000 samples. The computation is conducted using SPSS (IBM, New York, NY, USA). Source: Authors’ computation. Games 2020,11, 17 21 of 28 The average beliefs concerning the game elements are not consistent with the amount of provided information in the scenarios (Tables 2–4). Such an observation is partially unexpected, and it indicates that the other elements most likely influence the awareness of the game elements and game existence. This evidence can be explained by considering flaws of perception and reasoning that occur due to bounded awareness [ 4 , 5 ]. However, this indication requires more detailed insight into differences in game elements beliefs, given the information level provided. Scenarios differ given the provided information on the action, player(s), and payoff(Table 2). Given the provided information, scenarios are divided into three groups. The results (Table 5) show that there are statistically significant differences for player identification, expected payoff, possible outcome identification, derived GEE belief, and the difference ( βGEE −βGE ), given the amount of provided information (at a 5% level of statistical significance). This indicates that respondents, at least partially, manage to grasp the provided information. The statistically significant variables indicate the relevance of the information available for the identification, that is, the assessment. An interesting observation can be made in regards to the perceived payoffbelief (Table 4), which is negative for some of the scenarios. The outcomes identification beliefs are higher for the scenarios where the individual’s own perceived payoffis positive. Also, GE beliefs are somewhat larger for the scenarios with a negative payoff. It is possible that respondents assign higher levels of certainty to their own responses regarding the positive outcomes but do the opposite faced with the risk of loss. That could indicate an estimation bias towards the positive/negative outcome, which can be related to Baumeister et al. [ 20 ]. In addition, the findings can be explained through a lens of unexpected utility: players “sometimes value losses differently than gains and can have aversions toward (or preferences for) strategic ambiguity or uncertainty” [ 17 ], which is related to the prospect theory [ 34 ]. Descriptive statistics and previous research indicate that positive or negative payoff/outcomes can bias the estimation of the GE. Given the responses about expected positive or negative payoff, scenarios are divided in two groups. The Kruskal Wallis test (Table 5) shows that there are statistically significant differences in action detection belief, player detection belief, expected payoffbelief, and GE belief, given the perceived positive or negative payoff. The mean ranks show higher estimations of action detection belief and player detection belief for an expected negative payoff. The last statistically significant difference, GE belief, points to the payoffas a possible explanation for the differences in estimation of the GE, where higher estimation of GE belief occurs if the respondents expect negative payoff(which is in line with previous research). In addition, the perceived payoffseems relevant for the detection, that is, awareness. Action type differs over scenarios and appears in the forms of the concrete action, signal and cheap talk, and non-verbal behavior. Given the type of action, three subgroups were created to test the differences. Table 5shows that given the action type, there is a statistically significant difference only in the responses to the expected payoffbelief. The lack of differences in the action detection and action identification beliefs given the action type is unexpected and it suggests that the respondents equally successfully interpret explicit action, signal, and non-verbal behavior. The highest derived game existence belief is estimated for Scenario 8 (followed by Scenarios 3 and 7 ), and the lowest for Scenario 5. The value of the game existence belief for Scenario 5 is unexpected, given that information regarding all game elements is provided. Perhaps the reason for this is that 42.86% of the students found the action to be undeliberate or perceived that they would receive a team grade regardless of their own efforts in performing the assignment part. However, such a situation can also occur if the action is recognized as a type of deception [ 2 ]. Given this observation, it is necessary to examine whether the game existence estimations differ given the perceived deliberation of the interaction. The results show that there are statistically significant differences in action detection, player detection, player identification, possible outcomes identification, GE belief, and derived GEE belief, given the perceived deliberation. The deliberation seems to be the most significant assessment factor, as it reveals the differences in most of the observed variables (Table 5). It is interesting to notice that there is no statistically significant difference in expected payoffbased on the deliberation. That can Games 2020,11, 17 22 of 28 lead to an assumption that the activity may be assessed as being deliberate or intentional, but that this will not be a cause of respondents’ diminishing (or increasing) belief of their expected payoff. The GE belief shows statistically significant differences only, given the deliberation and payoff. That indicates that the respondents’ awareness of the game—the belief of the game’s existence, does not depend on the context, provided information, or action type. However, as observed in combination with Tables 3and 4, the results show that the respondents are at least partially aware and that the information amount does not imply complete awareness at the individual level. It is interesting to notice that the action detection does not show statistically significant differences regarding the information amount and action type, while action identification appears unaffected by any of the observed influences. Those insights indicate that respondents’ beliefs include information that has no relation to the underlying game or actual payoffs [13]. The difference ( βGEE −βGE ), which points out to differences in estimation of the GE belief from the values estimated by the assumed underlying function, shows statistically significant differences regarding the scenario, information, payoff, and deliberation. The current observations and results indicate the relevance of the difference and its role in GE belief formation, but do not enable inconclusive conclusions. Hence, it is necessary to examine if there exist statistically significant differences in game elements beliefs and game existence belief, given the difference ( βGEE −βGE ). The data was divided into three groups regarding the positive, negative, or zero difference ( βGEE −βGE ). The Kruskal Wallis test with the Monte Carlo method was employed again. The results show that there are statistically significant differences regarding observed game elements, apart from the expected payoff. It seems that a statistically significant difference of the game elements belief occurs that can be detected with the overestimation and underestimation of the GE belief in comparison with GEE belief, expressed in difference ( βGEE −βGE ). The mean ranks show that the respondents with a positive difference ( βGEE −βGE ) tend to overestimate game element beliefs (higher mean rank; except of the expected payoffbelief) in comparison to the other two groups. The results indicate that both GE belief and GEE belief differ due to differences, with a lower mean rank scored for a negative difference and higher mean rank scored for a positive difference. That suggests that the difference does not only measure the deviation from the presumed underlying assessment process, but is related to most of the assessment factors, which indicates the presence of psychological biases [4,5] or intuitive weighting of the probabilities [33]. The GE belief differs given the payoff, deliberation (Table 5), and the difference (Table 6), where GE belief mean ranks are higher for the expected negative payoff, deliberate action, and positive difference. However, the provided analysis does not reveal the relation of all game elements belief to GE belief. Table 6. Differences between game elements estimates given the difference (βGEE −βGE). Grouping Variable Parametar Action Detection βA Action Identification βB Player Detection βC Player Identification βD Possible Outcomes Identification βE Expected Payoff βF Game Existence Belief βGE Derived Game Elements Existence Belief βGEE Difference (βGEE − βGE) Chi-Square 81.505 114.113 128.015 161.526 151.123 1.390 143.340 339.866 df 2 2 2 2 2 2 2 2 Asymp. Sig. 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.499 0.000*** 0.000*** MC Sig. 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.519 0.000*** 0.000*** Notes: statistical significance at 5% and 1% level are denoted ** and ***, respectively; M. C. stands for Monte Carlo; the Monte Carlo method is based on 1000 samples. The computation was conducted using SPSS. Source: Author’s computation. Thus, it remains necessary to examine the correlation between the game elements belief and the GE belief. It was suggested earlier in the article that it is expected that the GE estimation will be close to the derived estimation of the GEE, and that the small deviation points to underlying patterns in forming the GE belief that take in account the beliefs assigned to GEE detection and identification. Games 2020,11, 17 23 of 28 The correlation analysis points out the linear numerical relationship between observed elements and GE beliefs. Table 7shows the result of the correlation analysis. Table 7. Correlation analysis of the game elements existence beliefs and the game existence belief. Parameter βAβBβCβDβEβFβGE βGEE βGEE −βGE βGE Pearson Correlation 0.327** 0.270** 0.465** 0.350** 0.127** − 0.116* 1 0.306** −0.125** Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.008 0.016 0.000 0.009 N 432 432 432 432 432 432 432 432 432 Bootstrap Bias − 0.002 − 0.001 0.000 0.001 0.000 0.000 0 − 0.001 0.000 Std. Error 0.057 0.052 0.050 0.051 0.051 0.048 0 0.041 0.047 95% Confidence Interval Lower 0.212 0.163 0.363 0.253 0.030 − 0.214 1 0.222 −0.218 Upper 0.437 0.370 0.566 0.445 0.230 − 0.020 1 0.390 −0.030 βGEE Pearson Correlation 0.383** 0.505** 0.474** 0.580** 0.582** 0.013 0.306** 1 0.906** Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 0.784 0.000 0.000 N 432 432 432 432 432 432 432 432 432 Bootstrap Bias 0.001 0.001 0.002 0.002 0.001 0.002 − 0.001 0 0.000 Std. Error 0.021 0.024 0.021 0.022 0.023 0.050 0.041 0 0.008 95% Confidence Interval Lower 0.343 0.458 0.437 0.540 0.536 − 0.082 0.222 1 0.890 Upper 0.422 0.555 0.516 0.625 0.628 0.110 0.390 1 0.922 βGEE − βGE Pearson Correlation 0.254** 0.407** 0.287** 0.449** 0.550** 0.065 − 0.125** 0.906** 1 Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 0.177 0.009 0.000 N 432 432 432 432 432 432 432 432 432 Bootstrap Bias 0.002 0.002 0.002 0.001 0.001 0.002 0.000 0.000 0 Std. Error 0.031 0.033 0.031 0.033 0.029 0.050 0.047 0.008 0 95% Confidence Interval Lower 0.191 0.340 0.228 0.391 0.491 − 0.032 − 0.218 0.890 1 Upper 0.314 0.470 0.348 0.516 0.610 0.159 − 0.030 0.922 1 Notes: statistical significance at 5% and 1% level are denoted * and **, respectively; Bootstrap results are based on 1000 stratified bootstrap samples (strata: scenario). The computation is conducted using SPSS. Source: Author’s computation. The correlation analysis reveals a statistically significant and positive, but weak to moderate linear correlation between all the game element beliefs and GE beliefs. Similarly, game elements (except for expected payoff) correlate with derived GEE and with the difference. While correlation exists and indicates that individuals use all game elements in game existence assessment, those correlations are moderate, indicating a possible weighting of the beliefs and/or underlying function that is not linear. Also, it is interesting to notice the negative relationship between the expected payoffand the GE belief. That means that a negative payoffleads to the higher estimation of GE belief, while positive payoffleads to lower estimation of GE belief. Although the relationship is weak, it is an additional indication that respondents estimate game existence differently based on different payoff, that is, they view situations differently given their expected losses or gains [ 17 , 20 , 34 ]. A similar relationship occurs for the difference. That weak negative correlation shows that for the negative differences, the GE belief is higher while the GE is lower for the positive differences. Besides that, there is a strong positive correlation between the derived GEE and the difference. Interpreting those two coefficients in combination, it might be that the difference is also an indication of internal correction processes, whether to account for uncertainty or to correct for overconfidence in game elements belief estimation. 4. Discussion and Conclusions Game theory strives to model, explain, and predict human behavior in strategic interactions. A part of the research is devoted to individual behavior. While most models in game theory set a framework with the predefined rules and assuming that the players understand the game in the same way as the modeler, some research points out that such approach does not manage to grasp the reality of human behavior [ 1 ]. One of the gaps that occur relate to an individual’s awareness of the game Games 2020,11, 17 24 of 28 and game elements. The research of (un)awareness in game theory aims to explain and to fill that gap. The theoretical framework is significantly developed, but the empirical studies on the topic are scarce. The importance of empirical insights lies in the results’ implications, both for human interaction and game theory models. As game theory models aim to approximate human strategic behavior, the empirical data can confirm if the existing development of the (un)awareness in game theory heads to the right direction and provide valuable insights for theoretical modeling. An individual who is unaware of a game-like situation will fail to assess possibilities for strategic behavior, will not search for additional information, and will not reach the stage where awareness and assessment of the in-game elements play a role in the situation’s outcome. Therefore, it is reasonable to suggest the awareness examination occurs prior to game modeling. The purpose of this research is to examine individuals’ awareness and assessment of game existence and to provide insights from the empirical data regarding the individuals’ detection and description of game elements and assigned beliefs in contextually different situations. The emphasis of the analysis is based on the quantification of beliefs assigned to awareness and assessment of the game elements and game existence, as well as the patterns in their relationship. Given that games in everyday life do not occur with predefined assumptions and rules, it is important to learn how successfully individuals manage to assess game existence and game elements. Insights into individual game existence assessment have strategic implications on game outcomes and suggest a new approach for applications of (un)awareness game theory models to real-life situations. Do the respondents understand the game the same way the modeler does? The results provide empirical insights in respondents’ game understanding, their deviating from provided information, breaking of the given framework, and deviating from the presumed underlying assessment function. This is revealed in the structured scenarios. All these findings support the critique of the standard game representation [ 1 ] and show that some of the respondents and the modeler do not understand the game in the same way. While this notion previously existed in theoretical approach, this research enables its empirical reinforcement. The implications of such behavior can relate to inclusion of the ‘virtual’ moves and players’ payoffbeliefs that include moves that have no relation to the actual game and payoff[ 13 ]. That suggest the necessity for future empirical examination of the awareness in the sequential games as well as individuals’ ability to reveal the underlying game [1]. Do the respondents’ awareness and assessment of game and game elements differ over the scenarios, and do they differ given provided information amount and type? The average awareness and assessment of game elements are inconsistent with provided information and in some cases, are lower than expected. As previously stated, the results indicate that individuals fail to utilize the provided information, but also use other information. The responses about action detection, possible outcomes identification, expected payoff, and game existence belief differed across the scenarios. The responses about player identification, expected payoff, and possible outcome identification belief differed given the information amount. The lack of statistical differences in most game elements (except for the payoff) given the action type suggests that respondents equally successfully interpret explicit action, signal, and non-verbal behavior. The insights from the identification answers reveal that many of them recognize the elements and decision-making situation, but only a part of those answers indicate consideration of strategic behavior and their own role in the outcome. The interpretation of those insights suggests that in most of simple real-life game-like economic situations, some individuals will not practice strategic behavior, and will only make decisions regarding the immediate choice (disregarding strategic implications) or passively accept the changes. In spite of the fact that GE beliefs were found to be smaller than expected, they do exist and indicate that, on average, the individuals are at least partially aware of the given information. The possible implications of the findings relate to modeling strategic interaction with incomplete information and uncertainty, as they highlight the role of information in game elements assessment. Also, the lack of any difference regarding the action type indicates that respondents do not assess explicit action as successfully as expected but do assess signal/non-verbal behavior more successfully than expected. That suggests that the