Smart allocation of a developer's spending on product quality and non-salary employee benefits in a supply chain of apps

Maly, Leonard Omer; Avinadav, Tal Article Smart allocation of a developer's spending on product quality and non-salary employee benefits in a supply chain of apps Operations Research Perspectives Provided in Cooperation with: Elsevier Suggested Citation: Maly, Leonard Omer; Avinadav, Tal (2025) : Smart allocation of a developer's spending on product quality and non-salary employee benefits in a supply chain of apps, Operations Research Perspectives, ISSN 2214-7160, Elsevier, Amsterdam, Vol. 14, pp. 1-15, https://doi.org/10.1016/j.orp.2024.100320 This Version is available at: https://hdl.handle.net/10419/325800 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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This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/bync/4.0/). Smart allocation of a developer’s spending on product quality and non-salary employee benefits in a supply chain of apps Leonard Omer Maly * , Tal Avinadav Department of Management, Bar-Ilan University, Ramat Gan 5290002, Israel ARTICLE INFO Keywords: Supply chain management Revenue sharing Quality Non-salary benefits ABSTRACT Qualified and capable employees are crucial for the success of high-tech companies. With an ever-shrinking pool of talent, employers are forced to devise creative recruitment and retention methods, which increasingly take the form of heavy spending on non-salary benefits. The present study contributes to the existing supply-chain literature through examining the role played by such benefits in a two-agent system consisting of a platform and an app developer. In particular, we examine the effect of non-salary benefits on the outgoing quality created by the employees of the app developer. The parties follow a Stackelberg sequential game led by the platform to accurately reflect the interaction in the market, allowing us to reach equilibrium using backward induction. Our results indicate that when app developers are more risk averse or face greater uncertainty, they spend a greater amount on non-salary benefits and comparatively less on app quality. This finding highlights the importance of investing in workers, particularly in uncertain times. We further extend the applicability and robustness of our findings by introducing multiple developers to our two-agent system. The extension proves that the platform charges a universal commission rate, irrespective of the number of developers –a finding that is consistent with current practice. Given the non-linear effect of key model parameters on the profits of the supply-chain members in both the single and the multiple-developer setups, we also utilize numerical analyses and arrive at telling managerial implications for all parties. 1. Introduction While base salaries continue to play a fundamental role in attracting capable employees to workplaces [15], recently, non-salary benefits and “perks”seem to have taken center stage. High-tech and innovation-based companies regularly publicize their offerings, including leisure and relaxation facilities, quality catering and onsite wellness activities [7]. For example, Israeli high-tech firms organize extravagant parties and all-inclusive vacations to the Caribbean. Some tech workers reportedly approach recruiters in anticipation of a set standard of such benefits when joining a company, suggesting their capacity to facilitate recruitment efforts [17]. This strategy corresponds to the ever-growing shortage of tech professionals [8], encouraging high-tech firms to diversify their spending on non-salary benefits and set themselves apart from the rest. Firms that develop mobile and computer apps (hereafter “apps”) seem to have adopted this approach as high-tech ventures. Tinder, for example, offers its employees legal assistance, paid vacations, and training mentorship, among other benefits. 1 Although revenue from digital apps was projected to reach $430B in 2022 within the mobile sector alone (with an average annual growth of approximately 10 %), 2 as mentioned, the pool of talent within the tech industry remains limited. Therefore, it could be worthwhile offering non-salary benefits in order to attract quality employees, although caution needs to be exercised when using such a strategy given the uncertain nature of the effect of such perks on employee performance [17]. Due to the special features of apps as virtual products [10], an app development firm primarily incurs costs related to the quality of the product. More specifically, spending on elements such as visual design, functionality, reliability, and security usually raises the quality of the app, which is essential for its competitive positioning [1]. Since human developers can exercise a substantial influence on app quality (for empirical evidence of the phenomenon for software developers, see [16]), in addition to the aforementioned quality-inducing elements, this * Corresponding author. E-mail address: [email protected] (L.O. Maly). 1 https://www.glassdoor.com/Benefits/Tinder-US-Benefits-EI_IE916118.0,6_IL.7,9_IN1.htm. 2 https://www.statista.com/outlook/dmo/app/worldwide. Contents lists available at ScienceDirect Operations Research Perspectives journal homepage: www.elsevier.com/locate/orp https://doi.org/10.1016/j.orp.2024.100320 Received 23 July 2024; Received in revised form 3 December 2024; Accepted 3 December 2024 Operations Research Perspectives 14 (2025) 100320 2 study considers the effect of non-salary benefits on app-quality achievement. Developers of mobile apps commonly reach their end customers by offering the app via a distribution platform (hereafter, “platform”). The biggest platforms are Apple’s App Store and Google Play (together accounting for 95 % of the market outside China 3 ). With millions of apps on each of these platforms, both offer a universal contract to app developers, which stipulates that the platform will keep a defined percentage of the revenue generated by the app (15–30 %). The platform facilitates the distribution efforts and billing process, while the developers maintain ownership of their apps. 4 Therefore, the interaction between the two parties resembles a consignment contract with revenue sharing [1]. This study models the business interaction as a two-agent system consisting of a platform (“it”) and a developer (“he/she”). Using a gametheoretic approach, we construct the following Stackelberg game led by the platform: First, the platform sets the contract term, i.e., the percentage of the product’s revenue that it charges as commission. Second, the developer makes two decisions simultaneously –his/her intended level of app quality and the amount spent on non-salary benefits for his/ her employees. The game’s nature reflects the interaction in the app market, as developers follow the platform’s existing terms when launching their app on it (as in [2,4]). As suggested by previous studies [1,2,10], we only consider the cost of quality incurred by the developer; the platform is assumed to have negligible marginal costs. This assumption aligns with the characteristics of apps as digital products since their inception over a decade ago [9], allowing platforms to timelessly-distribute millions of apps 5 with ample capacity to fulfill demand. Since we assume that non-salary benefits have an effect on app quality –but one that is uncertain in nature –we consider the developer’s attitude towards risk in his/her objective function. We focus on non-salary benefits in the form of initiatives (such as onsite activities, parties, and trips) rather than common per-employee benefits (such as insurance or retirement benefits). Our reasoning is twofold. First, common per-employee benefits tend to be agreed upon when hiring each individual worker nowadays, and given the competitive market for tech workers, they tend to be matched across the industry (similarly to the base salary). 6 Therefore, per-employee benefits are assumed to be fixed –unlike benefits issued through initiatives, which are external to contracts and can be designed with greater flexibility. Furthermore, the fact that initiative-based benefits are external to contracts means that they are more likely to be able to affect employee performance, particularly since employees often receive the benefit free of tax. 7 Our second reason for focusing on initiative-based benefits is that this strategy has become increasingly popular in recent years, particularly in the high-tech sector, such that it is worthwhile analyzing the effect of this approach independently of other forms of compensation. Note, that our model focuses on any initiative-based non-salary benefit that involves spending by the employer. These include indirect monetary benefits (e.g., free concerts by leading artists or lucrative excursions, see [17]) as well as intangible elements (such as providing work flexibility for new parents, or inducing a positive working atmosphere, e.g., the slides installed in many Google offices, see [33]). Given the recent rise in popularity of initiative-based benefits in the form of substantial spending [17], combined with the theoretical framework developed in this study, our paper provides a unique and important outlook on the potential value of such benefits both for employee recruitment and for the achievement of quality. To the best of our knowledge, this study is the first to introduce non-salary benefits into a model of the interaction between parties in a supply chain. Using the mean-risk framework to model the developer’s risk attitude (proved to be consistent with second-degree stochastic dominance by [38]), we aim to answer the following research questions: •How does the developer’s attitude towards risk affect the parties’ decisions, as well as their expected profits, at equilibrium? •How is the developer’s budget divided, at equilibrium, between investing in product quality and funding non-salary benefits to employees, and which factors affect this allocation? The rest of the study is structured as follows. Section 2 reviews the relevant literature, thereby highlighting the original contribution of this study. In Section 3, we construct the analytical model of the two-agent system, while in Section 4, we present its results at equilibrium. Section 5 extends the primary model to include multiple competing developers, thus strengthening the robustness and applicability of our analysis. Lastly, Section 6 expands upon the conclusions and managerial implications derived from our results, and offers potential directions for future study. 2. Literature review The present study relates to three main areas of research: (a) nonsalary compensation and its effect on employee performance; (b) supply chains of virtual products; and (c) the mean-risk criterion. The following sections review the existing literature under each of these domains. Key relevant studies are mapped and classified by their characteristics in the Author-contribution table below Table 1. 2.1. Non-salary benefits and their effect on employee performance A multitude of empirical studies have found a positive correlation between wage and productivity, as firms minimize their labor costs while maintaining efficiency [28]. Levine [32] further elaborated on this hypothesis, and proved empirically that the increased productivity following a salary increase more than offsets the increase in labor costs. Most recently, Mariev et al. [35] tested the effect of several factors on worker productivity in various Russian firms, including from the high-tech sector. Interestingly, they found that salary was the most important factor influencing a worker’s willingness to contribute. Yet, Fisher et al. [19] showed that a salesperson’s performance reaches saturation once they are paid beyond a specific threshold. In contrast, literature on non-salary benefits is rather limited. Schmidt-Sørensen [40] introduced non-salary benefits into the basic efficiency-wage model, on the basis that they were becoming a more prominent share of labor costs. His theoretical analysis highlighted the complex effect of such benefits on productivity, which may explain why later studies do not produce consistent findings. On the one hand, Gilchrist et al. [23] discovered, using an empirical approach, that unexpected and unconditional benefits given to workers boost productivity in a similar manner to hiring additional workers. An empirical study of American university staff showed that college tuition waivers offered to the workers’dependents increased both retention and productivity [41]. On the other hand, Sung and Choi [42] found that when employers fund external education for workers (as opposed to internal training), the organization’s innovation performance can deteriorate. Our study, to the best of our knowledge, is the first to consider initiative-based benefits in the high-tech sector. Under the assumption that such benefits have an uncertain yet notable effect on productivity as 3 As Google Play is banned in China, see https://www.businessofapps.com/ data/app-stores/. 4 https://support.google.com/googleplay/android-developer/answer/ 112622?hl=en;https://developer.apple.com/programs/whats-included/. 5 By the last quarter of 2022, over 3.5 million and 1.6 million applications were available on Google Play and App Store, respectively (https://www.statis ta.com/statistics/276623/number-of-apps-available-in-leading-app-stores/). 6 https://www.betterup.com/blog/types-of-employee-benefits. 7 See, for example, the terms in the USA: https://digit.business/financial-lite racy/office-christmas-parties-fringe-benefits-tax; or the UK: https://www.gov. uk/tax-company-benefits/taxfree-company-benefits. L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 3 expressed through app quality, we use the mean-risk framework to analyze the decisions of the developer, who is an employer acting under uncertainty. Unlike the empirical approach taken by almost all previous papers on non-salary benefits (except for [40]), our model provides an analytical investigation of the topic. 2.2. Supply chains of virtual products The rollout of advanced technologies in the 21st century resulted in a surge of new categories of intangible goods, commonly classified as virtual products [9]. Unlike tangible products, which involve inventory, delivery, distribution and other costly procedures, the supply of virtual products is carried out instantaneously at negligible unit cost [3,4]. These unique features have piqued the curiosity of numerous researchers in the fields of operations and supply-chain management. Most researchers considered a two-echelon chain, consisting of a manufacturer (often an app/software developer) and a distributer (e.g., a platform or retailer), which operates under a Stackelberg game led by either the distributer [1–4,11,26] or the manufacturer [10]. The interaction has generally been analyzed under either a fixed-fee contract (relevant to supply chains of mobile games; see [25,26]) or a commission-rate contract (relevant to mobile apps; see [3]). Only a few studies introduced additional members into the chain, such as an investor [1], another platform [12] or multiple competing developers [4]. Avinadav et al. [3] recognized the effect of quality on demand in such chains –along with the possibility of influencing this relationship via quality investment. Most subsequent studies considered the virtual product’s price, and either the investment in quality or the desired level of quality, as the sole influencers of demand –where these decisions are commonly assumed to be set by the manufacturer. To prevent the scenario where the investment in quality at equilibrium is infinite, the cost of quality is usually considered to take on a quadratic form (assuming diminishing returns; see [1]). Other variables that have been considered include the sales effort [25] and marketing investment [26]. Chernonog [11] further generalized these decisions into a vector of activities to be performed, with the goal of influencing either the revenue or the costs. The involvement of uncertainty in the majority of operational decisions [14] has led researchers to incorporate it into their theoretical analyses of supply chains of virtual products. Many researchers have investigated uncertain demand by incorporating a random variable into the deterministic demand function, using either addition or multiplication (e.g., [2–4]). Using the mean-variance (MV) criterion to represent the attitudes of supply-chain members towards risk, most authors have reported that the retailer’s risk attitude is irrelevant to equilibrium decisions due to the retailer’s profit structure (e.g., [3]). Only Chernonog [11] has investigated uncertainty with respect to the cost of creating quality. In particular, she assumed that, under information asymmetry, the retailer estimates the manufacturer’s cost function. Information asymmetry has also been considered in other recent studies of supply chains of virtual products [2,26]. Our study makes a unique contribution to the existing literature, as we introduce a new decision variable –the non-salary benefits offered by the developer to his/her employees, which does not directly affect the demand for the app. Specifically, we capture the uncertain nature of the effect of non-salary benefits on the cost of quality (using a random variable). In addition, our model incorporates multiple developers within the supply chain, a scenario that has rarely been investigated in previous publications (aside from [4]). Note that our decision to ignore both the costs and the risk attitude of the platform is in line with the findings of the aforementioned studies. 8 2.3. The mean-risk criterion Decision-making under uncertain conditions inevitably reflects the decision-maker’s attitude towards risk. If only the expected value of the decision’s outcome is considered, then this reflects risk-neutral behavior, thereby ignoring the risk-averse or risk-seeking patterns that frequently characterize decision-makers. Having made this observation, the Nobel laureate Markowitz created the MV criterion for financial decisions, which considers the spread of the random variable in the form of its variance [13]. Walls and Dyer [44] later showed empirically that the MV criterion successfully predicts optimal decisions across industries. In order to focus the analysis on negative outcomes (which are central to risk attitudes), researchers often replace variance with semivariance characteristics, such as the standard deviation (SD) or absolute semi-deviation of the random variable. The use of such modified MV criteria has been further justified by the finding that they are analytically consistent with the rules of second-degree stochastic dominance 9 – unlike the original MV criterion [38]. Substituting variance with a different characteristic of the random variable’s distribution (usually the SD, as in the financial calculation of VaR) is commonly referred to as the mean-risk (MR) criterion [13]. Over recent decades, studies in operations and supply-chain management have incorporated the MV criterion into their analyses of decisions under uncertainty [13]. As mentioned previously, chains of virtual products often consider uncertain demand, and the vast majority of studies have used the original MV criterion (e.g., [2,3]). The introduction of an investor as a third player in the supply chain led Avinadav and Bunker [1] to discover that the more risk-averse the developer, the Table 1 Author-contribution table (N/A denotes not applicable). Authors Stackelberg game Nash game Horizontal competition Wholesale price contract Revenuesharing contract Linear cost function Quadradic cost function Uncertain cost function Risk investigation [3] V   V V VMV [4] V V V V V   MV [10] V   VV  UF [26] V   V  VN/A [1] V    VVMV [25]VV  VMV [11] V    V  V N/A [2] V    VVMV Current paper V V V VV V MR Risk investigation legend: UF –Utility Function; MV –Mean Variance; MR –Mean Risk. 8 The platform is assumed to incur negligible distribution costs [4]. Additionally, numerous studies with similar formulations have concluded that the platform’s attitude towards risk has no effect on decisions at equilibrium [1,3,4, 10]. 9 Ogryczak &Ruszczy´ nski [38] limited this conclusion to cases where the "trade-off" coefficient λis smaller than 1, given two possible uncertain alternatives for the decision-maker. Since our analysis considers only one, this limitation does not apply to our use of the criterion. L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 4 more likely he/she is to seek external funding. Although studies of supply chains of tangible goods have evolved to incorporate MR analyses [14], research on supply chains of virtual products tends to adhere to the original MV criterion. Our study is original in its use of the MR criterion, while relying on its proven analytical credibility. The MR criterion has the potential to ease analytical processing [31] and yield results that are more intelligible than the basic MV criterion. As mentioned, uncertain costs in supply chains of virtual products have only been investigated in one previous study [11] and have never been examined using the MR criterion. To determine whether uncertainty has a positive or negative effect on a company’s spending patterns (in terms of costs), we refer to several empirical studies conducted on the matter. Most of these detected a negative relationship, i.e., greater uncertainty leads to curbed spending –particularly for high uncertainty levels [6]. Moreover, greater risk-aversion levels were found to exacerbate this negative relationship [36]. Therefore, in the current study, where the MR criterion is used to model the developer’s target function, the product of uncertainty (represented by the SD) and risk-aversion levels is subtracted from the expected value. Thus, we employ the same negative relationship as that adopted in previous MV applications (i.e., E−λV), but note that in these applications, it was used to introduce uncertainty into other elements of the target function (e.g., uncertain base demand in [1]). 3. Model formulation Consider a two-agent system of an app consisting of the app developer and a platform. Users can either acquire the app for free or at a cost, where in the former case, the app can generate revenue through one of the following methods: subscription fees (e.g., a subscription to the New York Times); a paid, premium version of the app; or in-app ads or purchases. Note that all notations used in this study appear in Table A in the Appendix, and key assumptions are summarized in the following subsection. The demand for the app is affected by two elements –its quality, q, and the average revenue per user (ARPU), p. Specifically, the demand is given by D(q) = a q √− α p(1) where ais the market scale parameter, and α represents the sensitivity of demand with regard to p. In line with existing literature, we use the square root function to convey the diminishing returns of consumers from the app’s quality level [1]. The ARPU of the app (representing the revenue generated by the app per user from all its potential sources) is assumed to be exogenous, reflecting the intense competition among apps [39]. Logically, it has a negative linear effect on demand (since the ARPU is equivalent to the unit-price variable used in [3,9], and [10]). By using the ARPU to represent p, we accurately reflect reality in the sense that apps tend to make use of diverse revenue streams, in line with the current industry standard. In contrast, the aforementioned studies (listed in the previous set of parentheses) artificially constrained their models such that only paid apps were considered. Similar to those studies, we introduce the parameter α , which for paid apps simply stands for the price sensitivity of demand. For free apps, however, we assume that a higher ARPU would imply that the user’s welfare is reduced in a similar fashion to when paying a higher selling price (through more ads, higher subscription fees, etc.), and the extent of this effect is depicted through α . Note that the demand for the app is deterministic throughout our analysis, despite the rarity of such a scenario in real life. This assumption however allows us to focus on uncertainty tied to cost (rarely discussed in closely related literature, e.g., [11]), while maintaining satisfactory resemblance to the behavior of an uncertain demand function. The developer, in order to develop the app and position it competitively on the market, invests in quality incurring the following cost: C(q,v) = ε v ρ q2(2) where ε is a normally distributed random element with mean 1, vis the amount that the developer spends on non-salary benefits, and ρ is a scale parameter represents the developer’s economic efficiency in translating the invested sum into quality. The cost of creating quality clearly depends on the desired app-quality level, q, and the assumed quadratic relationship reflects the expected diminishing returns of quality investments [18,34]. The efficiency in achieving the desired quality level has been assumed to be constant by previous researchers (e.g., [1,25]), ignoring the possibility that its value might change according to the decisions of the developer. Therefore, our model breaks down the efficiency in creating quality into two elements. With respect to ρ , the higher its value, the more costly it would be to achieve a desired quality level. The fraction ε /vcorresponds to the presumed effect of non-salary benefits on the creation of app quality by the developer’s employees. We assume that v(the amount that the developer spends on non-salary benefits) has a hyperbolic effect 10 with regards to the efficiency in achieving quality, expressed through the reciprocal presence of vin Eq. (2). Namely, the marginal worker efficiency gained from increasing v when it is already high, is smaller than when vis initially of a low value (following the findings of Fisher et al., 2006 11 ). Considering the previously-discussed uncertain effect of v, we introduce a normally distributed random variable over the vicinity of one, expressed by ε ∼ N(1, σ 2). We further assume that σ ≤0.33, such that the probability of ε being negative is sufficiently small to be disregarded. In so doing, we reflect the assumption that benefits offered to employees result in some positive marginal utility for the average worker. Using a Stackelberg non-cooperative sequential game, we model the interaction between the two members of the chain as presented in Fig. 1. The two largest platforms in the world for apps –Apple’s App Store and Google Play –offer a non-negotiable contract to app developers, which Fig. 1. The sequence of events. 10 The hyperbolic function, expressed through the appearance of the variable in the reciprocal, has been chosen for its following two characteristics to represent the relation between v (the amount that the developer spends on nonsalary benefits) and the efficiency coefficient for creating quality: (a) It decreases with respect to the variable, i.e., greater spending on non-salary benefits increases efficiency. (b) Its increments are smaller as the values of the variable increase, similar to law of diminishing returns, i.e., when efficiency is low – spending on non-salary benefits would improve it more significantly than when efficiency is already high, as a more substantial spending is required to increase it in the same manner. Furthermore, the function allows to reach analytical solutions to our theoretical setup, leading to useful conclusions and implications. Additionally, the hyperbolic function has been used previously in Operations Management literature to demonstrate a similar effect [24]. 11 Their research is relevant only to a limited extent, since they did not focus on non-salary benefits. However, their finding of employee saturation from compensation fits the logic behind the law of diminishing marginal productivity. L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 5 allows these platforms to interact effectively with hundreds of thousands of app developers. At the core of the contract lies the revenue-sharing agreement, which secures the platform 15–30 % 4 of the revenue generated from the app. Therefore, the first stage of the game is the platform’s announcement of its desired fraction η (0< η <1).Note that the only options open to the developer are to accept or reject the contract entirely; hence, we only address the scenario in which the developer is willing to enter into the agreement (similar to [3,4,25]). At the second stage, the developer determines both qand vin preparation for his/her app being launched via the platform. Lastly, once the app has been launched, the demand is realized and the revenue is split between the two members of the supply chain. Deduction of the developer’s costs from his/her share of the revenue (as the only party to incur costs in the analysis) results in the following profits for the platform and the developer, respectively: π p( η ) = η pD(q)(3) π d(q,v) = (1− η )pD(q)− v−C(q,v).(4) Note that vappears in the developer’s profit function as an independent cost (in addition to its effect on the aforementioned efficiency in creating quality). Therefore, vdoes not include common per-employee non-salary benefits (e.g., health insurance, pension plans), which are hardly adjusted (if at all) by high-tech employers due to their commitment to matching the market’s hiring standards. Naturally, salaryrelated benefits (such as bonus payments) adhere to similar market pressures [20], and consequently cannot be viewed in the same manner as v, i.e., as an independent cost and decision variable. Furthermore, we assume that issuing initiative-based benefits (e.g., costly and lengthy vacations abroad, [17]) does not aim to improve outgoing quality directly, 12 albeit their regarded possible effect on its cost. Salary rates and salary-related benefits, on the other hand, are deployed predominantly as instruments for leveraging employee performance 13 (i.e., for influencing the quality of the output). Therefore, any spending that is primarily intended to improve quality (including increased salaries, improved equipment, and training) appears under the cost of quality C(q,v)(and not under v). To summarize, our unique formulation captures all significant costs associated with running a contemporary app-development firm. 3.1. Key assumptions •The platform incurs negligible marginal costs. •Demand is proportional to the square-root of the quality level of the app. •The app’s ARPU is exogenously determined by market forces. •The cost of quality creation is proportional to the square of the app’s quality level. •The developer’s spending on non-salary benefits has a hyperbolic effect on the efficiency in creating quality. •Initiative-based benefits do not aim to improve app quality directly. 4. Equilibrium results Each player’s objective is to maximize its own expected utility by fine-tuning its respective decision variables. We adopt the MR criterion as a surrogate utility function for the developer, who faces cost uncertainty, as it captures the preference for a high expected profit and a low SD of the profit. Since the parties’decisions are made in two stages (see Fig. 1), we use backward induction to reach equilibrium. This well-used method aligns with the nature of the sequential game lead by the platform (as used by the vast majority of researchers in the field, e.g., [2–4, 26]), namely, the platform sets the contract term by extrapolating the developer’s decisions (i.e., best response) –in contrast to a Nash Equilibrium, in which the parties make their decisions simultaneously (see Section 5). 4.1. Second stage of decision making: the developer sets v and q As illustrated in Fig. 1, the developer makes his/her decisions only after the platform has announced the contract term, i.e., the developer is the second party to move in the sequential game. The developer sets v(the monetary value of non-salary benefits to his/her employees) and q(the app’s desired quality level) simultaneously, aiming to maximize the utility of his/her profit, as captured by the mean-risk criterion. The criterion expresses the desire of the developer to obtain a high expected profit while, at the same time, avoiding uncertainty, which is captured by subtracting a proportion of the profit’s standard deviation from its mean value. As in previous studies using the MV criterion (e.g., [1]), λ(where commonly, |λ|≪1; see, e.g., [3]) represents the developer’s level of risk aversion (when positive) or risk-seeking behavior (when negative), while σ stands for the SD of the random element. For simplicity of presentation, we substitute the expression (1+λ σ ) with ψ , which is of positive value throughout our entire analysis (see Appendix). Then, by inserting ψ into Eq. (4), alongside the demand function in Eq. (1) and the cost of quality in Eq. (2), we arrive (as detailed in the Appendix) at the following formulation of the developer’s optimization problem with regard to the mean-risk of his/her profit: max q,v{MRd(q,v)=(1− η )p(a q √− α p)− v−1 v ρψ q2}.(5) Since MRd(q,v)is a concave function with a single local (which is also a global) maximum of (q,v), we arrive at the following proposition: Proposition 1.The developer’s best-response is given by q( η ) = 1 ρψ (ap(1− η ) 4)2 ,v( η ) = 1  ρψ √(ap(1− η ) 4)2 .(6) Proof. See Appendix. The decision variables at equilibrium are proportional with coefficient  ρψ √. It can be seen that, already at this stage, the expressions depend directly on all the parameters of the analysis with the exception of the price (equivalent) sensitivity of demand ( α ). The two decision variables are directly proportional to a2,p2and (1− η )2(i.e., the square of the developer’s revenue share). While q( η )is proportional to the inverse of ρ and ψ ,v( η )is proportional to the square-root of their inverse. A larger market (a) or a greater fraction of the revenue for the developer (1− η )logically leads to greater investments in both quality and employee benefits, as well as greater efficiency in creating quality (expressed by a lower value of ρ )or greater certainty in the efficiency of creating quality (a lower value of σ ). Since ψ >0 for both negative and positive values of λ(i.e., for riskseeking and risk-averse behaviors, respectively), our analysis is robust for both of these scenarios. According to Eq. (6), the less risk-averse the developer (which refers to decreasing |λ|when λ>0) or the more riskseeking the developer is (increasing |λ|when λ<0), the greater his/her investments in both quality and employee benefits. Note that the best response q( η )is directly proportional to p2. In our analysis, however, the developer is merely a ‘price-taker’and has no control over the price. That is, the developer adjusts his/her sources of revenue so as to match the market’s ARPU (through the app’s selling price, the in-app ad intensity, and the price of in-app purchases). This characteristic firmly reflects the reality observed in the vast majority of 12 Primarily, initiative-based non-salary benefits are reportedly issued with the goal of recruiting "top quality new employees while retaining existing ones" [17]. 13 https://www.wtwco.com/en-NL/Insights/2021/12/compensation-trendsspotlight-tech-and-media. L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 6 app markets, which seem to closely resemble perfect competition. 14 Nevertheless, we conclude that a higher (lower) market ARPU would push the developer to raise (reduce) his/her app’s quality in order to match the customers’expectation of a higher (lower) utility from using the app (a phenomenon proved empirically for paid apps by [45] 15 ). 4.2. First stage of decision making: the platform sets η Based on the developer’s best response (see Eq. (6)), the platform initiates the game by setting its desired commission rate (0 < η <1), while aiming to maximize its profit. This simulates the platform’s decision making in reality, setting the contract terms for its millions of app developers, aiming to assess how they would react prior to making its final decision. This estimation would have been conducted to set the current terms for both existing and new apps, standing at 15–30 % on Google Play and App Store. Highlighting the importance of the platform’s decision, amending existing terms rarely takes place nowadays due to its significant effect on the market, although recently both Apple and Google decided to lower the commission rate on their respective app stores for the majority of developers from 30 % down to 15 % [21]. Their decision is a direct result of predictions on the developer’s best-response to new contract terms, primarily through his/her quality investments [1]. Unlike the developer, the profit of the platform is essentially deterministic since all its factors presented in Eq. (3) are independent of the random element ε . This comes as a result of the definition of the demand function as deterministic throughout our analysis, focusing on uncertainty related to the developer’s efficiency in creating quality (see Section 3). Nevertheless, its profit is indirectly affected by this form of uncertainty due to the sequential nature of the game –utilizing the developer’s aforementioned response to make its decisions, which indeed is tied to the random element (through the integrated parameter ψ , as indicated in Eq. (6)). Therefore, it is possible to express the platform’s profit by simply inserting the demand function (1) into Eq. (3), while incorporating the developer’s best response for q( η ), given in Eq. (6). Applying rudimentary algebraic reductions to the resulting expression leads the platform to solve the following maximization problem: max η { π p( η )=p2 η (a2(1− η ) 4 ρψ √− α )}.(7) The platform’s profit is a concave function of η . Therefore, at equilibrium, it sets η to the value of the single maximum of π p( η ), as presented in the following proposition: Proposition 2.At equilibrium, η ∗=0.5−2 α a2 ρψ √.(8) Proof. See Appendix. 4.3. Equilibrium results and discussion Corollary 1.At equilibrium, the platform stipulates a commission rate that is <50 % of the developer’s revenue. Proof. Straightforward from Proposition 2. Interestingly, the commission rate at equilibrium illustrates a wellestablished practice in the world of apps. By Corollary 1, the platform would never set a commission rate in excess of 50 % of the developr’s revenue, which is consistent with the reality that this rate typically ranges from 15 to 30 % 4 . This finding further testifies to the applicability of our analysis. Corollary 2.At equilibrium, the platform’s requested commission rate increases when i. The market scale parameter increases; ii. The demand is less sensitive to price (or equivalent); iii. The developer is more economically efficient in creating quality; iv. Uncertainty with regard to the effect of non-salary benefits on quality creation is lower; v. The developer is either less risk-averse or more risk-seeking. Proof. Straightforward from Proposition 2. The conclusions of Corollary 2 seem to follow common sense, and resemble some of the findings of previous papers (e.g., [1]). In essence, the platform permits itself to charge a higher commission rate when the developer’s circumstances are better, i.e., serving more customers, serving customers who are less sensitive to price (or, interchangeably, ARPU), enjoying greater certainty, or producing quality more efficiently. Similarly, the platform’s commission rate increases when the developer is either less risk-averse (which would mean that |λ|declines when λ>0) or more risk-seeking (|λ|grows when λ<0).This apparent pursuit of a fair rate corresponds to the fact that the developer cannot enter into negotiations with regard to the platform’s requested commission rate –both in our analysis and in reality5 (as well as in previous literature; see, e.g., [3,4]). By inserting the value of η ∗from Proposition 2 into the aforementioned expressions (followed by algebraic manipulations), we arrive at the equilibrium values for the developer’s decisions, the developer’s cost of creating quality, and the parties’profits: Corollary 3.At equilibrium: i. The developer’s decisions are given by q∗=1 ρψ (p(a2+4 α  ρψ √) 8a)2 , v∗= 1  ρψ √(p(a2+4 α  ρψ √) 8a)2 ; ii. The developer’s expected cost of creating quality is given by E[C(q∗, v∗)] = 1 ψ  ρψ √(p(a2+4 α  ρψ √) 8a)2 ; iii. The platform’s profit and the developer’s expected profit are given by π p( η ∗) = 1  ρψ √(p(4 α  ρψ √−a2) 4a)2 , E[ π d(q∗,v∗)] = p2(a2+4 α  ρψ √)(a2(3 ψ −1)− 4 α (5 ψ +1) ρψ √) 64a2 ψ  ρψ √; iv. The expected value of the profit of the channel is given by E[ π ch( η ∗,q∗, v∗)] = p2(a4(7 ψ −1)− 8 α  ρψ √(a2(5 ψ +1)+2 α ( ψ +1) ρψ √)) 64a2 ψ  ρψ √. Proof. Straightforward from Proposition 2, along with Eqs. (5),(6) and (7). Proposition 3.At equilibrium, v∗/E[C(q∗,v∗)] = ψ ; Thus, the following statements apply to the uncertainty σ and the developer’s level of risk sensitivity λ: i. These are the only parameters that affect the developer’s allocation of his/ her spending between product quality and non-salary benefits; 14 App markets meet most of the conditions of perfect competition (see [39]): millions of independent app developers and consumers; most apps have a multitude of nearly identical competitors; developers and consumers have abundant information about the apps (mostly available via the platform); very few barriers to enter/leave the market (https://www.investopedia.com/ter ms/p/perfectcompetition.asp, and [30]). 15 Zolkepli et al. [45] proved that "Users are […] willing to pay for apps that have a higher rating"; these app star-ratings have been repeatedly used to indicate user-perceived quality (see [37]). L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 7 ii. An increase (decrease) in the value of each parameter would result in the developer allocating a larger (smaller) share of his/her investment to nonsalary benefits. Proof. See Appendix. Proposition 3 reveals a noteworthy characteristic regarding the developer’s allocation decision, which lies at the core of this study. Although all equilibrium decisions and profits of both players (appearing in Corollary 3) depend on all of the model parameters (presented in Table A in the Appendix), the developer’s allocation of resources (between non-salary benefits and the creation of quality) depends solely on two parameters. The first is the level of uncertainty, particularly with regard to the effect of investing in non-salary benefits on the efficiency of quality creation (as incorporated in Eq. (2)). Interestingly, the lower the level of certainty regarding this effect, the higher the developer’s investment in non-salary benefits (instead of quality creation). A plausible analytical explanation for the developer’s behavior is the desire to increase his/her deterministic spending (v) while reducing the uncertain cost of quality creation (C(q,v)). The second parameter, which is the developer’s level of risk sensitivity, seems to follow a similar pattern. The more risk-averse (or less risk-taking) the developer, the lower the budget he/she allocates to quality creation, preferring instead to invest in non-salary benefits. Thus, the conservative developer prefers to invest in his/her workers, which is the safer alternative for enhancing efficiency in the long run. Our findings are consistent with evidence provided in various publications, highlighting that investment in human capital (particularly non-salary benefits) is a superior tool for boosting productivity to capital investments [22], particularly in uncertain times [5]. Given the central influence of both parameters encompassed within ψ ( ≡ 1+λ σ )on equilibrium decisions, we hereby constrain its value in order to ensure that the platform’s commission rate is a positive fraction (0 < η ∗<1). Since Corollary 1 guarantees an upper limit for the commission rate of 0.5, it is only necessary to limit the parameters of its expression to ensure that η ∗>0. Performing rudimentary algebraic manipulations on this inequality, we state the following condition: ψ <1 ρ (a2 4 α )2 .(9) Corollary 4.While the platform’s profit at equilibrium is always positive, the developer’s expected profit is positive only when a >2 α  ψσ √ √⋅  5 ψ +1 3 ψ −1 √and the channel’s expected profit is positive only when a >2 α  ψσ √ √⋅ 5 ψ +1+4 ψ (1+2 ψ ) √ 7 ψ −1 √. Proof. Straightforward from the expressions in Corollary 3 and given the condition in Eq. (9). In line with the decision to disregard any costs associated with the platform (see subSection 2.2), by Corollary 4, the platform will always be positively rewarded as a result of interacting with the developer. On the contrary, the developer’s expenses on quality creation and nonsalary benefits lead him/her to lose when the above condition is not met. Combining the profits of the two, the entire channel could also experience losses, albeit for a less tight condition (because the platform always has a positive profit). Ultimately, the developer will lose when his/her market appears to be too small (i.e., when ais lower than the minimum stipulated in Corollary 4), although both the platform and the channel may still be profitable. Therefore, future studies could consider a scenario in which the platform further lowers its commission rate in order to ensure that the developer can be profitable (e.g., by offering a side payment), thus making it worthwhile for the latter to operate under the non-negotiable contract of the platform. 4.4. Numeric exploration Assuming that the developer’s operations are profitable (i.e., the condition from Corollary 4 is met), we are still unable to explore analytically the effect of ψ ( ≡ 1+λ σ )on the players’profits (given the Fig. 2. The effect of ψ on the platform’s, the developer’s and the channel’s expected profits. The setting used is a=100, p=1, α =1 and ρ =0.05. L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 8 non-linear effect of ψ on the profit expressions presented in Corollary 3). Therefore, we perform a numerical analysis for each expression that satisfies the condition in Eq. (9) and meets the additional conditions in Corollary 4. As demonstrated in Fig. 2, we use a=100,p=1, α =1,and ρ =0.05 as the parameter values (resembling the numerical analysis of [1]) and vary the integrated parameter ψ between its extreme values (0.67 < ψ <1.33; see Appendix). Note that our analysis also holds for more extreme parameter values. 16 The platform’s profit decreases (albeit nonlinearly) with an increase in ψ , meaning that the platform achieves lower profits as the developer becomes more risk-averse (i.e., as |λ|grows when λ>0 or as |λ|declines when λ<0). This finding replicates the results of multiple previous studies of app supply chains (e.g., [4]). However, the relation between the platform’s profit and the level of uncertainty (particularly the level of uncertainty with regard to the effect of non-salary benefits on the efficiency of quality creation) is discontinuous. Specifically, when the uncertainty increases (i.e., higher σ )and the developer is more risk-averse (risk-seeking), the platform’s profit will decrease (increase). Thus, the platform is harmed by non-salary ambiguity when the developer is risk-averse, but benefits from it when the developer is risk-seeking. This non-intuitive result implies that the platform would wish to increase the uncertainty faced by the risk-seeking developer with regard to the effectiveness of non-salary benefits. This could be achieved by the platform issuing such benefits to its own workers, and then entering into competition for employees with the developer. We therefore recommend that future studies should consider a platform that also acts as an employer of app developers (similarly to Apple and Google). The importance of studying this extension is further justified by considering the social planner’s perspective, as the expected profit of the entire channel is dominated by the trend of the platform’s profit (i.e., the channel’s expected profit decreases in ψ similarly to the platform’s profit). Unlike the platform’s and the channel’s profits, the developer’s expected profit behaves differently depending on whether the developer is risk-averse (λ>0) or risk-seeking (λ<0). Peaking around riskneutrality (λ=0 implying ψ =1, see Fig. 2(b)), the expected profit decreases as the developer faces greater uncertainty (higher σ ) or as the developer adopts a more extreme risk attitude (higher |λ|). Thus, the developer could consider adopting methods to reduce one (or both) of these parameters, such as business intelligence to determine the nonsalary benefits offered by his/her competitors or objective decisionsupport systems (DSS) 17 to allow the developer to adopt a more neutral attitude towards risk. To strengthen the validity of our numeric exploration above, we have repeated the analysis for six additional settings of parameter values. In particular, we modified the values of p, α and ρ by 50 % above and below the original values used in this section (i.e., p={0.5, 1.5}, α ={0.5, 1.5} and ρ ={0.025, 0.075}), while keeping the other parameter values fixed (in order to isolate the effect of each parameter on the results). The effect of ψ on the platform’s, the developer’s and the channel’s expected profits under this extended analysis appear in Figures A1-A6 in the Online Appendix. Comparing the results in Figures A1-A6 with those of Fig. 2 shows that our main findings are robust to such modifications of the parameter values. 5. Model extension: multiple developers 5.1. Introduction and market contextualization Initiative-based non-salary benefits are granted primarily in order to attract new workers and retain existing ones 12 , as a response to global labor shortages –particularly in the high-tech sector. Employers are compelled to compete for the existing pool of capable workers, offering unconventional benefits in an attempt to win over major talents. Therefore, it is imperative to consider employer competition when discussing non-salary benefits. Moreover, researchers of supply chains of virtual products have rarely discussed competition between developers (one of the few studies that has considered such competition is [4]) and, to the best of our knowledge, have never considered competition between developers with regard to attracting employees. We extend the original two-agent system to a system of Napp developers who compete for employees through the use of initiativebased non-salary benefits. Note that throughout the following analysis, we use the same notations as those presented in Table A (see Appendix), while introducing the index ito denote the particular app developer (out of a total of Ndevelopers) to whom the variable or parameter applies. An additional adaptation involves the definition of α , which, from this point on, denotes the average price-equivalent sensitivity of demand for all the other (N−1) competing apps. Lastly, we introduce parameter β(0<β<1)to represent the intensity of the competition between app developers for available employees; a higher value of βindicates that the employees working for a particular developer are more strongly influenced by the initiative-based nonsalary benefits offered by competing developers (and vice versa for a lower value of β). To allow for an elaborate analytical investigation, we consider app developers with similar values for all the parameters presented in Table A (see Appendix). Besides the universality achieved thanks to the analytical nature of our exploration (avoiding the resort to casespecific numerical analyses, e.g., for specific company sizes and markets), our concentration on developers with similar parameter values has been adopted by similar studies previously [4] as well as depicts real examples from the world of apps (see Table 2). Accordingly, our analysis focuses on app developers who serve the same category or market (i.e., with similar values for p, a, and α ) and have comparable internal organization (similar ρ and λ). The level of uncertainty (represented through σ ), particularly regarding the effect of investing in non-salary benefits on the efficiency of quality creation, is assumed to be identical for all developers given the lack of conclusive evidence on the matter across the entire industry, as well as to gives rise to explicit results for the optimal solution. Since we wish to isolate the effect of employer competition, in this extension, we assume that the apps do not incur a purchase price (paid apps accounted for <6 % of available apps on Apple’s App Store and Google Play in 2023), 18 while the ARPU represents the per-user revenue from all non-price equivalents (e.g., the average revenue per user from viewing in-app ads). Our setup closely resembles numerous notable examples from the world of competing apps, and several of them appear on Table 2. Specifically, the rivals on each category appear to share analogous characteristics that align with our assumption of identical parameters. Firstly, all apps are downloaded free-of-charge and offer in-app purchases of comparable sums (within each category), supporting our assumption of a shared p. When considered alongside with similar average revenues per user, 19 it is possible to suppose that the demand faced by each app developer behaves similarly, i.e., with corresponding market scale (a) and price sensitivity ( α ). Lastly, the competing apps share a similar economic efficiency in creating quality ( ρ ), as reflected 16 We performed numerical analyses using parameter values much higher than those stated above, as well as values closer to those required to meet the condition in equation (9) and the additional conditions in Corollary 4. 17 https://www.investopedia.com/terms/d/decision-support-system.asp. 18 Approximately 95% of mobile apps (both in Google Play and in Apple’s App Store) are free to download: https://www.statista.com/statistics/263797/nu mber-of-applications-for-mobile-phones/ 19 Commonly used to characterize the app’s active user base: https://www. appsflyer.com/glossary/arpu/ L.O. Maly and T. Avinadav Operations Research Perspectives 14 (2025) 100320 15 maximizing the platform’s profit, d d ηπ p( η ) = − Np2 2(a2( η −0.5)  ρψ √+2 α )=0, leads to η ∗=0.5−2 α a2 ρψ √. Proof of Proposition 6 i. 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