The role of reputation in sequel production

Khac Minh Duc Do; Knyazev, Dmitriy Article The role of reputation in sequel production Games Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Khac Minh Duc Do; Knyazev, Dmitriy (2025) : The role of reputation in sequel production, Games, ISSN 2073-4336, MDPI, Basel, Vol. 16, Iss. 3, pp. 1-7, https://doi.org/10.3390/g16030023 This Version is available at: https://hdl.handle.net/10419/330137 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. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. 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/ Academic Editor: Marco A. Marini Received: 28 February 2025 Revised: 29 April 2025 Accepted: 7 May 2025 Published: 8 May 2025 Citation: Do, K. M. D., & Knyazev, D. (2025). The Role of Reputation in Sequel Production. Games,16(3), 23. https://doi.org/10.3390/g16030023 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article The Role of Reputation in Sequel Production Khac Minh Duc Do 1and Dmitriy Knyazev 2,* 1TWS Partners, 10117 Berlin, Germany; [email protected] 2Department of Business Decisions and Analytics, University of Vienna, Oskar-Morgenstern-Platz 1, 1180 Vienna, Austria *Correspondence: dmitriy[email protected]; Tel.: +43-1-4277-38164 Abstract: This paper develops a simple model of sequel production for experience goods, showing how reputation shapes a producer’s incentives. Producers differ in productivity, which determines how much effort they invest. A sequel is made only if the previous installment exceeds a quality threshold, capturing the idea that consumers base future consumption on past success. Although high-productivity producers create higher-quality originals and sequels, the conditioning on successful originals still makes sequels, on average, worse than their predecessors. This aligns with evidence of sequel underperformance in media markets. Keywords: sequel; reputation; experience goods; producer incentives 1. Introduction This paper aims to develop a simple model of the role of reputation in producing sequels. In particular, we show why there may be incentives for a producer to create a sequel of lower quality. Our motivation stems from the evidence that many movie sequels tend to be worse than their original counterparts. Helmer (2011) compares the scores of selected original and sequel movies (taken from the review aggregator Rotten Tomatoes) against each other. He finds that there are only a few examples where the sequel outperforms the original, such as Star Trek II or The Dark Knight, which are usually considered as the best movies in the respective series. But the vast majority of sequels perform worse than the respective originals. In this paper, we provide a model to explain this fact. Nelson (1970) introduced the concept of experience goods, which are goods for which the consumer is not fully informed about quality before purchase or consumption. Because it is unclear how much utility the consumer will derive before making the decision to acquire or consume the good, the consumer only learns this ex post. In the literature, goods such as books and movies are often modeled as experience goods. In theory, consumer “tastes” can differ, leading each consumer to derive different utility from the same good. Since consumers do not know ex ante how much utility they will gain, they only discover it ex post. As a result, reputation may influence the consumption of a sequel, since it provides consumers with information about the expected utility of the product. Among other factors, this reputation can be derived from the quality of earlier installments that the consumer has already experienced. This paper develops a simple theoretical model to explain why sequels of experience goods often end up with lower quality than their predecessors despite being produced by the same firm. We consider a risk-neutral producer whose productivity can be either high or low and is known only to themselves. The producer’s effort and an exogenous Games 2025,16, 23 https://doi.org/10.3390/g16030023 Games 2025,16, 23 2 of 7 shock jointly determine a product’s realized quality. Crucially, a sequel is only viable if the quality of the original surpasses a certain threshold, creating a reputation for the producer. It increases buyers’ willingness to consume the sequel. Since the producer’s type is not known to the consumers and the qualities of products are the only variables observable by consumers, the reputation of a producer in our model is related only to the quality of their past products. Our analysis shows that high-productivity producers exert higher effort and thus deliver higher expected quality for both original and sequel productions (Proposition 1). The higher effort of producers of a higher type results in a higher expected quality of their goods (Proposition 2). Besides that, they produce sequels more often (Proposition 3). However, even these producers cannot fully escape the sequel-quality drop, because only sufficiently successful originals move on to a sequel. This selection effect implies that once a producer decides to make a sequel, the conditioning on the original’s successful outcome renders the expected sequel quality lower than the expected quality of the original (Proposition 4). These findings align with observed tendencies in the movie industry, offering a formal explanation for why many sequels underperform relative to their originals despite a clear reputation-based incentive to sustain high quality. Our motivation for adopting a two-type framework is to keep the model analytically tractable and to clearly illustrate the core mechanisms by which reputation affects sequel production incentives. The main qualitative insights—such as the reputation threshold inducing higher effort from high-productivity producers, the selection effect behind sequel underperformance, and the persistence of quality gaps—are robust to richer settings. In particular, the comparative statics and selection effects would extend to environments with a continuous productivity distribution. The paper is structured as follows. In the next section, we provide a review of the related literature. In Section 3, we formulate the model. Section 4presents our analysis and the main results. Section 5concludes the paper. 2. Related Literature Building on Nelson’s insights, Shapiro (1983) formalized how reputational premiums emerge. Firms that continually provide higher quality can command price premiums because consumers trust their reputation. This reputational signaling dynamic underpins incentives to maintain quality across multiple “installments” or product lines. Extending these foundational ideas, Mailath and Samuelson (2001) examined how reputation evolves in repeated interactions. They showed that maintaining a good reputation can yield long-term benefits, but incentives to deviate—and produce lower quality at times—may also exist if near-term gains outweigh future losses. This tension resonates with the puzzle of sequel quality: a producer might see short-run profit benefits from lowering production costs, even if doing so risks harming the franchise’s long-term reputation. Tadelis (2002) studied a market for reputations, providing further insight into how brand names (or “reputation capital”) can be traded or inherited, potentially encouraging or discouraging effort. While his analysis is more general, it clarifies how reputational considerations might vary with different producer types (e.g., highvs. low-productivity firms) and over time. There is also literature on how the experience of one consumer can influence others. For instance, Reinstein and Snyder (2005) examine the role of expert reviews on the consumption of experience goods in the context of movie releases. They find some evidence that positive reviews correlate with higher earnings, although the effect’s significance varies with the scope of release and movie genre. Gemser et al. (2007) build on these findings, comparing the impact of expert reviews on small-release art-house movies and wide-release Games 2025,16, 23 3 of 7 mainstream movies. While reviews significantly affect revenues for smaller releases, they do not have the same measurable impact on wider-release mainstream movies, supporting the findings by Reinstein and Snyder (2005). Moretti (2011) further shows that social learning from non-professional opinions also affects movie revenues. Relatively little literature addresses the impact of an original on subsequent sequel consumption. For example, Karniouchina (2011) provides evidence that being a sequel can positively affect a movie’s revenues. Similarly, B. I. Situmeang et al. (2014) show that originals can influence sequel consumption in video games, with both the quality of past editions and the variance in reviews playing a role. 3. Model There is a risk-neutral producer who may provide a good at period t≥ 0 with quality qt by choosing effort level xt . The good produced at t= 0 is referred to as original and the good produced at any t> 0 as sequel. Producer is characterized by type θi , where i indicates whether they have high productivity θh or low productivity θl , such that θi∈ {θl ; θh} and θl<θh . Only the producer knows its own productivity type. We further assume that some error term ϵi t affects the good’s quality in addition to the producer’s effort. This error term is uniformly distributed on the interval [−a , a] , ϵi t∼U[−a , a] , and is independent and identically distributed over time. The quality of the good produced in period t is qt=θixt+ϵi t . As a result of exerting effort xt , the producer incurs a cost given by the quadratic cost function cx2 t 2. Consumers do not know the quality ex ante. They cannot observe the producer’s type or effort. They only observe the realized quality qt after consumption. We assume that the consumers will be willing to consume the sequel only if its predecessor is of sufficiently high quality. Namely, a sequel at any t> 0 can be produced only if the quality qt−1 in period t− 1 exceeds a constant over time threshold ¯ q . If qt−1≤¯ q , a sequel at period t cannot be produced. We assume that the threshold ¯ q is substantially low to ensure a positive optimal level of effort. In particular, we assume: ¯ q<2θl2 c. (1) We also assume that the error term ϵi is sufficiently noisy to ensure that the solution is well behaved, i.e., a>2θl2 c−¯ q. (2) We assume that the earnings from selling the good are proportional to its quality qt . Thus, producer’s profit Πtin period t>0 is the following: Πi t=qt−cx2 t 2. The producer discounts the future value of t+ 1 by a discount factor β , β∈[ 0, 1 ] . Hence, the effort chosen in period taffects potential revenue in period t+1. 4. Analysis First, we obtain the following value for the producer in period t: Vt=max xt≥0nEΠt+βVt+1Pr(θixt+ϵi t>¯ q)o. Games 2025,16, 23 4 of 7 The term Pr(θixt+ϵt>¯ q) represents the probability that a sequel can be produced. If this event does not occur, its contribution to the expected value is zero. Thus, we obtain the following Bellman equation: Vt=max xt≥0θixt−cx2 t 2+βVt+11−¯ q−θixt+a 2a. (3) We solve for the optimum effort level by computing the first-order condition: dVt dxt =θi−cxt+βθiVt+1 2a=0 ⇒xt=θi c+βθiVt+1 2ac . (4) The second-order condition is fulfilled because d2Vt dx2 t =−c<0, which indicates that condition (4) indeed determines the optimal effort. Notice that the problem is stationary in time. Hence, for every type θi , the value and the optimal effort are constant over time. Denote Vi and xi as the value and the optimal level of effort for the producer of type θi. Thus, xi=θi c+βθiVi 2ac . (5) Plugging it back into Bellman Equation (3), we obtain Vi=θixi−c(xi)2 2+βVi1−¯ q−θixi+a 2a. (6) ⇔Vi=2aθixi−ac(xi)2 2a−β(a−¯ q+θixi). (7) Now, we are ready to provide the main results of our analysis. First, we show that the producers of higher type will supply a higher level of effort. Proposition 1. The optimal level of effort of the producer of a higher type is higher than the optimal level of effort of the producer of a lower type, i.e., xh>xl. Proof. We show this by contradiction. First, assume that xl≥xh . Since θl<θh , Equation (5) implies that to have xl≥xhit must be that Vl>Vh. Define function Φ(x,θ) = 2aθx−ac(x)2 2a−β(a−¯ q+θx). Notice that for any i∈ {h,l} Φ(xi,θi) = Vi. Since Vl>Vh, it follows that Φ(xl,θl)>Φ(xh,θh). Games 2025,16, 23 5 of 7 By definition of Vh, it follows that Φ(xh,θh)≥Φ(x,θh) for any x∈R+. This implies that Φ(xh,θh)≥Φ(xl,θh). Next, notice that function Φ(x , θ) is increasing in θ because its numerator is increasing, the denominator is decreasing in θ , and the Assumptions (1) and (2) guarantee that both the numerator and denominator of Φ are positive for the respective parameter ranges. Hence, Φ(xl,θh)≥Φ(xl,θl). Finally, combining the last two inequalities, we obtain Vh=Φ(xh,θh)≥Φ(xl,θh)≥Φ(xl,θl) = Vl. This is a contradiction to Vl>Vh. Next, we demonstrate that the expected quality of originals and sequels is higher for the producer with high type. Proposition 2. The expected quality of good of originals and all sequels is higher for the producer of a higher type than for the producer with a lower type, i.e., for any t ≥0 Eqh t>Eql t. Proof. We show this by computing the expected value and comparing the results for the optimum effort levels. Eqi t=θixi+Eϵi t=θixi. (8) Since θh>θland from Proposition 1 we have xh>xl, it follows that θhxh>θlxl. Besides that, we can demonstrate that the producer of the high type is more likely to produce a sequel than the producer of the low type. Proposition 3. The producer of the high type produces sequels more often than the producer of the low type. Proof. The probability of producing a sequel for each good produced at t is equal to Pr(ϵi t>¯ q−θixi t). From Proposition 2, we know that θhxh>θlxl. Hence, Pr(ϵh t>¯ q−θhxh)>Pr(ϵl t>¯ q−θlxl). Games 2025,16, 23 6 of 7 Our last result concerns the quality of each sequel compared to its predecessor. Proposition 4. The expected quality of each good that receives a sequel is higher than the expected quality of that sequel. Proof. To prove this result, we just need to note that if some good produced at t receives a sequel, the expected quality of this good is E[qi t|qi t>¯ q] . This conditional expectation is greater than the unconditional expectation, i.e., E(qi t|qi t>¯ q)>Eqi t. Finally, from Proposition 2, it follows that Eqi t=θixi=Eqi t+1. Thus, we obtain that E(qi t|qi t>¯ q)>Eqi t+1. This result is consistent with the anecdotal evidence presented in the introduction. Intuitively, sequels are usually produced for goods of sufficiently high quality. Thus, even if the producer applies the same level of effort to producing a sequel, the fact that the decision was made to produce it means that the expected quality of the sequel will be lower than the expected quality of the original. 5. Conclusions In this paper, we designed a model in which reputation in the form of the previous period’s quality influences the production of a sequel. Our model predicts that producers of higher types will apply higher effort, produce better originals and sequels, and produce sequels more often than the producers of lower types. However, for both types of producers, sequels will have a lower expected quality than their predecessors. Reputation in our model is represented by the equality of the product developed in the previous period. The unobservability of the producer’s type to consumers is important because in the model with complete information, the consumers should make their consumption decisions based on the observable type of the producer and not on the quality of the good in the previous problem. Given the type of the producer, they would be also able to solve the optimization problem of the producer and compute the expected quality of the product. The analysis will be less interesting in this case, because any dynamics would disappear. Author Contributions: Conceptualization, D.K.; Formal analysis, K.M.D.D. and D.K. Writing— original draft, K.M.D.D.; Writing—review & editing, D.K.; Supervision, D.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Austrian National Bank through the OeNB Jubiläumsfonds grant number 19021. Data Availability Statement: No new data were created or analyzed in this study. Conflicts of Interest: Author Khac Minh Duc Do was employed by the company TWS Partners. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. Games 2025,16, 23 7 of 7 References B. I. Situmeang, F., A. A. M. Leenders, M., & M. Wijnberg, N. (2014). The good, the bad and the variable. European Journal of Marketing, 48(7/8), 1466–1486. Gemser, G., Van Oostrum, M., & Leenders, M. A. (2007). The impact of film reviews on the box office performance of art house versus mainstream motion pictures. Journal of Cultural Economics,31(1), 43–63. [CrossRef] Helmer, E. (2011). The sequel map—Which sequels were better or worse than the original? Available online: https://web.archive.org/web/ 20160305051621/http://boxofficequant.com/sequel-map/ (accessed on 18 February 2025). Karniouchina, E. V. (2011). Impact of star and movie buzz on motion picture distribution and box office revenue. International Journal of Research in Marketing,28(1), 62–74. Mailath, G. J., & Samuelson, L. (2001). Who wants a good reputation? Review of Economic Studies,68(2), 415–441. [CrossRef] Moretti, E. (2011). Social learning and peer effects in consumption: Evidence from movie sales. Review of Economic Studies,78(1), 356–393. [CrossRef] Nelson, P. (1970). Information and consumer behavior. Journal of Political Economy,78(2), 311–329. Reinstein, D. A., & Snyder, C. M. (2005). The influence of expert reviews on consumer demand for experience goods: A case study of movie critics. Journal of Industrial Economics,53(1), 27–51. Shapiro, C. (1983). Premiums for high quality products as returns to reputations. Quarterly Journal of Economics,98(4), 659–679. [CrossRef] Tadelis, S. (2002). The market for reputations as an incentive mechanism. Journal of Political Economy,110(4), 854–882. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.