We argue in favor of a departure from the equilibrium approach in game theory towards the less ambitious goal of describing only the actual behavior of rational players. The notions of Nash equilibrium and its refinements require a specification of the players’ choices and beliefs not only along the equilibrium play but also at counterfactual histories. We discuss an alternative—counterfactual-free—approach that focuses on choices and beliefs along the actual play, while being silent on choices and beliefs at unreached histories. Such an approach was introduced in an earlier paper that considered only perfect-information games. Here we extend the analysis to general extensive-form games (allowing for imperfect information) and put forward a behavioral notion of self-confirming play, which is close in spirit to the literature on self-confirming equilibrium. We also extend, to general extensive-form games, the characterization of rational play that is compatible with pure-strategy Nash equilibrium.
{"title":"Rational Play in Extensive-Form Games","authors":"G. Bonanno","doi":"10.3390/g13060072","DOIUrl":"https://doi.org/10.3390/g13060072","url":null,"abstract":"We argue in favor of a departure from the equilibrium approach in game theory towards the less ambitious goal of describing only the actual behavior of rational players. The notions of Nash equilibrium and its refinements require a specification of the players’ choices and beliefs not only along the equilibrium play but also at counterfactual histories. We discuss an alternative—counterfactual-free—approach that focuses on choices and beliefs along the actual play, while being silent on choices and beliefs at unreached histories. Such an approach was introduced in an earlier paper that considered only perfect-information games. Here we extend the analysis to general extensive-form games (allowing for imperfect information) and put forward a behavioral notion of self-confirming play, which is close in spirit to the literature on self-confirming equilibrium. We also extend, to general extensive-form games, the characterization of rational play that is compatible with pure-strategy Nash equilibrium.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"72"},"PeriodicalIF":0.9,"publicationDate":"2022-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43721146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a market setting where a consumer holds either a naive or sophisticated perception of their preference over products. We introduce the concept of a cognitive equilibrium, in which the consumer can transition between the cognitive states of naiveté and sophistication depending on the degree of exploitation in the market. We compare market outcomes under monopoly and competition. While competition unambiguously improves market outcomes when the consumer’s cognitive state is exogenous, it can strictly lower gains from trade when cognitive states are endogenously determined.
{"title":"Misperception and Cognition in Markets","authors":"B. Young","doi":"10.3390/g13060071","DOIUrl":"https://doi.org/10.3390/g13060071","url":null,"abstract":"We consider a market setting where a consumer holds either a naive or sophisticated perception of their preference over products. We introduce the concept of a cognitive equilibrium, in which the consumer can transition between the cognitive states of naiveté and sophistication depending on the degree of exploitation in the market. We compare market outcomes under monopoly and competition. While competition unambiguously improves market outcomes when the consumer’s cognitive state is exogenous, it can strictly lower gains from trade when cognitive states are endogenously determined.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"71"},"PeriodicalIF":0.9,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47755310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.
{"title":"Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts","authors":"R. Gholami, L. Sandal, J. Ubøe","doi":"10.3390/g13060070","DOIUrl":"https://doi.org/10.3390/g13060070","url":null,"abstract":"Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"70"},"PeriodicalIF":0.9,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42126955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Burton-Chellew, Victoire D'Amico, Claire Guérin
The strategy method is often used in public goods games to measure an individual’s willingness to cooperate depending on the level of cooperation by their groupmates (conditional cooperation). However, while the strategy method is informative, it risks conflating confusion with a desire for fair outcomes, and its presentation may risk inducing elevated levels of conditional cooperation. This problem was highlighted by two previous studies which found that the strategy method could also detect equivalent levels of cooperation even among those grouped with computerized groupmates, indicative of confusion or irrational responses. However, these studies did not use large samples (n = 40 or 72) and only made participants complete the strategy method one time, with computerized groupmates, preventing within-participant comparisons. Here, in contrast, 845 participants completed the strategy method two times, once with human and once with computerized groupmates. Our research aims were twofold: (1) to check the robustness of previous results with a large sample under various presentation conditions; and (2) to use a within-participant design to categorize participants according to how they behaved across the two scenarios. Ideally, a clean and reliable measure of conditional cooperation would find participants conditionally cooperating with humans and not cooperating with computers. Worryingly, only 7% of participants met this criterion. Overall, 83% of participants cooperated with the computers, and the mean contributions towards computers were 89% as large as those towards humans. These results, robust to the various presentation and order effects, pose serious concerns for the measurement of social preferences and question the idea that human cooperation is motivated by a concern for equal outcomes.
{"title":"The Strategy Method Risks Conflating Confusion with a Social Preference for Conditional Cooperation in Public Goods Games","authors":"M. Burton-Chellew, Victoire D'Amico, Claire Guérin","doi":"10.3390/g13060069","DOIUrl":"https://doi.org/10.3390/g13060069","url":null,"abstract":"The strategy method is often used in public goods games to measure an individual’s willingness to cooperate depending on the level of cooperation by their groupmates (conditional cooperation). However, while the strategy method is informative, it risks conflating confusion with a desire for fair outcomes, and its presentation may risk inducing elevated levels of conditional cooperation. This problem was highlighted by two previous studies which found that the strategy method could also detect equivalent levels of cooperation even among those grouped with computerized groupmates, indicative of confusion or irrational responses. However, these studies did not use large samples (n = 40 or 72) and only made participants complete the strategy method one time, with computerized groupmates, preventing within-participant comparisons. Here, in contrast, 845 participants completed the strategy method two times, once with human and once with computerized groupmates. Our research aims were twofold: (1) to check the robustness of previous results with a large sample under various presentation conditions; and (2) to use a within-participant design to categorize participants according to how they behaved across the two scenarios. Ideally, a clean and reliable measure of conditional cooperation would find participants conditionally cooperating with humans and not cooperating with computers. Worryingly, only 7% of participants met this criterion. Overall, 83% of participants cooperated with the computers, and the mean contributions towards computers were 89% as large as those towards humans. These results, robust to the various presentation and order effects, pose serious concerns for the measurement of social preferences and question the idea that human cooperation is motivated by a concern for equal outcomes.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"69"},"PeriodicalIF":0.9,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45529338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the strategic nature of farmers’ groundwater usage with a rich dataset from the American Midwest. We propose a new revealed preference test for the groundwater interaction as a dynamic game. We reject a view of groundwater usage decisions as strategic substitutes in favor of strategic complements as a better description.
{"title":"Groundwater Usage and Strategic Complements: Part II (Revealed Preferences)","authors":"Caleb M. Koch, H. Nax","doi":"10.3390/g13050068","DOIUrl":"https://doi.org/10.3390/g13050068","url":null,"abstract":"We investigate the strategic nature of farmers’ groundwater usage with a rich dataset from the American Midwest. We propose a new revealed preference test for the groundwater interaction as a dynamic game. We reject a view of groundwater usage decisions as strategic substitutes in favor of strategic complements as a better description.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"68"},"PeriodicalIF":0.9,"publicationDate":"2022-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45706846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We test whether the decisions in a common-pool resource game are better modeled game-theoretically as strategic substitutes or complements using an individual-level dataset of groundwater usage that accounts for 3% of US irrigated agriculture. Based on a regression framework with instrumental variables, we find support for strategic complements, suggesting that reciprocity– and/or race-to-depletion–like dynamics are key to understanding groundwater usage.
{"title":"Groundwater Usage and Strategic Complements: Part I (Instrumental Variables)","authors":"Caleb M. Koch, H. Nax","doi":"10.3390/g13050067","DOIUrl":"https://doi.org/10.3390/g13050067","url":null,"abstract":"We test whether the decisions in a common-pool resource game are better modeled game-theoretically as strategic substitutes or complements using an individual-level dataset of groundwater usage that accounts for 3% of US irrigated agriculture. Based on a regression framework with instrumental variables, we find support for strategic complements, suggesting that reciprocity– and/or race-to-depletion–like dynamics are key to understanding groundwater usage.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"67"},"PeriodicalIF":0.9,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43561469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a clearing problem in peer-to-peer energy markets, where prosumers can trade energy among each other and with the main grid to meet their energy demands. By using a game-theoretic formulation and exploiting operator-theoretic methods for generalized Nash equilibrium seeking, we propose two variants of the state-of-the-art distributed market clearing mechanism with improved convergence speeds. Furthermore, we design a third variant that allows for equilibrium selection, i.e., computing a specific market solution based on a convex preference function of the network operator, e.g., a congestion cost. We provide convergence guarantees and numerically show the advantages of our proposed algorithms in terms of convergence speed up and obtaining reduced grid congestion.
{"title":"Equilibrium Seeking and Optimal Selection Algorithms in Peer-to-Peer Energy Markets","authors":"W. Ananduta, Sergio Grammatico","doi":"10.3390/g13050066","DOIUrl":"https://doi.org/10.3390/g13050066","url":null,"abstract":"We consider a clearing problem in peer-to-peer energy markets, where prosumers can trade energy among each other and with the main grid to meet their energy demands. By using a game-theoretic formulation and exploiting operator-theoretic methods for generalized Nash equilibrium seeking, we propose two variants of the state-of-the-art distributed market clearing mechanism with improved convergence speeds. Furthermore, we design a third variant that allows for equilibrium selection, i.e., computing a specific market solution based on a convex preference function of the network operator, e.g., a congestion cost. We provide convergence guarantees and numerically show the advantages of our proposed algorithms in terms of convergence speed up and obtaining reduced grid congestion.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"66"},"PeriodicalIF":0.9,"publicationDate":"2022-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48214334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate whether tournament prizes that depend on joint output (“variable prize tournaments”) can alleviate the sabotage problem which is otherwise inherent in tournament structures. In a game-theoretical model with three contestants, we compare fixed-prize tournaments with tournaments where prizes depend on contestants’ joint output. Our analysis suggests that the incentives to sabotage in a fixed-prize tournament may be counteracted in a variable-prize tournament such that contestants no longer sabotage, but help one another. We empirically test the implications of our model with the help of a classroom experiment where we compare participants’ choices in a fixed-prize treatment () with those of a variable-prize treatment () in a between-subjects design. Given our parametrization, we expect efforts to be identical in both treatments, and we expect sabotage in the treatment and no sabotage in the treatment. In accordance with the model, we find that participants in the fixed-prize tournament sabotage one another, whereas participants in the variable-prize tournament help one another. At the same time, participants’ effort levels do not vary between the two treatments.
{"title":"Do Output-Dependent Prizes Alleviate the Sabotage Problem in Tournaments?","authors":"Thomas Glökler, Kerstin Pull, M. Stadler","doi":"10.3390/g13050065","DOIUrl":"https://doi.org/10.3390/g13050065","url":null,"abstract":"We investigate whether tournament prizes that depend on joint output (“variable prize tournaments”) can alleviate the sabotage problem which is otherwise inherent in tournament structures. In a game-theoretical model with three contestants, we compare fixed-prize tournaments with tournaments where prizes depend on contestants’ joint output. Our analysis suggests that the incentives to sabotage in a fixed-prize tournament may be counteracted in a variable-prize tournament such that contestants no longer sabotage, but help one another. We empirically test the implications of our model with the help of a classroom experiment where we compare participants’ choices in a fixed-prize treatment () with those of a variable-prize treatment () in a between-subjects design. Given our parametrization, we expect efforts to be identical in both treatments, and we expect sabotage in the treatment and no sabotage in the treatment. In accordance with the model, we find that participants in the fixed-prize tournament sabotage one another, whereas participants in the variable-prize tournament help one another. At the same time, participants’ effort levels do not vary between the two treatments.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"65"},"PeriodicalIF":0.9,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49340275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Why do some incomplete information markets feature intermediaries while others do not? I study the allocation of two goods in an incomplete information setting with a single principal, multiple agents with unit demand, and interdependent valuations. I construct a novel dynamic mechanism implemented by a principal who faces a set of intermediaries, each of whom represents an ex ante identical set of agents. This mechanism has a unique (up to permutation) weak perfect Bayesian equilibrium. The dynamic mechanism is inefficient with positive probability. Nevertheless, under mild conditions the agents are ex ante better off under the dynamic mechanism relative to a Vickrey-like auction because the intermediaries are more able to exploit information asymmetries in the dynamic mechanism than agents are able to exploit information asymmetries in the Vickrey-like auction. Finally, I show that in large markets the dynamic mechanism and Vickrey-like auction have the same expected total surplus. The comparison between the two mechanisms gives a stylized intuition for the hierarchical structure of larger markets and institutions.
{"title":"Informational Hold Up and Intermediaries","authors":"Naomi Utgoff","doi":"10.3390/g13050063","DOIUrl":"https://doi.org/10.3390/g13050063","url":null,"abstract":"Why do some incomplete information markets feature intermediaries while others do not? I study the allocation of two goods in an incomplete information setting with a single principal, multiple agents with unit demand, and interdependent valuations. I construct a novel dynamic mechanism implemented by a principal who faces a set of intermediaries, each of whom represents an ex ante identical set of agents. This mechanism has a unique (up to permutation) weak perfect Bayesian equilibrium. The dynamic mechanism is inefficient with positive probability. Nevertheless, under mild conditions the agents are ex ante better off under the dynamic mechanism relative to a Vickrey-like auction because the intermediaries are more able to exploit information asymmetries in the dynamic mechanism than agents are able to exploit information asymmetries in the Vickrey-like auction. Finally, I show that in large markets the dynamic mechanism and Vickrey-like auction have the same expected total surplus. The comparison between the two mechanisms gives a stylized intuition for the hierarchical structure of larger markets and institutions.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"63"},"PeriodicalIF":0.9,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46476331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study two-sided matching contests with two sets, A and B, each of which includes a finite number of heterogeneous agents with commonly known types. The agents in each set compete in a lottery (Tullock) contest, and then are assortatively matched, namely, the winner of set A is matched with the winner of set B and so on until all the agents in the set with the smaller number of agents are matched. Each agent has a match value that depends on their own type and the type of their match. We assume that the agents’ efforts do not affect their match values and that they have a positive effect on welfare. Therefore, an interior equilibrium in which at least some of the agents are active is welfare superior to a corner equilibrium in which the agents choose to be non-active. We analyze the conditions under which there exists a (partial) interior equilibrium where at least some of the agents compete against each other and exert positive efforts.
{"title":"Assortative Matching by Lottery Contests","authors":"Chen Cohen, Ishay Rabi, A. Sela","doi":"10.3390/g13050064","DOIUrl":"https://doi.org/10.3390/g13050064","url":null,"abstract":"We study two-sided matching contests with two sets, A and B, each of which includes a finite number of heterogeneous agents with commonly known types. The agents in each set compete in a lottery (Tullock) contest, and then are assortatively matched, namely, the winner of set A is matched with the winner of set B and so on until all the agents in the set with the smaller number of agents are matched. Each agent has a match value that depends on their own type and the type of their match. We assume that the agents’ efforts do not affect their match values and that they have a positive effect on welfare. Therefore, an interior equilibrium in which at least some of the agents are active is welfare superior to a corner equilibrium in which the agents choose to be non-active. We analyze the conditions under which there exists a (partial) interior equilibrium where at least some of the agents compete against each other and exert positive efforts.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"64"},"PeriodicalIF":0.9,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41991031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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