The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent‐specific micro component, with a law of large numbers for the latter. This macro–micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their beliefs about the cross‐section distribution of types and other macro variables, and by their beliefs about the cross‐section distribution of other agents' strategies. Any probability distribution over cross‐section distributions of types and other macro variables is compatible with a fully specified belief system, but not every function from types to such probability distributions is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of such a function with a common prior.
{"title":"Incomplete-Information Games in Large Populations with Anonymity","authors":"M. Hellwig","doi":"10.2139/ssrn.3676323","DOIUrl":"https://doi.org/10.2139/ssrn.3676323","url":null,"abstract":"The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent‐specific micro component, with a law of large numbers for the latter. This macro–micro decomposition of uncertainty is implied by a condition of \u0000 exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their beliefs about the cross‐section distribution of types and other macro variables, and by their beliefs about the cross‐section distribution of other agents' strategies. Any probability distribution over cross‐section distributions of types and other macro variables is compatible with a fully specified belief system, but not every function from types to such probability distributions is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of such a function with a common prior.\u0000","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134403506","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 information design in a regime change context. A continuum of agents choose independently whether to attack the current regime and will succeed if and only if the mass of attackers outweighs the regime's strength. The strength is uncertain, and the information designer chooses a strength-dependent experiment to maintain the status quo. The optimal information structure randomizes between partial truth-telling and local exaggeration across agents: some agents receive a signal matching the true strength of the status quo, and others receive an elevated signal professing slightly higher strength. Optimal local obfuscation strictly dominates public signals, and in certain cases where public signals become futile, local obfuscation still guarantees the status quo's survival.
{"title":"Global Manipulation by Local Obfuscation","authors":"Fei Li, Yangbo Song, Mofei Zhao","doi":"10.2139/ssrn.3471491","DOIUrl":"https://doi.org/10.2139/ssrn.3471491","url":null,"abstract":"We study information design in a regime change context. A continuum of agents choose independently whether to attack the current regime and will succeed if and only if the mass of attackers outweighs the regime's strength. The strength is uncertain, and the information designer chooses a strength-dependent experiment to maintain the status quo. The optimal information structure randomizes between partial truth-telling and local exaggeration across agents: some agents receive a signal matching the true strength of the status quo, and others receive an elevated signal professing slightly higher strength. Optimal local obfuscation strictly dominates public signals, and in certain cases where public signals become futile, local obfuscation still guarantees the status quo's survival.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124583735","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}
This paper looks to see if subjects approach long, indefinitely repeated Prisoner's Dilemma games featuring discounted payoffs with an option to opt out differently from how they approach long, indefinitely repeated Prisoner's Dilemma games that are randomly terminated. I show under relatively general assumptions that the critical δ ∗ -value, above which cooperation can be supported as a Subgame Perfect Equilibrium, differs between the two environments. A between-subject design with δ = 0.98 was used to determine if subject behavior did vary by treatment. First period and all period cooperation rates were found to be higher in the random termination treatment compared to the discounted treatment. The evolution of cooperation across supergames also differed between the two treatments. Behavior in the discounted treatment did not follow the patterns typically observed in the literature. Lastly, the Strategy Frequency Estimation Method (SFEM) was used to determine whether or not subjects in different treatments used different repeated game strategies. I find that subjects in the discounted treatment were more likely to play strategies that defect initially (All D, STFT), but cooperative subjects tended to play more forgiving strategies (TFT, STFT). Conversely, subjects in the randomly terminated treatment tended to play more initially cooperative, yet less forgiving strategies (Grim, Grim2).
{"title":"Long Horizon Repeated Games: How Does Ending Rule Affect Decisions in High Δ Games","authors":"Christopher Candreva","doi":"10.2139/ssrn.3147228","DOIUrl":"https://doi.org/10.2139/ssrn.3147228","url":null,"abstract":"This paper looks to see if subjects approach long, indefinitely repeated Prisoner's Dilemma games featuring discounted payoffs with an option to opt out differently from how they approach long, indefinitely repeated Prisoner's Dilemma games that are randomly terminated. I show under relatively general assumptions that the critical δ ∗ -value, above which cooperation can be supported as a Subgame Perfect Equilibrium, differs between the two environments. A between-subject design with δ = 0.98 was used to determine if subject behavior did vary by treatment. First period and all period cooperation rates were found to be higher in the random termination treatment compared to the discounted treatment. The evolution of cooperation across supergames also differed between the two treatments. Behavior in the discounted treatment did not follow the patterns typically observed in the literature. Lastly, the Strategy Frequency Estimation Method (SFEM) was used to determine whether or not subjects in different treatments used different repeated game strategies. I find that subjects in the discounted treatment were more likely to play strategies that defect initially (All D, STFT), but cooperative subjects tended to play more forgiving strategies (TFT, STFT). Conversely, subjects in the randomly terminated treatment tended to play more initially cooperative, yet less forgiving strategies (Grim, Grim2).","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115702656","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 a bargaining model in which a buyer makes frequent offers to a privately informed seller, while gradually learning about the seller’s type from “news.” We show that the buyer’s ability to leverage this information to extract more surplus from the seller is remarkably limited. In fact, the buyer gains nothing from the ability to negotiate a better price despite the fact that a negotiation must take place in equilibrium. During the negotiation, the buyer engages in a form of costly “experimentation” by making offers that are sure to earn her negative payoffs if accepted, but speed up learning and improve her continuation payoff if rejected. We investigate the effects of market power by comparing our results to a setting with competitive buyers. Both efficiency and the seller’s payoff can decrease by introducing competition among buyers. (JEL C78, D82, D83)
{"title":"Bargaining and News","authors":"Brendan Daley, Brett Green","doi":"10.2139/ssrn.2767147","DOIUrl":"https://doi.org/10.2139/ssrn.2767147","url":null,"abstract":"We study a bargaining model in which a buyer makes frequent offers to a privately informed seller, while gradually learning about the seller’s type from “news.” We show that the buyer’s ability to leverage this information to extract more surplus from the seller is remarkably limited. In fact, the buyer gains nothing from the ability to negotiate a better price despite the fact that a negotiation must take place in equilibrium. During the negotiation, the buyer engages in a form of costly “experimentation” by making offers that are sure to earn her negative payoffs if accepted, but speed up learning and improve her continuation payoff if rejected. We investigate the effects of market power by comparing our results to a setting with competitive buyers. Both efficiency and the seller’s payoff can decrease by introducing competition among buyers. (JEL C78, D82, D83)","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130923501","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}
Competing firms may engage in group buying to benefit from quantity discount from the common supplier. There are two prevailing power structures in industry practice: Nash group buying in which two competing firms possess similar powers, and Stackelberg group buying in which one firm serves as the leader to initiate group buying contract. We investigate how the competitors' power structure affects their group buying behaviors and the performances of all stakeholders (including the supplier, the two firms, and the end consumers). Our paper is the first to study the impact of power structure on group buying between competitors in B2B context. We employ a game-theoretic framework in which two firms facing Cournot competition can group their purchase if it is beneficial over individual purchasing. As part of the framework, we model firms' group buying based on their endowed power structures. For each power structure, we derive equilibrium firm behaviors and characterize the conditions under which firms have a group buying incentive. We compare the group buying behaviors and performances across different power structures and demonstrate the determinant of power structure: Different power structures may fundamentally alter firms' group buying incentives. Furthermore, different power structures lead to different joint performance and neither form of group buying can dominate the others. Our results suggest that either Nash or Stackelberg group buying between competing firms may achieve Pareto improvement over individual purchasing in the sense that all the parties are better off. One distinctive insight is that when the two firms are highly asymmetric in their market bases, Nash group buying is unattainable due to severe co-opetition conflict and only Stackelberg group buying may be possible. Moreover, under certain conditions, the smaller-firm-led Stackelberg group buying (i.e., the smaller firm moves first and acts as the leader) can be Pareto optimal among all power structures.
{"title":"Group Buying between Competitors: The Determinant of Power Structure","authors":"Ke Fu, Guoming Lai, Weixin Shang, Jiayan Xu","doi":"10.2139/ssrn.3435526","DOIUrl":"https://doi.org/10.2139/ssrn.3435526","url":null,"abstract":"Competing firms may engage in group buying to benefit from quantity discount from the common supplier. There are two prevailing power structures in industry practice: Nash group buying in which two competing firms possess similar powers, and Stackelberg group buying in which one firm serves as the leader to initiate group buying contract. We investigate how the competitors' power structure affects their group buying behaviors and the performances of all stakeholders (including the supplier, the two firms, and the end consumers). Our paper is the first to study the impact of power structure on group buying between competitors in B2B context. We employ a game-theoretic framework in which two firms facing Cournot competition can group their purchase if it is beneficial over individual purchasing. As part of the framework, we model firms' group buying based on their endowed power structures. For each power structure, we derive equilibrium firm behaviors and characterize the conditions under which firms have a group buying incentive. We compare the group buying behaviors and performances across different power structures and demonstrate the determinant of power structure: Different power structures may fundamentally alter firms' group buying incentives. Furthermore, different power structures lead to different joint performance and neither form of group buying can dominate the others. Our results suggest that either Nash or Stackelberg group buying between competing firms may achieve Pareto improvement over individual purchasing in the sense that all the parties are better off. One distinctive insight is that when the two firms are highly asymmetric in their market bases, Nash group buying is unattainable due to severe co-opetition conflict and only Stackelberg group buying may be possible. Moreover, under certain conditions, the smaller-firm-led Stackelberg group buying (i.e., the smaller firm moves first and acts as the leader) can be Pareto optimal among all power structures.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129153242","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}
I consider a scenario where a social planner suspects that a crime has been committed. There are many suspects and at most one of them is guilty. I characterize the optimal mechanism for the social planner under different assumptions with respect to her commitment power. I find that the optimal mechanism is a “confession inducing mechanism”: Before an investigation, each agent can confess to being guilty in exchange for a reduced punishment. I find that these mechanisms do better than the traditional trial mechanism because of information externalities: When an agent credibly confesses his guilt, he reveals everyone else's innocence.
{"title":"If We Confess Our Sins","authors":"Francisco Silva","doi":"10.1111/iere.12390","DOIUrl":"https://doi.org/10.1111/iere.12390","url":null,"abstract":"I consider a scenario where a social planner suspects that a crime has been committed. There are many suspects and at most one of them is guilty. I characterize the optimal mechanism for the social planner under different assumptions with respect to her commitment power. I find that the optimal mechanism is a “confession inducing mechanism”: Before an investigation, each agent can confess to being guilty in exchange for a reduced punishment. I find that these mechanisms do better than the traditional trial mechanism because of information externalities: When an agent credibly confesses his guilt, he reveals everyone else's innocence.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117958802","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}
Behaviors and information often spread via person-to-person diffusion. This paper highlights how diffusion processes can facilitate coordination. I study contagion in a discrete network with Bayesian players. In addition to characterizing the extent and rate of adoption, we uncover a new effect: when large cascades are possible in equilibrium, exposure conveys information about a player’s network position. This effect underscores a novel trade-off in the design of marketing campaigns, suggesting conditions under which word-of-mouth is relatively more effective. A generalization of the model to multi-type networks suggests a new approach to targeted seeding. (JEL D83, D85, M31, M37, Z13)
{"title":"Diffusion Games","authors":"Evan Sadler","doi":"10.2139/ssrn.2624865","DOIUrl":"https://doi.org/10.2139/ssrn.2624865","url":null,"abstract":"Behaviors and information often spread via person-to-person diffusion. This paper highlights how diffusion processes can facilitate coordination. I study contagion in a discrete network with Bayesian players. In addition to characterizing the extent and rate of adoption, we uncover a new effect: when large cascades are possible in equilibrium, exposure conveys information about a player’s network position. This effect underscores a novel trade-off in the design of marketing campaigns, suggesting conditions under which word-of-mouth is relatively more effective. A generalization of the model to multi-type networks suggests a new approach to targeted seeding. (JEL D83, D85, M31, M37, Z13)","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130377538","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}
Both excludable public goods with non-rivalry and private goods with network externalities have a coordination problem.
In this study, we define generalized non-rivalry to investigate coordination mechanisms for both types of goods.
We focus on the equal cost-sharing with maximal participation (ECSMP) mechanism, which has been studied as a mechanism for excludable public goods with non-rivalry, and we find that this mechanism is optimal with respect to two welfare criteria in an environment with generalized non-rivalry. Moreover, we characterize the ECSMP mechanism within this environment.
{"title":"Cost-Sharing Mechanism for Excludable Goods With Generalized Non-Rivalry","authors":"Tatsuhiro Shichijo, Emiko Fukuda","doi":"10.2139/ssrn.2694899","DOIUrl":"https://doi.org/10.2139/ssrn.2694899","url":null,"abstract":"Both excludable public goods with non-rivalry and private goods with network externalities have a coordination problem.<br><br>In this study, we define generalized non-rivalry to investigate coordination mechanisms for both types of goods.<br><br>We focus on the equal cost-sharing with maximal participation (ECSMP) mechanism, which has been studied as a mechanism for excludable public goods with non-rivalry, and we find that this mechanism is optimal with respect to two welfare criteria in an environment with generalized non-rivalry. Moreover, we characterize the ECSMP mechanism within this environment.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129289927","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}
Brinkmanship is a “threat that leaves something to chance” – creating a risk of catastrophe that is high enough to deter the adversary but low enough to be acceptable to oneself. The Cuban missile crisis is offered as a classic example. We argue that in that crisis both sides lost control over the risk. We build a dynamic model of a chicken game, and use parameters based on historical narrative studies. We find that over the thirteen days of the crisis, the probability of a nuclear war got as high as 60%.
{"title":"'We Haven’t Got But One More Day': The Cuban Missile Crisis as a Dynamic Chicken Game","authors":"A. Dixit, David McAdams, Susan Skeath","doi":"10.2139/ssrn.3406265","DOIUrl":"https://doi.org/10.2139/ssrn.3406265","url":null,"abstract":"Brinkmanship is a “threat that leaves something to chance” – creating a risk of catastrophe that is high enough to deter the adversary but low enough to be acceptable to oneself. The Cuban missile crisis is offered as a classic example. We argue that in that crisis both sides lost control over the risk. We build a dynamic model of a chicken game, and use parameters based on historical narrative studies. We find that over the thirteen days of the crisis, the probability of a nuclear war got as high as 60%.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124044460","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 develop an index of competitiveness and cooperativeness which is based on the primitives of a normal-form game, i.e. players, strategies and payoffs. The index relies on a unique decomposition of a given game into a zero-sum game and a common-interest game. The index decreases in the distance to its zero-sum part and it increases in the distance to its common-interest part. Alternatively, the index increases if the share of variation in payoffs captured by the zero-sum part increases We compute our index for well-known classes of games such as Prisoner's Dilemma,games with Strategic Complements and Substitutes, All-pay auctions, Tullock contests, and Public Goods games. The comparative statics of our index coincide with economic intuition. The index does well in explaining experimental
{"title":"Measuring Competitiveness and Cooperativeness","authors":"T. Demuynck, C. Seel, Giang Tran","doi":"10.2139/ssrn.3379758","DOIUrl":"https://doi.org/10.2139/ssrn.3379758","url":null,"abstract":"We develop an index of competitiveness and cooperativeness which is based on the primitives of a normal-form game, i.e. players, strategies and payoffs. The index relies on a unique decomposition of a given game into a zero-sum game and a common-interest game. The index decreases in the distance to its zero-sum part and it increases in the distance to its common-interest part. Alternatively, the index increases if the share of variation in payoffs captured by the zero-sum part increases We compute our index for well-known classes of games such as Prisoner's Dilemma,games with Strategic Complements and Substitutes, All-pay auctions, Tullock contests, and Public Goods games. The comparative statics of our index coincide with economic intuition. The index does well in explaining experimental","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116237434","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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