Scientific models structure our perception of reality. This paper studies how we choose among them under expert advise. Scientific models are formalised as probability distributions over possible scenarios. An expert is assumed to know the most likely model and seeks to communicate it to a decision maker, but cannot prove it. As a result, communication is a cheap talk game over models. The decision maker is in a situation of model-uncertainty and is ambiguity sensitive. I show that information transmission depends on the strategic misalignment of players and, unlike similar models in the literature, a form of consensus among scientific models. When science is divided, there is an asymmetry in information transmission when the receiver has maxmin expected utility preferences. No information can be conveyed over models above a certain threshold. All equilibria of the game are outcome equivalent to a partitional equilibria and the most informative one is interim Pareto dominant.
{"title":"Expert-Based Knowledge: Communicating Over Scientific Models","authors":"Philippe Coló","doi":"10.2139/ssrn.3938978","DOIUrl":"https://doi.org/10.2139/ssrn.3938978","url":null,"abstract":"Scientific models structure our perception of reality. This paper studies how we choose among them under expert advise. Scientific models are formalised as probability distributions over possible scenarios. An expert is assumed to know the most likely model and seeks to communicate it to a decision maker, but cannot prove it. As a result, communication is a cheap talk game over models. The decision maker is in a situation of model-uncertainty and is ambiguity sensitive. I show that information transmission depends on the strategic misalignment of players and, unlike similar models in the literature, a form of consensus among scientific models. When science is divided, there is an asymmetry in information transmission when the receiver has maxmin expected utility preferences. No information can be conveyed over models above a certain threshold. All equilibria of the game are outcome equivalent to a partitional equilibria and the most informative one is interim Pareto dominant.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125817216","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 the design of profit-maximizing mechanisms in environments with interdependent values. A single unit of a good is for sale. There is a known joint distribution of the bidders' values for the good. Two programs are considered: (i) Max (over mechanisms) min (over information structures and equilibria) profit; (ii) Min (over information structures) max (over mechanisms and equilibria) profit. We show that it is without loss to restrict attention to solutions of (i) and (ii) in which actions and signals belong to the same linearly ordered space, equilibrium actions are equal to signals, and the only binding equilibrium constraints are those associated with local deviations. Under such restrictions, the non-linear programs (i) and (ii) become linear programs that are dual to one another in an approximate sense. In particular, the restricted programs have the same optimal value, which we term the profit guarantee. These results simplify the task of computing and characterizing informationally robust optimal auctions and worst-case information structures with general value distributions. The framework can be generalized to include additional feasibility constraints, multiple goods, and ambiguous value distributions.
{"title":"On the Structure of Informationally Robust Optimal Auctions","authors":"Benjamin Brooks, Songzi Du","doi":"10.2139/ssrn.3663721","DOIUrl":"https://doi.org/10.2139/ssrn.3663721","url":null,"abstract":"We study the design of profit-maximizing mechanisms in environments with interdependent values. A single unit of a good is for sale. There is a known joint distribution of the bidders' values for the good. Two programs are considered: (i) Max (over mechanisms) min (over information structures and equilibria) profit; (ii) Min (over information structures) max (over mechanisms and equilibria) profit. We show that it is without loss to restrict attention to solutions of (i) and (ii) in which actions and signals belong to the same linearly ordered space, equilibrium actions are equal to signals, and the only binding equilibrium constraints are those associated with local deviations. Under such restrictions, the non-linear programs (i) and (ii) become linear programs that are dual to one another in an approximate sense. In particular, the restricted programs have the same optimal value, which we term the profit guarantee. These results simplify the task of computing and characterizing informationally robust optimal auctions and worst-case information structures with general value distributions. The framework can be generalized to include additional feasibility constraints, multiple goods, and ambiguous value distributions.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116438032","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 game of price competition amongst firms selling homogeneous goods defined by the property that a firm's revenue is independent of any competing prices that are strictly lower. This property is induced by any customer choice model involving utility-maximizing choice from an adaptively determined consideration set, encompassing a variety of empirically validated choice models studied in the literature. For these games, we show a one-to-one correspondence between pure-strategy local Nash equilibria with distinct prices and the prices generated by the firms sequentially setting local best-response prices in different orders. In other words, despite being simultaneous-move games, they have a sequential-move equilibrium structure. Although this structure is attractive from a computational standpoint, we find that it makes these games particularly vulnerable to the existence of strictly-local Nash equilibria, in which the price of a firm is only a local best-response to competitors' prices when a globally optimal response with a potentially unboundedly higher payoff is available. Our results thus suggest that strictly-local Nash equilibria may be more prevalent in competitive settings than anticipated. We moreover show, both theoretically and empirically, that price dynamics resulting from the firms utilizing gradient-based dynamic pricing algorithms to respond to competition may often converge to such an undesirable outcome. We finally propose an algorithmic approach that incorporates global experimentation to address this concern under certain regularity assumptions on the revenue curves.
{"title":"Pseudo-Competitive Games and Algorithmic Pricing","authors":"Chamsi Hssaine, Vijay Kamble, Siddhartha Banerjee","doi":"10.2139/ssrn.3925242","DOIUrl":"https://doi.org/10.2139/ssrn.3925242","url":null,"abstract":"We study a game of price competition amongst firms selling homogeneous goods defined by the property that a firm's revenue is independent of any competing prices that are strictly lower. This property is induced by any customer choice model involving utility-maximizing choice from an adaptively determined consideration set, encompassing a variety of empirically validated choice models studied in the literature. For these games, we show a one-to-one correspondence between pure-strategy local Nash equilibria with distinct prices and the prices generated by the firms sequentially setting local best-response prices in different orders. In other words, despite being simultaneous-move games, they have a sequential-move equilibrium structure. Although this structure is attractive from a computational standpoint, we find that it makes these games particularly vulnerable to the existence of strictly-local Nash equilibria, in which the price of a firm is only a local best-response to competitors' prices when a globally optimal response with a potentially unboundedly higher payoff is available. Our results thus suggest that strictly-local Nash equilibria may be more prevalent in competitive settings than anticipated. We moreover show, both theoretically and empirically, that price dynamics resulting from the firms utilizing gradient-based dynamic pricing algorithms to respond to competition may often converge to such an undesirable outcome. We finally propose an algorithmic approach that incorporates global experimentation to address this concern under certain regularity assumptions on the revenue curves.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"868 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113995509","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}
Each year, millions of high school graduates in China take a standardized test and compete for college seats. Unlike other countries, college admissions in China have a distinct feature: both test scores and colleges’ preferences coexist in the market. To alleviate the misalignment problem between test scores and colleges’ preferences, the government implements a so-called “dummy quota policy”. The Chinese parallel (CP) mechanism, based on this policy, is a variant of the serial dictatorship (SD) mechanism but has various drawbacks. In this paper, we consider two scenarios depending on whether the dummy quota policy is maintained or abandoned. For each scenario, we propose a modified parallel mechanism to improve the allocation outcome of the CP mechanism.
{"title":"Misalignment between Test Scores and Colleges' Preferences: Chinese College Admission Reconsidered","authors":"Yuanju Fang, Yosuke Yasuda","doi":"10.2139/ssrn.3914742","DOIUrl":"https://doi.org/10.2139/ssrn.3914742","url":null,"abstract":"Each year, millions of high school graduates in China take a standardized test and compete for college seats. Unlike other countries, college admissions in China have a distinct feature: both test scores and colleges’ preferences coexist in the market. To alleviate the misalignment problem between test scores and colleges’ preferences, the government implements a so-called “dummy quota policy”. The Chinese parallel (CP) mechanism, based on this policy, is a variant of the serial dictatorship (SD) mechanism but has various drawbacks. In this paper, we consider two scenarios depending on whether the dummy quota policy is maintained or abandoned. For each scenario, we propose a modified parallel mechanism to improve the allocation outcome of the CP mechanism.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132525015","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 hypothesised that people and companies non-anonymously donate to signal their intention to cooperate with observers; consequently, non-anonymous donation works as a coordination device between donors and observers. To test this, we conducted a laboratory experiment where a participant ('donor') determined how much to give to another participant and then played a repeated prisoner's dilemma game with a different participant ('third party'). Our hypothesis was supported by the findings that donors correlated their cooperation rate with their giving amount only when the amount was visible to a third party and, mediated by this amount, donors' and third-parties' cooperation rates correlated.
{"title":"Strategic donation as a signal of cooperation intention: a laboratory experiment","authors":"T. Kusakawa, Kazuhito Ogawa, Tatsuhiro Shichijo","doi":"10.2139/ssrn.3915289","DOIUrl":"https://doi.org/10.2139/ssrn.3915289","url":null,"abstract":"We hypothesised that people and companies non-anonymously donate to signal their intention to cooperate with observers; consequently, non-anonymous donation works as a coordination device between donors and observers. To test this, we conducted a laboratory experiment where a participant ('donor') determined how much to give to another participant and then played a repeated prisoner's dilemma game with a different participant ('third party'). Our hypothesis was supported by the findings that donors correlated their cooperation rate with their giving amount only when the amount was visible to a third party and, mediated by this amount, donors' and third-parties' cooperation rates correlated.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131147446","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 introduce experimental persuasion between Sender and Receiver. Sender chooses an experiment to perform from a feasible set of experiments. Receiver observes the realization of this experiment and chooses an action. We characterize optimal persuasion in this baseline regime and in an alternative regime in which Sender can commit to garble the outcome of the experiment. Our model includes Bayesian persuasion as the special case in which every experiment is feasible; however, our analysis does not require concavification. Since we focus on experiments rather than beliefs, we can accommodate general preferences including costly experiments and non-Bayesian inference.
{"title":"Experimental Persuasion","authors":"Ian Ball, José‐Antonio Espín‐Sánchez","doi":"10.2139/ssrn.3906869","DOIUrl":"https://doi.org/10.2139/ssrn.3906869","url":null,"abstract":"We introduce experimental persuasion between Sender and Receiver. Sender chooses an experiment to perform from a feasible set of experiments. Receiver observes the realization of this experiment and chooses an action. We characterize optimal persuasion in this baseline regime and in an alternative regime in which Sender can commit to garble the outcome of the experiment. Our model includes Bayesian persuasion as the special case in which every experiment is feasible; however, our analysis does not require concavification. Since we focus on experiments rather than beliefs, we can accommodate general preferences including costly experiments and non-Bayesian inference.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115192593","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 examine how policies for the ownership and control of consumer-generated data affect market outcomes in the online advertising industry. When advertisers have strong property rights over data regarding consumers' active purchase interests, competition between ad exchanges leads to too little sharing of data between advertisers. This harms consumers, who receive too few pertinent ads, and advertisers themselves can also be harmed due to a situation resembling a prisoner's dilemma. We show that giving consumers property rights over their own data can improve outcomes; this happens when consumers can directly share data about their browsing history with ad exchanges. On the other hand, simpler consumer data rights, such as the right to not be tracked, can actually harm consumers due to how ad exchanges respond. Finally, initiatives by Apple and Google to limit third-party tracking, and introduce alternative tracking systems such as FLoCs, can benefit consumers by weakening the property rights of advertisers over consumer data. Because more data is shared by default under such systems, this is true even if these systems are less accurate than the third-party cookie system.
{"title":"Online Advertising, Data Sharing, and Consumer Control","authors":"Justin P. Johnson, Thomas Jungbauer, M. Preuß","doi":"10.2139/ssrn.3898798","DOIUrl":"https://doi.org/10.2139/ssrn.3898798","url":null,"abstract":"We examine how policies for the ownership and control of consumer-generated data affect market outcomes in the online advertising industry. When advertisers have strong property rights over data regarding consumers' active purchase interests, competition between ad exchanges leads to too little sharing of data between advertisers. This harms consumers, who receive too few pertinent ads, and advertisers themselves can also be harmed due to a situation resembling a prisoner's dilemma. We show that giving consumers property rights over their own data can improve outcomes; this happens when consumers can directly share data about their browsing history with ad exchanges. On the other hand, simpler consumer data rights, such as the right to not be tracked, can actually harm consumers due to how ad exchanges respond. Finally, initiatives by Apple and Google to limit third-party tracking, and introduce alternative tracking systems such as FLoCs, can benefit consumers by weakening the property rights of advertisers over consumer data. Because more data is shared by default under such systems, this is true even if these systems are less accurate than the third-party cookie system.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115131432","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 addresses two related questions: How can we capture different degrees of sharing a language with pre-specified meanings? And, how do we expect such a language to be used?
{"title":"Meaning in Communication Games","authors":"A. Blume","doi":"10.2139/ssrn.3893109","DOIUrl":"https://doi.org/10.2139/ssrn.3893109","url":null,"abstract":"This paper addresses two related questions: How can we capture different degrees of sharing a language with pre-specified meanings? And, how do we expect such a language to be used?","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"12378 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122080975","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}
Understanding how to distribute a fixed budget among decentralized intermediaries is a relevant investment problem, that has been recently introduced in the context of mathematical economics and operations research. While existing contributions focus on incentive mechanisms driving the actions of the decentralized intermediaries, the idea of a budget partitioning that balances fairness and efficiency has not been part of the debate. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. For the equilibrium characterization, we propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures). This reformulation allows the reduction of a complex bilevel optimization model (resulting from the extensive formulation of the Nash bargaining partitioning in decentralized portfolio selection) to a convex separable knapsack problem. As empirically shown using stock returns data from U.S. listed enterprises, the notion of emph{quasi-homogeneity} not only allows to numerically characterize a budget partitioning that balances fairness and efficiency in decentralized investment, but also give rise to a computational approach that reduces its complexity and solves the vast majority of large-scale investment problems in less than a minute.
{"title":"Nash Bargaining Partitioning in Decentralized Portfolio Management","authors":"Fancisco Benita, Stefano Nasini, R. Nessah","doi":"10.2139/ssrn.3884009","DOIUrl":"https://doi.org/10.2139/ssrn.3884009","url":null,"abstract":"Understanding how to distribute a fixed budget among decentralized intermediaries is a relevant investment problem, that has been recently introduced in the context of mathematical economics and operations research. While existing contributions focus on incentive mechanisms driving the actions of the decentralized intermediaries, the idea of a budget partitioning that balances fairness and efficiency has not been part of the debate. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. For the equilibrium characterization, we propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures). This reformulation allows the reduction of a complex bilevel optimization model (resulting from the extensive formulation of the Nash bargaining partitioning in decentralized portfolio selection) to a convex separable knapsack problem. As empirically shown using stock returns data from U.S. listed enterprises, the notion of emph{quasi-homogeneity} not only allows to numerically characterize a budget partitioning that balances fairness and efficiency in decentralized investment, but also give rise to a computational approach that reduces its complexity and solves the vast majority of large-scale investment problems in less than a minute.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"934 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127023193","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}
In priority-based two-sided matchings, a respecting-improvements property of a mechanism requires that an agent should get weakly better off when she is assigned a higher priority. Not only is it a normative desideratum, it is also important for ex-ante investments and for disclosure of non-preference information. In the general model of matching with contracts, we demonstrate that respect for improvements is closely related to strategy-proofness (with respect to preference information): With a number of different sets of assumptions and two definitions of improvements, a stable mechanism respects improvements if and ``almost'' only if it is strategy-proof, although the precise statements vary across different layers of our assumptions. Our results suggest that strategy-proofness is desirable not only as a strategic property, but also for its normative implication. We also provide a new sufficient condition for the cumulative offer mechanism to be strategy-proof, which also suffices for respect for improvements.
{"title":"Stability, Strategy-Proofness, and Respecting-Improvements Properties","authors":"D. Hirata, Yusuke Kasuya, Yasunori Okumura","doi":"10.2139/ssrn.3876865","DOIUrl":"https://doi.org/10.2139/ssrn.3876865","url":null,"abstract":"In priority-based two-sided matchings, a respecting-improvements property of a mechanism requires that an agent should get weakly better off when she is assigned a higher priority. Not only is it a normative desideratum, it is also important for ex-ante investments and for disclosure of non-preference information. In the general model of matching with contracts, we demonstrate that respect for improvements is closely related to strategy-proofness (with respect to preference information): With a number of different sets of assumptions and two definitions of improvements, a stable mechanism respects improvements if and ``almost'' only if it is strategy-proof, although the precise statements vary across different layers of our assumptions. Our results suggest that strategy-proofness is desirable not only as a strategic property, but also for its normative implication. We also provide a new sufficient condition for the cumulative offer mechanism to be strategy-proof, which also suffices for respect for improvements.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134411858","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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