Rational players in game theory are neoliberal in the sense that they can choose any available action so as to maximize their payoffs. It is well known that this can result in Pareto inferior outcomes (e.g. the Prisoner's Dilemma). Classical liberalism, in contrast, argues that people should be constrained by a no-harm principle (NHP) when they act. We show, for the first time to the best of our knowledge, that rational players constrained by the NHP will produce Pareto efficient outcomes in n-person non-cooperative games. We also show that both rationality and the NHP are required for this result.
{"title":"Liberalism, Rationality, and Pareto Optimality","authors":"S. Heap, Mehmet S. Ismail","doi":"10.2139/ssrn.3771955","DOIUrl":"https://doi.org/10.2139/ssrn.3771955","url":null,"abstract":"Rational players in game theory are neoliberal in the sense that they can choose any available action so as to maximize their payoffs. It is well known that this can result in Pareto inferior outcomes (e.g. the Prisoner's Dilemma). Classical liberalism, in contrast, argues that people should be constrained by a no-harm principle (NHP) when they act. We show, for the first time to the best of our knowledge, that rational players constrained by the NHP will produce Pareto efficient outcomes in n-person non-cooperative games. We also show that both rationality and the NHP are required for this result.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126613891","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 one-to-one two-sided matching market in which each man has a common value for all women and a private value specific to each woman. We introduce a new mechanism, called a proposing mechanism, which is a novel interpretation of the deferred acceptance mechanism. We show that these mechanisms can be replicated by another mechanism, which is memoryless, in which a woman proposes to a random man in each step. We prove that envy in a matching market is bounded by envy in this class of mechanisms, in which there is just one woman and two types of men. We conclude that envy is bounded by the inverse of the square root of the number of men in each type. Therefore, in large matching markets, envy becomes zero; on top of that, the women-optimal stable matching mechanism is approximately strategy-proof.
{"title":"Incentive Compatibility and Envy in Large Matching Markets with Incomplete Information","authors":"Behrang Kamali-Shahdadi, Seyed Kourosh Khounsari","doi":"10.2139/ssrn.3763658","DOIUrl":"https://doi.org/10.2139/ssrn.3763658","url":null,"abstract":"We study a one-to-one two-sided matching market in which each man has a common value for all women and a private value specific to each woman. We introduce a new mechanism, called a proposing mechanism, which is a novel interpretation of the deferred acceptance mechanism. We show that these mechanisms can be replicated by another mechanism, which is memoryless, in which a woman proposes to a random man in each step. We prove that envy in a matching market is bounded by envy in this class of mechanisms, in which there is just one woman and two types of men. We conclude that envy is bounded by the inverse of the square root of the number of men in each type. Therefore, in large matching markets, envy becomes zero; on top of that, the women-optimal stable matching mechanism is approximately strategy-proof.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129987363","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}
Pub Date : 2020-12-23DOI: 10.1007/978-3-030-52970-3_5
Ngo van Long
{"title":"Dynamic Games of Common-Property Resource Exploitation When Self-Image Matters","authors":"Ngo van Long","doi":"10.1007/978-3-030-52970-3_5","DOIUrl":"https://doi.org/10.1007/978-3-030-52970-3_5","url":null,"abstract":"","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129052233","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}
Abstract Mixed strategy equilibria — Nash (NE) and maximin (MM) — are cornerstones of game theory, but their empirical relevance has always been questionable. We study in the laboratory two games, each with a unique NE and a unique (and distinct) MM in completely mixed strategies. Treatment variables include the matching protocol (pairwise random vs population mean matching), whether time is discrete or continuous, and whether players can specify explicit mixtures or only pure strategy realizations. NE mixes predict observed behavior relatively well in population mean matching treatments, and predict better than MM in all treatments. However, in most random pairwise treatments, uniform mixes predict better than NE. Regret-based and sign preserving dynamics capture regularities across all treatments.
{"title":"When Are Mixed Equilibria Relevant?","authors":"D. Friedman, Shuchen Zhao","doi":"10.2139/ssrn.3444439","DOIUrl":"https://doi.org/10.2139/ssrn.3444439","url":null,"abstract":"Abstract Mixed strategy equilibria — Nash (NE) and maximin (MM) — are cornerstones of game theory, but their empirical relevance has always been questionable. We study in the laboratory two games, each with a unique NE and a unique (and distinct) MM in completely mixed strategies. Treatment variables include the matching protocol (pairwise random vs population mean matching), whether time is discrete or continuous, and whether players can specify explicit mixtures or only pure strategy realizations. NE mixes predict observed behavior relatively well in population mean matching treatments, and predict better than MM in all treatments. However, in most random pairwise treatments, uniform mixes predict better than NE. Regret-based and sign preserving dynamics capture regularities across all treatments.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116869104","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 matching model with salaries in which firms face budget constraints. Due to budget constraints, the existence of a stable matching is not guaranteed. We show that if workers are homogeneous, from the firms' point of view, then a weak stable matching always exists; furthermore, when a strong stable matching does not exist, there is a nearby budget vector for firms such that a strong stable matching exists for the problem with perturbed budgets. On the flip side, if firms are homogeneous from the workers' point of view, a stable matching may not exist; however, one can reach a stable matching by changing the budget of firms where the total budget remains the same and each firm's budget change is bounded by the value of at most one worker to that firm.
{"title":"Matching with Budget Constraints","authors":"A. Ahmadzadeh, Behrang Kamali-Shahdadi","doi":"10.2139/ssrn.3730941","DOIUrl":"https://doi.org/10.2139/ssrn.3730941","url":null,"abstract":"We study a matching model with salaries in which firms face budget constraints. Due to budget constraints, the existence of a stable matching is not guaranteed. We show that if workers are homogeneous, from the firms' point of view, then a weak stable matching always exists; furthermore, when a strong stable matching does not exist, there is a nearby budget vector for firms such that a strong stable matching exists for the problem with perturbed budgets. On the flip side, if firms are homogeneous from the workers' point of view, a stable matching may not exist; however, one can reach a stable matching by changing the budget of firms where the total budget remains the same and each firm's budget change is bounded by the value of at most one worker to that firm.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125093191","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}
Competition between heterogeneous participants often leads to low effort provision in contests. We consider a principal who can divide her fixed budget between skill-enhancing training and the contest prize. Training can reduce heterogeneity, which increases effort. But it also reduces the contest prize, which makes effort fall. We set up an incomplete-information contest with heterogeneous players and show how this trade-off is related to the size of the budget when the principal maximizes expected effort. A selection problem can also arise in this framework in which there is a cost associated with a contest win by the inferior player. This gives the principal a larger incentive to train the expected laggard, reducing the size of the prize on offer.
{"title":"Fatter or Fitter? On Rewarding and Training in a Contest","authors":"Derek J. Clark, T. Nilssen","doi":"10.2139/ssrn.3732926","DOIUrl":"https://doi.org/10.2139/ssrn.3732926","url":null,"abstract":"Competition between heterogeneous participants often leads to low effort provision in contests. We consider a principal who can divide her fixed budget between skill-enhancing training and the contest prize. Training can reduce heterogeneity, which increases effort. But it also reduces the contest prize, which makes effort fall. We set up an incomplete-information contest with heterogeneous players and show how this trade-off is related to the size of the budget when the principal maximizes expected effort. A selection problem can also arise in this framework in which there is a cost associated with a contest win by the inferior player. This gives the principal a larger incentive to train the expected laggard, reducing the size of the prize on offer.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126168435","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 subgame-perfect implementation (SPI) mechanisms that have been proposed as a solution to incomplete contracting problems. We show that these mechanisms, which are based on off-equilibrium arbitration clauses that impose large fines for lying and the inappropriate use of arbitration, have severe behavioral constraints because the fines induce retaliation against legitimate uses of arbitration. Incorporating reciprocity preferences into the theory explains the observed behavioral patterns and helps us develop a new mechanism that is more robust and achieves high rates of truth-telling and efficiency. Our results highlight the importance of tailoring implementation mechanisms to the underlying behavioral environment. (JEL C92, D44, D82, D86, D91)
{"title":"Behavioral Constraints on the Design of Subgame-Perfect Implementation Mechanisms","authors":"E. Fehr, M. Powell, Tom Wilkening","doi":"10.2139/ssrn.2479922","DOIUrl":"https://doi.org/10.2139/ssrn.2479922","url":null,"abstract":"We study subgame-perfect implementation (SPI) mechanisms that have been proposed as a solution to incomplete contracting problems. We show that these mechanisms, which are based on off-equilibrium arbitration clauses that impose large fines for lying and the inappropriate use of arbitration, have severe behavioral constraints because the fines induce retaliation against legitimate uses of arbitration. Incorporating reciprocity preferences into the theory explains the observed behavioral patterns and helps us develop a new mechanism that is more robust and achieves high rates of truth-telling and efficiency. Our results highlight the importance of tailoring implementation mechanisms to the underlying behavioral environment. (JEL C92, D44, D82, D86, D91)","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128056523","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 report three pre-registered studies (total N=1,799) exploring the effect of nudging personal and injunctive norms in decisions that involve a trade-off between objective equality and efficiency. The first two studies provide evidence that: (i) nudging the personal norm has a similar effect to nudging the injunctive norm; (ii) when both norms are nudged towards the same direction, there is no additive effect; (iii) when the personal norm and the injunctive norm are nudged towards opposite directions, some people tend to follow the personal norm, while others tend to follow the injunctive norm. Study 3 tests whether these two classes of people, those who tend to follow the injunctive norm and those who tend to follow the personal norm, map onto the two sub-dimensions of Aquino and Reed’s moral identity scale. We find partial evidence of this hypothesis: people higher in the symbolisation dimension are weakly more likely to follow the injunctive norm; however, we do not find any evidence that people higher in the internalisation dimension are more likely to follow the personal norm.
{"title":"The Effect of Nudging Personal and Injunctive Norms on the Trade-Off Between Objective Equality and Efficiency","authors":"Steven J Human, V. Capraro","doi":"10.2139/ssrn.3703684","DOIUrl":"https://doi.org/10.2139/ssrn.3703684","url":null,"abstract":"We report three pre-registered studies (total N=1,799) exploring the effect of nudging personal and injunctive norms in decisions that involve a trade-off between objective equality and efficiency. The first two studies provide evidence that: (i) nudging the personal norm has a similar effect to nudging the injunctive norm; (ii) when both norms are nudged towards the same direction, there is no additive effect; (iii) when the personal norm and the injunctive norm are nudged towards opposite directions, some people tend to follow the personal norm, while others tend to follow the injunctive norm. Study 3 tests whether these two classes of people, those who tend to follow the injunctive norm and those who tend to follow the personal norm, map onto the two sub-dimensions of Aquino and Reed’s moral identity scale. We find partial evidence of this hypothesis: people higher in the symbolisation dimension are weakly more likely to follow the injunctive norm; however, we do not find any evidence that people higher in the internalisation dimension are more likely to follow the personal norm.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123176648","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}
Youngseok Park, J. Rabanal, Olga A. Rud, P. Grossman
Abstract We present an endogenous-timing conflict game of incomplete information under strategic complementarity. The model predicts multiple equilibria, in which the outcome follows either a simultaneous move game (Baliga and Sjostrom, 2004) or a sequential game, which improves social welfare. We study the three families of games in the laboratory using gender-balanced sessions. Our results suggest that: (i) social welfare is higher in the endogenous-timing and sequential games compared to the simultaneous game; (ii) men and women make similar decisions in the simultaneous and sequential-move games; and (iii) in the endogenous-timing game women are less willing to commit to the risky action.
{"title":"An Endogenous-Timing Conflict Game","authors":"Youngseok Park, J. Rabanal, Olga A. Rud, P. Grossman","doi":"10.2139/ssrn.3703016","DOIUrl":"https://doi.org/10.2139/ssrn.3703016","url":null,"abstract":"Abstract We present an endogenous-timing conflict game of incomplete information under strategic complementarity. The model predicts multiple equilibria, in which the outcome follows either a simultaneous move game (Baliga and Sjostrom, 2004) or a sequential game, which improves social welfare. We study the three families of games in the laboratory using gender-balanced sessions. Our results suggest that: (i) social welfare is higher in the endogenous-timing and sequential games compared to the simultaneous game; (ii) men and women make similar decisions in the simultaneous and sequential-move games; and (iii) in the endogenous-timing game women are less willing to commit to the risky action.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"23 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113957081","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}
Abstract This paper considers the problem of cost sharing, in which a coalition of agents, each endowed with an input, shares the output cost incurred from the total inputs of the coalition. Two allocations—average cost pricing and the Shapley value—are arguably the two most widely studied solution concepts to this problem. It is well known in the literature that the two allocations can be respectively characterized by different sets of axioms and they share many properties that are deemed reasonable. We seek to bridge the two allocations from a different angle–allocation inequality. We use the partial order: Lorenz order (or majorization) to characterize allocation inequality and we derive simple conditions under which one allocation Lorenz dominates (or is majorized by) the other. Examples are given to show that the two allocations are not always comparable by Lorenz order. Our proof, built on solving minimization problems of certain Schur-convex or Schur-concave objective functions over input vectors, may be of independent interest.
{"title":"Allocation Inequality in Cost Sharing Problem","authors":"Zhi Chen, Zhenyu Hu, Qinshen Tang","doi":"10.2139/ssrn.2999238","DOIUrl":"https://doi.org/10.2139/ssrn.2999238","url":null,"abstract":"Abstract This paper considers the problem of cost sharing, in which a coalition of agents, each endowed with an input, shares the output cost incurred from the total inputs of the coalition. Two allocations—average cost pricing and the Shapley value—are arguably the two most widely studied solution concepts to this problem. It is well known in the literature that the two allocations can be respectively characterized by different sets of axioms and they share many properties that are deemed reasonable. We seek to bridge the two allocations from a different angle–allocation inequality. We use the partial order: Lorenz order (or majorization) to characterize allocation inequality and we derive simple conditions under which one allocation Lorenz dominates (or is majorized by) the other. Examples are given to show that the two allocations are not always comparable by Lorenz order. Our proof, built on solving minimization problems of certain Schur-convex or Schur-concave objective functions over input vectors, may be of independent interest.","PeriodicalId":423216,"journal":{"name":"Game Theory & Bargaining Theory eJournal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114390299","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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