Abstract This work focuses on (j, 2) games in which there are several levels of approval in the input, i. e. games with n players, j ordered qualitative alternatives in the input level and 2 possible ordered quantitative alternatives in the output. When considering (j, 2) games, we extend the Public Good index (PGI), the Null Player Free index (NPFI) and the Shift index (SI) and provide full characterizations of these extensions.
{"title":"Public Good Indices for Games with Several Levels of Approval","authors":"Sébastien Courtin, B. Tchantcho","doi":"10.1515/bejte-2019-0068","DOIUrl":"https://doi.org/10.1515/bejte-2019-0068","url":null,"abstract":"Abstract This work focuses on (j, 2) games in which there are several levels of approval in the input, i. e. games with n players, j ordered qualitative alternatives in the input level and 2 possible ordered quantitative alternatives in the output. When considering (j, 2) games, we extend the Public Good index (PGI), the Null Player Free index (NPFI) and the Shift index (SI) and provide full characterizations of these extensions.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2019-0068","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44267226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.
{"title":"On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy","authors":"Ronaldo Carpio, Meixin Guo","doi":"10.1515/bejte-2018-0144","DOIUrl":"https://doi.org/10.1515/bejte-2018-0144","url":null,"abstract":"Abstract We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2018-0144","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48093362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper analyses two properties of the core in a two-period exchange economy under uncertainty: the veto power of arbitrary sized coalitions; and coalitional fairness of core allocations. We study these properties in relation to classical (static) and sequential (dynamic) core notions and apply our results to asset markets and asymmetric information models. We develop a formal setting where consumption sets have no lower bound and impose a series of general restrictions on the first period trades of each agent. All our results are applications of the same lemma about improvements to an allocation that is either non-core or non-coalitionally fair. Roughly speaking, the lemma states that if all the members of a coalition achieve a better allocation in some way (for instance, by blocking the status quo allocation or because they envy the net trade of other coalitions) then an alternative improvement can be obtained through a perturbation of the initial improvement.
{"title":"Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies","authors":"Anuj Bhowmik, Maria Gabriella Graziano","doi":"10.1515/BEJTE-2018-0139","DOIUrl":"https://doi.org/10.1515/BEJTE-2018-0139","url":null,"abstract":"Abstract This paper analyses two properties of the core in a two-period exchange economy under uncertainty: the veto power of arbitrary sized coalitions; and coalitional fairness of core allocations. We study these properties in relation to classical (static) and sequential (dynamic) core notions and apply our results to asset markets and asymmetric information models. We develop a formal setting where consumption sets have no lower bound and impose a series of general restrictions on the first period trades of each agent. All our results are applications of the same lemma about improvements to an allocation that is either non-core or non-coalitionally fair. Roughly speaking, the lemma states that if all the members of a coalition achieve a better allocation in some way (for instance, by blocking the status quo allocation or because they envy the net trade of other coalitions) then an alternative improvement can be obtained through a perturbation of the initial improvement.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/BEJTE-2018-0139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46483716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We model private politics in the presence of two-sided incomplete information. An interest group (IG) threatens to inform consumers about a firm’s damaging technology should the firm not adopt a clean technology. The IG does not know how costly adopting the clean technology is and the firm does not know how much the IG cares about the damages. In equilibrium an IG who cares a lot signals its type to the firm and the firm is more inclined to adopt the clean technology if it receives such a signal. However, impasses can occur: the firm does not adopt the clean technology despite the fact that the IG has signaled that it cares a lot and threatens to inform a large fraction of the consumer population. The IG never informs all consumers: as soon as a certain fraction of the consumers is informed by the IG the firm reduces its price and thereby reveals to the remaining consumers that it is employing a damaging technology. The IG’s actions increase consumer well-being, but decrease total welfare unless the cost of adopting the clean technology is likely to be low. Yet, since the IG is inclined to target firms with this property, a regulator might want to delegate information provision to the IG.
{"title":"Strategic Activism in an Uncertain World","authors":"Allard van der Made","doi":"10.1515/bejte-2018-0103","DOIUrl":"https://doi.org/10.1515/bejte-2018-0103","url":null,"abstract":"Abstract We model private politics in the presence of two-sided incomplete information. An interest group (IG) threatens to inform consumers about a firm’s damaging technology should the firm not adopt a clean technology. The IG does not know how costly adopting the clean technology is and the firm does not know how much the IG cares about the damages. In equilibrium an IG who cares a lot signals its type to the firm and the firm is more inclined to adopt the clean technology if it receives such a signal. However, impasses can occur: the firm does not adopt the clean technology despite the fact that the IG has signaled that it cares a lot and threatens to inform a large fraction of the consumer population. The IG never informs all consumers: as soon as a certain fraction of the consumers is informed by the IG the firm reduces its price and thereby reveals to the remaining consumers that it is employing a damaging technology. The IG’s actions increase consumer well-being, but decrease total welfare unless the cost of adopting the clean technology is likely to be low. Yet, since the IG is inclined to target firms with this property, a regulator might want to delegate information provision to the IG.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2018-0103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42945614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract To punish an agent, the principal often incurs costs. I study a principal’s least costly reward and punishment scheme for an agent whose effort the principal cannot observe. I find the principal’s cost is sometimes minimized by using both costly rewards and costly punishments because (1) the agent has an outside option, or (2) a principal without commitment ability repeatedly interacts with the agent. I also find that when an agent’s effort is better at increasing the probability of a good outcome for the principal, the agent’s payoff may decrease, because the principal replaces rewards with punishments.
{"title":"Costly Rewards and Punishments","authors":"F. Lee","doi":"10.1515/bejte-2018-0131","DOIUrl":"https://doi.org/10.1515/bejte-2018-0131","url":null,"abstract":"Abstract To punish an agent, the principal often incurs costs. I study a principal’s least costly reward and punishment scheme for an agent whose effort the principal cannot observe. I find the principal’s cost is sometimes minimized by using both costly rewards and costly punishments because (1) the agent has an outside option, or (2) a principal without commitment ability repeatedly interacts with the agent. I also find that when an agent’s effort is better at increasing the probability of a good outcome for the principal, the agent’s payoff may decrease, because the principal replaces rewards with punishments.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2018-0131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49569015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider the allocation problem of infinitely divisible resources with at least three agents. For this problem, Thomson (Games and Economic Behavior, 52: 186-200, 2005) and Doğan (Games and Economic Behavior, 98: 165-171, 2016) propose “simple” but not “procedurally fair” game forms which implement the “no-envy” solution in Nash equilibria. By contrast, Galbiati (Economics Letters, 100: 72-75, 2008) constructs a procedurally fair but not simple game form which implements the no-envy solution in Nash equilibria. In this paper, we design a both simple and procedurally fair game form which implements the no-envy solution in Nash equilibria.
{"title":"A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution","authors":"Makoto Hagiwara","doi":"10.2139/ssrn.3411954","DOIUrl":"https://doi.org/10.2139/ssrn.3411954","url":null,"abstract":"Abstract We consider the allocation problem of infinitely divisible resources with at least three agents. For this problem, Thomson (Games and Economic Behavior, 52: 186-200, 2005) and Doğan (Games and Economic Behavior, 98: 165-171, 2016) propose “simple” but not “procedurally fair” game forms which implement the “no-envy” solution in Nash equilibria. By contrast, Galbiati (Economics Letters, 100: 72-75, 2008) constructs a procedurally fair but not simple game form which implements the no-envy solution in Nash equilibria. In this paper, we design a both simple and procedurally fair game form which implements the no-envy solution in Nash equilibria.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43135539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.
{"title":"Decision Making and Games with Vector Outcomes","authors":"Jaeok Park","doi":"10.1515/bejte-2018-0170","DOIUrl":"https://doi.org/10.1515/bejte-2018-0170","url":null,"abstract":"Abstract In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2018-0170","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42610458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This study investigates strategic aspect of leverage-driven bubbles from the viewpoint of game theory and behavioral finance. Even if a company is unproductive, its stock price grows up according to an exogenous reinforcement pattern. During the bubble, this company raises huge funds by issuing new shares. Multiple arbitrageurs strategically decide whether to ride the bubble by continuing to purchase shares through leveraged finance. We demonstrate two models that are distinguished by whether crash-contingent claim, i. e. contractual agreement such that the purchaser of this claim receives a promised monetary amount if and only if the bubble crashes, is available. We show that the availability of this claim deters the bubble; without crash-contingent claim, the bubble emerges and persists long even if the degree of reinforcement is insufficient. Without crash-contingent claim, high leverage ratio fosters the bubble, while with crash-contingent claim, it rather deters the bubble. We formulate these models as specifications of timing game with irrational types; each player selects a time in a fixed time interval, and the player who selects the earliest time wins the game. We assume that each player is irrational with a small but positive probability. We then prove that there exists the unique Nash equilibrium; according to it, every player never selects the initial time. By regarding arbitrageurs as players, we give careful conceptualizations that are necessary to interpret timing games as models of leverage-driven bubbles.
{"title":"Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims","authors":"Hitoshi Matsushima","doi":"10.1515/BEJTE-2018-0088","DOIUrl":"https://doi.org/10.1515/BEJTE-2018-0088","url":null,"abstract":"Abstract This study investigates strategic aspect of leverage-driven bubbles from the viewpoint of game theory and behavioral finance. Even if a company is unproductive, its stock price grows up according to an exogenous reinforcement pattern. During the bubble, this company raises huge funds by issuing new shares. Multiple arbitrageurs strategically decide whether to ride the bubble by continuing to purchase shares through leveraged finance. We demonstrate two models that are distinguished by whether crash-contingent claim, i. e. contractual agreement such that the purchaser of this claim receives a promised monetary amount if and only if the bubble crashes, is available. We show that the availability of this claim deters the bubble; without crash-contingent claim, the bubble emerges and persists long even if the degree of reinforcement is insufficient. Without crash-contingent claim, high leverage ratio fosters the bubble, while with crash-contingent claim, it rather deters the bubble. We formulate these models as specifications of timing game with irrational types; each player selects a time in a fixed time interval, and the player who selects the earliest time wins the game. We assume that each player is irrational with a small but positive probability. We then prove that there exists the unique Nash equilibrium; according to it, every player never selects the initial time. By regarding arbitrageurs as players, we give careful conceptualizations that are necessary to interpret timing games as models of leverage-driven bubbles.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/BEJTE-2018-0088","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48755144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Disequilibrium trade can occur in a market lacking both recontracting and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on the possible speed of adjustment when arbitrage among periods is feasible and the surplus loss. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone but on arbitrage opportunities and the willingness of agents to engage on them. We find that the upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when the market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. Moreover, faster price adjustments do not imply less surplus loss, because the effect of price changes on transactions via arbitrage. Finally, under weaker-than-efficient rationing there is a one period incentive compatible trading procedure in which most of the surplus is destroyed. The procedure has the property that almost every agent in the market trades.
{"title":"Disequilibrium Trade in a Large Market for an Indivisible Good","authors":"Luis C. Corchón, José Rueda-Llano","doi":"10.1515/bejte-2018-0194","DOIUrl":"https://doi.org/10.1515/bejte-2018-0194","url":null,"abstract":"Abstract Disequilibrium trade can occur in a market lacking both recontracting and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on the possible speed of adjustment when arbitrage among periods is feasible and the surplus loss. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone but on arbitrage opportunities and the willingness of agents to engage on them. We find that the upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when the market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. Moreover, faster price adjustments do not imply less surplus loss, because the effect of price changes on transactions via arbitrage. Finally, under weaker-than-efficient rationing there is a one period incentive compatible trading procedure in which most of the surplus is destroyed. The procedure has the property that almost every agent in the market trades.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/bejte-2018-0194","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45901553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider the implementation problem for incomplete information and private values. We investigate double implementability of social choice functions in dominant strategy equilibria and ex-post equilibria. We define a new strategic axiom that implies “strategy-proofness” and that is implied by “secure strategy-proofness,” but the converse of these relationships does not hold. We call it “weak secure-strategy-proofness.” We show that a social choice function is doubly implementable if and only if it is weakly securely-strategy-proof.
{"title":"Double Implementation in Dominant Strategy Equilibria and Ex-Post Equilibria with Private Values","authors":"Makoto Hagiwara","doi":"10.2139/ssrn.3411960","DOIUrl":"https://doi.org/10.2139/ssrn.3411960","url":null,"abstract":"Abstract We consider the implementation problem for incomplete information and private values. We investigate double implementability of social choice functions in dominant strategy equilibria and ex-post equilibria. We define a new strategic axiom that implies “strategy-proofness” and that is implied by “secure strategy-proofness,” but the converse of these relationships does not hold. We call it “weak secure-strategy-proofness.” We show that a social choice function is doubly implementable if and only if it is weakly securely-strategy-proof.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"125 s1","pages":"663 - 678"},"PeriodicalIF":0.4,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41259798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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