Recently, Dobzinski and Dughmi (FOCS '09) defined a class of truthful-in-expectation VCG-based mechanisms they termed maximal-in-distributional-range (MIDR). Using MIDR mechanisms, they derived the first truthful-in-expectation FPTAS for multi-unit auctions, and showed the first separation between the power of truthful-in-expectation and truthful mechanisms. Since then, there has been much speculation on whether exploiting randomization allows general positive results that have eluded deterministic mechanism design. We answer this question in the affirmative for the class of essentially all packing problems that admit an FPTAS. Using techniques from smoothed algorithm analysis, we show a black box reduction that converts an FPTAS for such a problem to a truthful-in-expectation FPTAS of the MIDR variety. Our techniques and results may hold promise for unlocking the powers of truthful-in-expectation algorithms for strongly NP-hard problems.
{"title":"Truthfulness via smoothed complexity","authors":"S. Dughmi, T. Roughgarden","doi":"10.1145/1807406.1807427","DOIUrl":"https://doi.org/10.1145/1807406.1807427","url":null,"abstract":"Recently, Dobzinski and Dughmi (FOCS '09) defined a class of truthful-in-expectation VCG-based mechanisms they termed maximal-in-distributional-range (MIDR). Using MIDR mechanisms, they derived the first truthful-in-expectation FPTAS for multi-unit auctions, and showed the first separation between the power of truthful-in-expectation and truthful mechanisms. Since then, there has been much speculation on whether exploiting randomization allows general positive results that have eluded deterministic mechanism design. We answer this question in the affirmative for the class of essentially all packing problems that admit an FPTAS. Using techniques from smoothed algorithm analysis, we show a black box reduction that converts an FPTAS for such a problem to a truthful-in-expectation FPTAS of the MIDR variety. Our techniques and results may hold promise for unlocking the powers of truthful-in-expectation algorithms for strongly NP-hard problems.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116947157","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}
A. Meca, M. G. Fiestras-Janeiro, M. Mosquera, I. García-Jurado
This paper studies the cost sharing problem in an inventory transportation system with multiple agents, where transportation costs are different for each agent. Orderings of a single item are placed jointly using an economic order quantity (EOQ) policy. Part of the ordering cost is shared, and part is specific to each agent and depends on the distance from the supplier (transportation cost). For this inventory situation, cooperation is not always profitable. We therefore examine when cooperation is profitable and how to divide the total cost in a way that ensures stability (no group of agents can improve by deviating from the total group) and computability. We use cooperative game theory to provide adequate answers to all those questions. We prove that if cooperation is profitable (the corresponding inventory game is subadditive), then we can always find coalitional stable allocations of the total cost (the core of the game is not empty). We further define two kinds of context-specific cost sharing rules and study their properties. The first one, which turns out to be coalitional stable (it always belongs to the core), is a cost sharing rule à la Shapley. The second one, simpler but not always coalitional stable, belongs to the family of proportional cost sharing rules.
{"title":"Cost sharing in distribution problems for franchise operations","authors":"A. Meca, M. G. Fiestras-Janeiro, M. Mosquera, I. García-Jurado","doi":"10.1145/1807406.1807482","DOIUrl":"https://doi.org/10.1145/1807406.1807482","url":null,"abstract":"This paper studies the cost sharing problem in an inventory transportation system with multiple agents, where transportation costs are different for each agent. Orderings of a single item are placed jointly using an economic order quantity (EOQ) policy. Part of the ordering cost is shared, and part is specific to each agent and depends on the distance from the supplier (transportation cost). For this inventory situation, cooperation is not always profitable. We therefore examine when cooperation is profitable and how to divide the total cost in a way that ensures stability (no group of agents can improve by deviating from the total group) and computability. We use cooperative game theory to provide adequate answers to all those questions. We prove that if cooperation is profitable (the corresponding inventory game is subadditive), then we can always find coalitional stable allocations of the total cost (the core of the game is not empty). We further define two kinds of context-specific cost sharing rules and study their properties. The first one, which turns out to be coalitional stable (it always belongs to the core), is a cost sharing rule à la Shapley. The second one, simpler but not always coalitional stable, belongs to the family of proportional cost sharing rules.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114179253","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 provides an axiomatic approach to characterizing the Nash architectures in directed networks. In a directed network (also called one-way flow networks) when player i establishes a link with player j, only player i is able to access player j's information. Player j must establish a separate link with i to gain access to her information. The common example of such a phenomenon would be visiting webpages. Following their introduction in the economics literature by Bala and Goyal (2000) there is a small but growing body of literature on directed networks. In such a network formation model, directed links are costly but provide benefits to those who establish them. The original Bala and Goyal model assumes that all model parameters (costs and benefits) are homogeneous. Galeotti (2006) introduces a type of heterogeneity into this set up by making cost and benefits depend on the identity of the player under consideration. Billand, Bravard and Sarangi (2009) consider a situation where costs and benefits in the network depend on the identity of the person with whom the link is being formed. Billand, Bravard and Sarangi (2008) examines the issue of existence of equilibrium in directed networks, while directed spillovers are examined by the same authors in another paper (2009). Our goal in this paper is to develop a set of properties of the payoff function under which the equilibria of different models can be easily obtained. The first of these axioms is about the profitability of individual players. It says that if player i is willing to connect to player j then a player to whom j is worth more should also be willing to connect to j. Hence it is about the attractiveness of partners in the network. The second one suggests a player will form fewer links in a network that gives her access to fewer resources. The third axiom called monotonicity with respect to players utilizes the same concept as the second axiom but for players instead of resources. The fourth axiom penalizes players for creating redundant links. We find that under monotonicity with respect to resources wheel type architectures predominate, though with more specific assumptions minimally connected networks can also arise. With player monotonicity, flower networks are the predominant strict Nash architecture. Examples in the paper demonstrate the independence of these axioms.
{"title":"Axiomatic characterization of Nash networks","authors":"P. Billand, C. Bravard, J. Kamphorst, S. Sarangi","doi":"10.1145/1807406.1807417","DOIUrl":"https://doi.org/10.1145/1807406.1807417","url":null,"abstract":"This paper provides an axiomatic approach to characterizing the Nash architectures in directed networks. In a directed network (also called one-way flow networks) when player i establishes a link with player j, only player i is able to access player j's information. Player j must establish a separate link with i to gain access to her information. The common example of such a phenomenon would be visiting webpages.\u0000 Following their introduction in the economics literature by Bala and Goyal (2000) there is a small but growing body of literature on directed networks. In such a network formation model, directed links are costly but provide benefits to those who establish them. The original Bala and Goyal model assumes that all model parameters (costs and benefits) are homogeneous. Galeotti (2006) introduces a type of heterogeneity into this set up by making cost and benefits depend on the identity of the player under consideration. Billand, Bravard and Sarangi (2009) consider a situation where costs and benefits in the network depend on the identity of the person with whom the link is being formed. Billand, Bravard and Sarangi (2008) examines the issue of existence of equilibrium in directed networks, while directed spillovers are examined by the same authors in another paper (2009).\u0000 Our goal in this paper is to develop a set of properties of the payoff function under which the equilibria of different models can be easily obtained. The first of these axioms is about the profitability of individual players. It says that if player i is willing to connect to player j then a player to whom j is worth more should also be willing to connect to j. Hence it is about the attractiveness of partners in the network. The second one suggests a player will form fewer links in a network that gives her access to fewer resources. The third axiom called monotonicity with respect to players utilizes the same concept as the second axiom but for players instead of resources. The fourth axiom penalizes players for creating redundant links.\u0000 We find that under monotonicity with respect to resources wheel type architectures predominate, though with more specific assumptions minimally connected networks can also arise. With player monotonicity, flower networks are the predominant strict Nash architecture. Examples in the paper demonstrate the independence of these axioms.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121872167","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}
The Braess Paradox is a major finding in the equilibrium analysis of routing decentralized traffic in directed networks that are susceptible to congestion. It demonstrates that removing one or more links from a network that is subject to congestion may under certain combinations of cost structure and number of network users decrease the cost of travel for all its users. The Braess Paradox (BP) may be illustrated in networks modeled as non-atomic games where the number of commuters is very large and, as a consequence, each commuter only controls a negligible fraction of the overall traffic. Alternatively, as in the present study, it may be illustrated in networks modeled as atomic selfish routing games, where each commuter has a non-negligible effect on the travel costs of all the other commuters. Arguments have been raised not against the counterintuitive finding of Braess but, rather, against its relevance to real life situations. The argument goes that these are highly abstract networks and their seemingly paradoxical implications arise from the many aspects in which they differ from reality rather than from these aspects that they share with it. If the BP is a rare event in selfish routing networks, restricted to judiciously chosen combinations of parameter values and very simple networks, then interest in it should clearly be limited. But if a substantial fraction of networks in communication and transportation are susceptible to the BP, then the problem of adding links to the basic network or, alternatively, removing links from the augmented network gains practical significance and should, therefore, be approached with considerable care. Our main purpose is to compare to each other two information conditions. In the PUBLIC condition, each user is informed of the route choices and payoffs of all the users. In the PRIVATE condition, each user is only informed of her own payoff. For this purpose, we construct a basic network where each of n=18 players has to choose one of four routes from a common origin to common destination. We also construct an augmented network with two additional cross road segments that give rise to the Braess paradox. We use a computer-controlled within-subject experimental design in which each player first chooses one of six routes in 60 iterations of the augmented network and then one of four routes in 60 additional iterations of the basic network. We show that when the stage game is iterated in time, under both information conditions and in both games aggregate route choices converge to equilibrium.
{"title":"Degrading network capacity may improve performance: information effects in the Braess Paradox","authors":"Eyran J. Gisches, A. Rapoport","doi":"10.1145/1807406.1807461","DOIUrl":"https://doi.org/10.1145/1807406.1807461","url":null,"abstract":"The Braess Paradox is a major finding in the equilibrium analysis of routing decentralized traffic in directed networks that are susceptible to congestion. It demonstrates that removing one or more links from a network that is subject to congestion may under certain combinations of cost structure and number of network users decrease the cost of travel for all its users. The Braess Paradox (BP) may be illustrated in networks modeled as non-atomic games where the number of commuters is very large and, as a consequence, each commuter only controls a negligible fraction of the overall traffic. Alternatively, as in the present study, it may be illustrated in networks modeled as atomic selfish routing games, where each commuter has a non-negligible effect on the travel costs of all the other commuters.\u0000 Arguments have been raised not against the counterintuitive finding of Braess but, rather, against its relevance to real life situations. The argument goes that these are highly abstract networks and their seemingly paradoxical implications arise from the many aspects in which they differ from reality rather than from these aspects that they share with it. If the BP is a rare event in selfish routing networks, restricted to judiciously chosen combinations of parameter values and very simple networks, then interest in it should clearly be limited. But if a substantial fraction of networks in communication and transportation are susceptible to the BP, then the problem of adding links to the basic network or, alternatively, removing links from the augmented network gains practical significance and should, therefore, be approached with considerable care.\u0000 Our main purpose is to compare to each other two information conditions. In the PUBLIC condition, each user is informed of the route choices and payoffs of all the users. In the PRIVATE condition, each user is only informed of her own payoff. For this purpose, we construct a basic network where each of n=18 players has to choose one of four routes from a common origin to common destination. We also construct an augmented network with two additional cross road segments that give rise to the Braess paradox. We use a computer-controlled within-subject experimental design in which each player first chooses one of six routes in 60 iterations of the augmented network and then one of four routes in 60 additional iterations of the basic network. We show that when the stage game is iterated in time, under both information conditions and in both games aggregate route choices converge to equilibrium.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130175195","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 analyze the complexity of computing pure strategy Nash equilibria (PSNE) inn symmetric games with a fixed number of actions, where the utilities are compactly represented. Such a representation is able to describe symmetric games whose number of players is exponential in the representation size. We show that in the general case, where utility functions are represented as arbitrary circuits, the problem of deciding the existence of PSNE is NP-complete. For the special case of games with two actions, there always exist a PSNE and we give a polynomial algorithm for finding one. We then focus on a natural representation of utility as piecewise-linear functions, and show that such a representation has nice computational properties. In particular, we give polynomial-time algorithms to count the number of PSNE (thus deciding if such an equilibrium exists) and to find a sample PSNE, when one exists.
{"title":"Symmetric games with piecewise linear utilities","authors":"C. Ryan, A. Jiang, Kevin Leyton-Brown","doi":"10.1145/1807406.1807447","DOIUrl":"https://doi.org/10.1145/1807406.1807447","url":null,"abstract":"We analyze the complexity of computing pure strategy Nash equilibria (PSNE) inn symmetric games with a fixed number of actions, where the utilities are compactly represented. Such a representation is able to describe symmetric games whose number of players is exponential in the representation size. We show that in the general case, where utility functions are represented as arbitrary circuits, the problem of deciding the existence of PSNE is NP-complete. For the special case of games with two actions, there always exist a PSNE and we give a polynomial algorithm for finding one. We then focus on a natural representation of utility as piecewise-linear functions, and show that such a representation has nice computational properties. In particular, we give polynomial-time algorithms to count the number of PSNE (thus deciding if such an equilibrium exists) and to find a sample PSNE, when one exists.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130424294","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 repeated games played among members of a society who are connected in a social network. Players can observe each others' play, but can only directly affect the payoffs of their social neighbors. We characterize the social network patterns that sustain repeated cooperative equilibrium behavior and are robust in various ways. High levels of cooperation can only be sustained as robust equilibria in specific sorts of social networks, and so analyzing repeated games can have strong implications for how social network structure affects its members' behaviors and welfare.
{"title":"Games and social network structure","authors":"M. Jackson","doi":"10.1145/1807406.1807407","DOIUrl":"https://doi.org/10.1145/1807406.1807407","url":null,"abstract":"We examine repeated games played among members of a society who are connected in a social network. Players can observe each others' play, but can only directly affect the payoffs of their social neighbors. We characterize the social network patterns that sustain repeated cooperative equilibrium behavior and are robust in various ways. High levels of cooperation can only be sustained as robust equilibria in specific sorts of social networks, and so analyzing repeated games can have strong implications for how social network structure affects its members' behaviors and welfare.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131789454","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}
Trust is indispensable to fiduciary fields (e.g., credit rating), where experts exercise wide discretion on behalf of others. Can the shame from a scandal sort trustworthy people out of a fiduciary field? I tested for the possibility that a shame externality can sort in a charitable contribution game where subjects could be "ungenerous" when unobserved. After establishing that "generosity" required a contribution of more than $6, subjects were given the choice of contributing either $5 publicly or $0--$10 privately. 20/22 control subjects chose to contribute privately less than $2. 10/26 treatment subjects, after being told the prediction that they were unlikely to contribute more than $2, if they contributed privately, contributed $5 publicly. (This group also showed higher shame sensitivity.) This suggests that the mere belief that a subject would exploit the greater discretion and unobservability of a fiduciary-like position can deter entry into such a position. Thus, scandals that create such a belief could repel shame-sensitive people from that field - possibly to the detriment of the field and the economy as a whole.
{"title":"Sorting with shame in the laboratory","authors":"David Ong","doi":"10.1145/1807406.1807491","DOIUrl":"https://doi.org/10.1145/1807406.1807491","url":null,"abstract":"Trust is indispensable to fiduciary fields (e.g., credit rating), where experts exercise wide discretion on behalf of others. Can the shame from a scandal sort trustworthy people out of a fiduciary field? I tested for the possibility that a shame externality can sort in a charitable contribution game where subjects could be \"ungenerous\" when unobserved. After establishing that \"generosity\" required a contribution of more than $6, subjects were given the choice of contributing either $5 publicly or $0--$10 privately. 20/22 control subjects chose to contribute privately less than $2. 10/26 treatment subjects, after being told the prediction that they were unlikely to contribute more than $2, if they contributed privately, contributed $5 publicly. (This group also showed higher shame sensitivity.) This suggests that the mere belief that a subject would exploit the greater discretion and unobservability of a fiduciary-like position can deter entry into such a position. Thus, scandals that create such a belief could repel shame-sensitive people from that field - possibly to the detriment of the field and the economy as a whole.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133453501","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}
Manjira Datta, Leonard J. Mirman, O. Morand, K. Reffett
Since the seminal work of Kydland and Prescott and Abreu, Pearce, and Stacchetti, researchers have sought to develop correspondence-based monotone continuation methods for constructing pure strategy sequential (subgame perfect) equilibrium, and/or pure strategy Markov perfect Nash equilibrium in classes of dynamic games. These are "strategic dynamic programming" methods (or, the so-called "APS approach") for mapping between spaces of correspondences to (i) verify the existence of subgame perfect Nash equilibrium, as well as (ii) suggesting explicit methods for computing approximate solutions. In the last decade, economists have attempted to extend these APS methods to study competitive equilibrium in dynamic general equilibrium models. In this line of work, emphasis has both been on analyzing sequential competitive equilibrium, as well as Markovian or recursive equilibrium. In this paper, we reconsider recent results reported in this emerging literature using "APS methods" for the existence and computation of recursive/Markov competitive equilibrium in nonoptimal competitive economies using function-based APS methods. And, to keep things simple, we consider these questions in the setting of a simple one-sector nonoptimal growth model with a state-contingent tax. We find several interesting results. First, we extend the uniqueness result for continuous Markov equilibrium for the policy iteration method proposed by Coleman to a larger class of functions (i.e., spaces of bounded functions). However, despite this generalization, there exist other fixed point procedures that potentially construct continuous Markov equilibrium that exist outside this set. This result shows the delicate nature of existing uniqueness results in the literature even for the simplest nonoptimal models. Next, we extend Coleman's policy iteration approach to prove existence of (locally Lipschitz) continuous recursive equilibrium in economies previously thought not to possess them. Specifically, we show the delicate nature of the existing correspondence-based continuation APS methods. In general, these APS methods do not verify the existence of recursive equilibrium (even for simple one-dimensional cases). Also, using constructive arguments, we show that even when existence of Markov equilibrium is known, the solutions to the abstract functional equations considered in the APS methods of Miao and Santos admit solutions or selections that are not necessarily Markov equilibrium. This is a serious problem for numerical work. In particular, even when existence of Markov equilibrium selections exist, our results show that current APS procedures for competitive economies do not, in general, provide a rigorous method for constructing or approximating a recursive equilibrium selection from the limiting (greatest fixed point) "equilibrium" correspondence even for very simple economies. To remedy this situation, we propose a new APS method with correspondences valued in function spaces
{"title":"Which recursive equilibrium?","authors":"Manjira Datta, Leonard J. Mirman, O. Morand, K. Reffett","doi":"10.1145/1807406.1807430","DOIUrl":"https://doi.org/10.1145/1807406.1807430","url":null,"abstract":"Since the seminal work of Kydland and Prescott and Abreu, Pearce, and Stacchetti, researchers have sought to develop correspondence-based monotone continuation methods for constructing pure strategy sequential (subgame perfect) equilibrium, and/or pure strategy Markov perfect Nash equilibrium in classes of dynamic games. These are \"strategic dynamic programming\" methods (or, the so-called \"APS approach\") for mapping between spaces of correspondences to (i) verify the existence of subgame perfect Nash equilibrium, as well as (ii) suggesting explicit methods for computing approximate solutions. In the last decade, economists have attempted to extend these APS methods to study competitive equilibrium in dynamic general equilibrium models. In this line of work, emphasis has both been on analyzing sequential competitive equilibrium, as well as Markovian or recursive equilibrium. In this paper, we reconsider recent results reported in this emerging literature using \"APS methods\" for the existence and computation of recursive/Markov competitive equilibrium in nonoptimal competitive economies using function-based APS methods. And, to keep things simple, we consider these questions in the setting of a simple one-sector nonoptimal growth model with a state-contingent tax. We find several interesting results. First, we extend the uniqueness result for continuous Markov equilibrium for the policy iteration method proposed by Coleman to a larger class of functions (i.e., spaces of bounded functions). However, despite this generalization, there exist other fixed point procedures that potentially construct continuous Markov equilibrium that exist outside this set. This result shows the delicate nature of existing uniqueness results in the literature even for the simplest nonoptimal models. Next, we extend Coleman's policy iteration approach to prove existence of (locally Lipschitz) continuous recursive equilibrium in economies previously thought not to possess them. Specifically, we show the delicate nature of the existing correspondence-based continuation APS methods. In general, these APS methods do not verify the existence of recursive equilibrium (even for simple one-dimensional cases). Also, using constructive arguments, we show that even when existence of Markov equilibrium is known, the solutions to the abstract functional equations considered in the APS methods of Miao and Santos admit solutions or selections that are not necessarily Markov equilibrium. This is a serious problem for numerical work. In particular, even when existence of Markov equilibrium selections exist, our results show that current APS procedures for competitive economies do not, in general, provide a rigorous method for constructing or approximating a recursive equilibrium selection from the limiting (greatest fixed point) \"equilibrium\" correspondence even for very simple economies. To remedy this situation, we propose a new APS method with correspondences valued in function spaces ","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132662343","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}
New insights into the theory of games with strategic substitutes (GSS) are developed. These games possess extremal serially undominated strategies that provide bounds on predicted behavior and on limiting behavior of adaptive dynamics, similar to games with strategic complements (GSC). In parameterized GSS, monotone equilibrium selections are dynamically stable under natural conditions, as in parameterized GSC. Dominance solvability in GSS is not equivalent to uniqueness of Nash equilibrium, but is equivalent to uniqueness of simply rationalizable strategies. Convergence of best response dynamics in GSS is equivalent to global convergence of adaptive dynamics, is equivalent to dominance solvability, and implies uniqueness of equilibrium, all in contrast to GSC. In particular, Cournot stability is equivalent to dominance solvability in GSS. The results shed light on predicted behavior, learning, global stability, uniqueness of equilibrium, and dynamic stability of monotone comparative statics in GSS. Several examples are provided.
{"title":"Rationalizability, adaptive dynamics, and the correspondence principle in games with strategic substitutes","authors":"Sunanda Roy, Tarun Sabarwal","doi":"10.1145/1807406.1807431","DOIUrl":"https://doi.org/10.1145/1807406.1807431","url":null,"abstract":"New insights into the theory of games with strategic substitutes (GSS) are developed. These games possess extremal serially undominated strategies that provide bounds on predicted behavior and on limiting behavior of adaptive dynamics, similar to games with strategic complements (GSC). In parameterized GSS, monotone equilibrium selections are dynamically stable under natural conditions, as in parameterized GSC. Dominance solvability in GSS is not equivalent to uniqueness of Nash equilibrium, but is equivalent to uniqueness of simply rationalizable strategies. Convergence of best response dynamics in GSS is equivalent to global convergence of adaptive dynamics, is equivalent to dominance solvability, and implies uniqueness of equilibrium, all in contrast to GSC. In particular, Cournot stability is equivalent to dominance solvability in GSS. The results shed light on predicted behavior, learning, global stability, uniqueness of equilibrium, and dynamic stability of monotone comparative statics in GSS. Several examples are provided.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115433379","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}
Experiments have been used to study the behavioural validity of the predictions of game theory. Unfortunately, almost all of the games studied by experimental economists require at least one maintained assumptions in order to interpret the payoffs faced by subjects as utilities: that the subject has a linear utility function defined over monetary payoffs. With some notable exceptions, experimental games reward subjects by giving them money. Money is not the same as utility, which is what game theory assumes payoffs to be defined in terms of. Moreover, linear transformations of money do not accurately reflect linear transformations of utility unless the subject is risk neutral. Since there is evidence that experimental subjects tend to behave as if risk averse over the domain of income involved in most experiments, there is a potential confound in the interpretation of behaviour in experimental games. This point is well known, in the sense that it is easy to find occasional references to it by careful students of experimental games. And there are some remarkable experimental designs that attempt to control for this confound. But there are also many experimental games in which the possibility of risk aversion makes inferences difficult, to say the least. The problem is that the experimenter has lost control of one of the fundamentals of the game, and simply cannot know with any certainty what utility payoffs the subject is facing. We follow Goeree, Holt and Palfrey GEB 2003, and propose joint econometric estimation of the utility function of individuals from behavior in an individual lottery choice task and in strategic games, where behavior in the latter is constrained to be a Quantal Response Equilibrium. We develop computational tools using GAMBIT and Stata to facilitate the maximum likelihood estimation of behavior in experimental games defined over utility. These tools are applied to evaluate behavior over a wide range of experimental games. Our approach generalizes to also allow for other specifications in which utility might not be the same as own-payoff, such as an allowance for social preferences.
{"title":"The games that experimental subjects play: the utility of payoffs","authors":"G. Harrison, Theodore L. Turocy","doi":"10.1145/1807406.1807485","DOIUrl":"https://doi.org/10.1145/1807406.1807485","url":null,"abstract":"Experiments have been used to study the behavioural validity of the predictions of game theory. Unfortunately, almost all of the games studied by experimental economists require at least one maintained assumptions in order to interpret the payoffs faced by subjects as utilities: that the subject has a linear utility function defined over monetary payoffs. With some notable exceptions, experimental games reward subjects by giving them money. Money is not the same as utility, which is what game theory assumes payoffs to be defined in terms of. Moreover, linear transformations of money do not accurately reflect linear transformations of utility unless the subject is risk neutral. Since there is evidence that experimental subjects tend to behave as if risk averse over the domain of income involved in most experiments, there is a potential confound in the interpretation of behaviour in experimental games. This point is well known, in the sense that it is easy to find occasional references to it by careful students of experimental games. And there are some remarkable experimental designs that attempt to control for this confound. But there are also many experimental games in which the possibility of risk aversion makes inferences difficult, to say the least. The problem is that the experimenter has lost control of one of the fundamentals of the game, and simply cannot know with any certainty what utility payoffs the subject is facing. We follow Goeree, Holt and Palfrey GEB 2003, and propose joint econometric estimation of the utility function of individuals from behavior in an individual lottery choice task and in strategic games, where behavior in the latter is constrained to be a Quantal Response Equilibrium. We develop computational tools using GAMBIT and Stata to facilitate the maximum likelihood estimation of behavior in experimental games defined over utility. These tools are applied to evaluate behavior over a wide range of experimental games. Our approach generalizes to also allow for other specifications in which utility might not be the same as own-payoff, such as an allowance for social preferences.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"226 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123508450","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：