Theory-of-mind (ToM) is the modeling of mental states (such as belief, desire, knowledge, perception) through recursive ("I think you think I think ...") type reasoning in order to plan one's action or anticipate others' action. Such reasoning forms the core of strategic analysis in the game-theoretic setting. Traditional analysis of rational behavior in games of complete information is centered on the axiom of "common knowledge," according to which all players know something to be true, know that all players know it to be true, know that all players know all players know it to be true, etc. Such axiom requires recursive modeling of players to the full depth, and seems to contradict human empirical behavior revealed by behavioral game literature. Here, I propose that such deviation from normative analysis may be due to players' building predictive mental models of their co-players based on experience and context without necessarily assuming a priori full rationality and common knowledge, rather than due to any lapse in "instrumental rationality" whereby players (and co-players) translate the predictions from their mental models to optimal choice. I investigate this mental model account of theory-of-mind reasoning by constructing a series of two-player, sequential-move matrix games all terminating in a maximal of three steps. By carefully designing payoff matrices, the depth of recursive reasoning (i.e., first-order ToM versus second-order ToM) can be contrasted based on participants' choice behavior in those games. Empirical findings support the idea that depth of ToM recursion (related to perspective-taking) and instrumental rationality (rational application of belief-desire to action) constitute separate processes. Finally, I present a theoretical analysis of repeated games, such as the Iterated Prisoner Dilemma, and show how mutual cooperation can arise as individually rational outcome due to expected future interaction with the opponent.
{"title":"Reflexive theory-of-mind reasoning in games: from empirical evidence to modeling","authors":"Jun Zhang","doi":"10.1145/1807406.1807435","DOIUrl":"https://doi.org/10.1145/1807406.1807435","url":null,"abstract":"Theory-of-mind (ToM) is the modeling of mental states (such as belief, desire, knowledge, perception) through recursive (\"I think you think I think ...\") type reasoning in order to plan one's action or anticipate others' action. Such reasoning forms the core of strategic analysis in the game-theoretic setting. Traditional analysis of rational behavior in games of complete information is centered on the axiom of \"common knowledge,\" according to which all players know something to be true, know that all players know it to be true, know that all players know all players know it to be true, etc. Such axiom requires recursive modeling of players to the full depth, and seems to contradict human empirical behavior revealed by behavioral game literature. Here, I propose that such deviation from normative analysis may be due to players' building predictive mental models of their co-players based on experience and context without necessarily assuming a priori full rationality and common knowledge, rather than due to any lapse in \"instrumental rationality\" whereby players (and co-players) translate the predictions from their mental models to optimal choice. I investigate this mental model account of theory-of-mind reasoning by constructing a series of two-player, sequential-move matrix games all terminating in a maximal of three steps. By carefully designing payoff matrices, the depth of recursive reasoning (i.e., first-order ToM versus second-order ToM) can be contrasted based on participants' choice behavior in those games. Empirical findings support the idea that depth of ToM recursion (related to perspective-taking) and instrumental rationality (rational application of belief-desire to action) constitute separate processes. Finally, I present a theoretical analysis of repeated games, such as the Iterated Prisoner Dilemma, and show how mutual cooperation can arise as individually rational outcome due to expected future interaction with the opponent.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128010390","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}
Although a national live-donor kidney exchange program is being launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible and incompatible pairs, and patients are indifferent over compatible pairs. Only two-way exchanges are permitted due to institutional constraints. We explore the structure of Pareto-efficient matchings in this framework. The mathematical structure of this model turns out to be quite novel. We show that under Pareto-efficient matchings, the same number of patients receive transplants, and it is possible to construct Pareto-efficient matchings that match the same incompatible pairs while matching the least number of compatible pairs. We non-trivially extend the famous Gallai-Edmonds Decomposition in the combinatorial optimization literature to our new framework.
{"title":"Altruistic kidney exchange","authors":"Tayfun Sönmez, M. Utku Ünver","doi":"10.1145/1807406.1807479","DOIUrl":"https://doi.org/10.1145/1807406.1807479","url":null,"abstract":"Although a national live-donor kidney exchange program is being launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible and incompatible pairs, and patients are indifferent over compatible pairs. Only two-way exchanges are permitted due to institutional constraints. We explore the structure of Pareto-efficient matchings in this framework. The mathematical structure of this model turns out to be quite novel. We show that under Pareto-efficient matchings, the same number of patients receive transplants, and it is possible to construct Pareto-efficient matchings that match the same incompatible pairs while matching the least number of compatible pairs. We non-trivially extend the famous Gallai-Edmonds Decomposition in the combinatorial optimization literature to our new framework.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122376896","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}
Congestion games are an elegant model to study the effects of resource usage and routing with strategic agents, but due to their simplicity they are inadequate to realistically model many features of traffic in computer and/or road networks. In my talk I survey our recent results on extensions of congestion games towards more realistic modeling of network routing scenarios. Our results concentrate on the existence and computational complexity of exact and approximate pure-strategy Nash and strong equilibria. Whereas in some cases it is possible to provide efficient algorithms for centralized computation, for a sufficient level of generality we can establish lower bounds by proving computational hardness results. In addition, we study the more demanding goal of reaching equilibria using decentralized protocols and the duration of the resulting improvement dynamics. More fundamentally, our treatment sheds light on the tractability of coordinated behavior of players in network routing.
{"title":"Coalitions and dynamics in network routing games","authors":"M. Hoefer","doi":"10.1145/1807406.1807410","DOIUrl":"https://doi.org/10.1145/1807406.1807410","url":null,"abstract":"Congestion games are an elegant model to study the effects of resource usage and routing with strategic agents, but due to their simplicity they are inadequate to realistically model many features of traffic in computer and/or road networks. In my talk I survey our recent results on extensions of congestion games towards more realistic modeling of network routing scenarios. Our results concentrate on the existence and computational complexity of exact and approximate pure-strategy Nash and strong equilibria. Whereas in some cases it is possible to provide efficient algorithms for centralized computation, for a sufficient level of generality we can establish lower bounds by proving computational hardness results. In addition, we study the more demanding goal of reaching equilibria using decentralized protocols and the duration of the resulting improvement dynamics. More fundamentally, our treatment sheds light on the tractability of coordinated behavior of players in network routing.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125104259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state (of the world) determines which action has higher payoff. Agents decide which agents to form a communication link with incurring the associated cost and receive a private signal correlated with the underlying state. They then exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from "information hubs", which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Finally, we show how these results can be applied to several commonly studied random graph models, such as preferential attachment and Erdos-Renyi graphs.
{"title":"Communication dynamics in endogenous social networks","authors":"K. Bimpikis, D. Acemoglu, A. Ozdaglar","doi":"10.1145/1807406.1807499","DOIUrl":"https://doi.org/10.1145/1807406.1807499","url":null,"abstract":"We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state (of the world) determines which action has higher payoff. Agents decide which agents to form a communication link with incurring the associated cost and receive a private signal correlated with the underlying state. They then exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from \"information hubs\", which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Finally, we show how these results can be applied to several commonly studied random graph models, such as preferential attachment and Erdos-Renyi graphs.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121506124","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 management game "How flow can you go?" is developed to convince decision makers of international logistic providers that their current planning methods of their transportation flows may be considerably improved using OR-techniques. In fact, we have tested the game with several planners of several logistic providers and it turns out that the mathematical tool included in the management game outperforms the planners' solutions, on average, by 10%. Next, we show that cooperation among different logistic providers or between individual business units of one provider may increase profit even more. Since a fair allocation of these extra profits is essential for a successful cooperation, we use cooperative game theory methodology. More precisely, we propose the Shapley value of a cooperative game that arises from the management game as a fair allocation. Finally, the management game is illustrated by means of a case of an international logistic provider.
{"title":"How flow can you go?: a logistic management game and profit sharing","authors":"R. Heesen, H. Hamers, K. Huisman","doi":"10.1145/1807406.1807414","DOIUrl":"https://doi.org/10.1145/1807406.1807414","url":null,"abstract":"The management game \"How flow can you go?\" is developed to convince decision makers of international logistic providers that their current planning methods of their transportation flows may be considerably improved using OR-techniques. In fact, we have tested the game with several planners of several logistic providers and it turns out that the mathematical tool included in the management game outperforms the planners' solutions, on average, by 10%. Next, we show that cooperation among different logistic providers or between individual business units of one provider may increase profit even more. Since a fair allocation of these extra profits is essential for a successful cooperation, we use cooperative game theory methodology. More precisely, we propose the Shapley value of a cooperative game that arises from the management game as a fair allocation. Finally, the management game is illustrated by means of a case of an international logistic provider.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128949410","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 decentralized transshipment problem is a two-stage decision making problem where the companies first choose their individual production levels in anticipation of random demands and after demand realizations they pool residuals via transshipment. The coordination will be achieved if at optimality all the decision variables, i.e. production levels and transshipment patterns, in the decentralized system are the same as those of centralized system. In this paper, we study the coordination via transshipment prices. We propose a procedure for deriving the transshipment prices based on the coordinating allocation rule introduced by Anupindi et al. [1]. With the transshipment prices being set, the companies are free to match their residuals based on their individual preferences. We draw upon the concept of pair-wise stability to capture the dynamics of corresponding matching process. As the main result of this paper, we show that with the derived transshipment prices, the optimum transshipment patterns are always pair-wise stable, i.e. there are no pairs of companies that can be jointly better off by unilaterally deviating from the optimum transshipment patterns.
{"title":"Transshipment prices and pair-wise stability in coordinating the decentralized transshipment problem","authors":"Behzad Hezarkhani, W. Kubiak","doi":"10.1145/1807406.1807439","DOIUrl":"https://doi.org/10.1145/1807406.1807439","url":null,"abstract":"The decentralized transshipment problem is a two-stage decision making problem where the companies first choose their individual production levels in anticipation of random demands and after demand realizations they pool residuals via transshipment. The coordination will be achieved if at optimality all the decision variables, i.e. production levels and transshipment patterns, in the decentralized system are the same as those of centralized system. In this paper, we study the coordination via transshipment prices. We propose a procedure for deriving the transshipment prices based on the coordinating allocation rule introduced by Anupindi et al. [1]. With the transshipment prices being set, the companies are free to match their residuals based on their individual preferences. We draw upon the concept of pair-wise stability to capture the dynamics of corresponding matching process. As the main result of this paper, we show that with the derived transshipment prices, the optimum transshipment patterns are always pair-wise stable, i.e. there are no pairs of companies that can be jointly better off by unilaterally deviating from the optimum transshipment patterns.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131035358","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}
There have been two major market price determination techniques in Economics: Auction and Competitive Equilibrium. While auction has found great applications in practical markets such as antique market, and recently sponsored search market, equilibrium has been used mostly in policy analysis such as by the World Bank. In this talk, we discuss the possibility equilibrium analysis could be applied to the advertising market, with complexity analysis and polynomial time algorithm designs. In addition, we study issues where two concepts relate to each other, as well as the interplays between the market maker and advertisers.
{"title":"Competitive equilibrium computation at advertising marketplaces","authors":"Xiaotie Deng","doi":"10.1145/1807406.1807470","DOIUrl":"https://doi.org/10.1145/1807406.1807470","url":null,"abstract":"There have been two major market price determination techniques in Economics: Auction and Competitive Equilibrium. While auction has found great applications in practical markets such as antique market, and recently sponsored search market, equilibrium has been used mostly in policy analysis such as by the World Bank. In this talk, we discuss the possibility equilibrium analysis could be applied to the advertising market, with complexity analysis and polynomial time algorithm designs. In addition, we study issues where two concepts relate to each other, as well as the interplays between the market maker and advertisers.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132976855","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 studies cheap talk games by imposing a monotonicity condition on Sender strategies and then applies iterative deletion of weakly dominated strategies. This procedure selects among Crawford and Sobel (1982) equilibria, typically selecting the outcome with the maximal number of induced actions. Other refinements, such as NITS, select the same outcome. It also predicts that Senders will inflate their communication using only relatively high messages in equilibrium.
{"title":"Effective communication in cheap-talk games","authors":"Navin Kartik, J. Sobel","doi":"10.1145/1807406.1807466","DOIUrl":"https://doi.org/10.1145/1807406.1807466","url":null,"abstract":"This paper studies cheap talk games by imposing a monotonicity condition on Sender strategies and then applies iterative deletion of weakly dominated strategies. This procedure selects among Crawford and Sobel (1982) equilibria, typically selecting the outcome with the maximal number of induced actions. Other refinements, such as NITS, select the same outcome. It also predicts that Senders will inflate their communication using only relatively high messages in equilibrium.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121393083","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 test a mechanism whereby groups are formed endogenously, through the use of voting. These groups play a public-goods game, where efficiency increases with group size (up to a limit, in one treatment). Information is provided about the contributions of others and it is feasible to exclude group members, exit one's group, or to form larger groups through mergers involving the consent of both merging groups. We find a great degree of success for this mechanism, as the average contribution rate is very high. The driving force appears to be the economies of scale combined with the awareness that bad behavior will result in (potentially-reversible) exclusion.
{"title":"Endogenous group formation and efficiency: an experimental study","authors":"G. Charness, Chun-Lei Yang","doi":"10.1145/1807406.1807463","DOIUrl":"https://doi.org/10.1145/1807406.1807463","url":null,"abstract":"We test a mechanism whereby groups are formed endogenously, through the use of voting. These groups play a public-goods game, where efficiency increases with group size (up to a limit, in one treatment). Information is provided about the contributions of others and it is feasible to exclude group members, exit one's group, or to form larger groups through mergers involving the consent of both merging groups. We find a great degree of success for this mechanism, as the average contribution rate is very high. The driving force appears to be the economies of scale combined with the awareness that bad behavior will result in (potentially-reversible) exclusion.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117011513","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}
Recent behavioral evidence suggests that mutation-susceptible, best-practice emulation is a common strategy updating mechanism among real world human actors. Unlike purely analytical models of non-cooperative strategic behavior, computational models employing mutation-susceptible emulation-based strategy updating mechanisms (e.g. elitist Genetic Algorithms) are susceptible to a process similar to genetic drift. This drift is known to disrupt the stability of an equilibria. This paper uses a computational, Genetic Algorithm based model to demonstrate that such equilibrium-disrupting drift resolves Selten's Chain Store Paradox. More broadly, this paper hopes to modestly demonstrate how results from behavioral game theory can fruitfully be used to select the mechanisms used in computational game theoretic models.
{"title":"Genetic drift resolves Selten's Chain Store Paradox","authors":"W. M. Tracy","doi":"10.1145/1807406.1807421","DOIUrl":"https://doi.org/10.1145/1807406.1807421","url":null,"abstract":"Recent behavioral evidence suggests that mutation-susceptible, best-practice emulation is a common strategy updating mechanism among real world human actors. Unlike purely analytical models of non-cooperative strategic behavior, computational models employing mutation-susceptible emulation-based strategy updating mechanisms (e.g. elitist Genetic Algorithms) are susceptible to a process similar to genetic drift. This drift is known to disrupt the stability of an equilibria. This paper uses a computational, Genetic Algorithm based model to demonstrate that such equilibrium-disrupting drift resolves Selten's Chain Store Paradox. More broadly, this paper hopes to modestly demonstrate how results from behavioral game theory can fruitfully be used to select the mechanisms used in computational game theoretic models.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126942458","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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