We develop a novel Bayesian model for the finite Iterated Prisoner's Dilemma that takes into consideration belief change and end-game effect. According to this model, mutual defection is always the Nash equilibrium at any stage of the game, but it is not the only Nash equilibrium under some conditions. The conditions for mutual cooperation to be Nash equilibrium are deduced. It reveals that cooperation can be achieved if both players believe that their opponents are likely to cooperate not only at the current stage but also in future stages. End-game effect cannot be backward induced in repeated games with uncertainty. We illustrate this by analyzing the unexpected hanging paradox.
{"title":"Finite iterated prisoner's dilemma revisited: belief change and end-game effect","authors":"Jiawei Li, G. Kendall","doi":"10.1145/1807406.1807454","DOIUrl":"https://doi.org/10.1145/1807406.1807454","url":null,"abstract":"We develop a novel Bayesian model for the finite Iterated Prisoner's Dilemma that takes into consideration belief change and end-game effect. According to this model, mutual defection is always the Nash equilibrium at any stage of the game, but it is not the only Nash equilibrium under some conditions. The conditions for mutual cooperation to be Nash equilibrium are deduced. It reveals that cooperation can be achieved if both players believe that their opponents are likely to cooperate not only at the current stage but also in future stages. End-game effect cannot be backward induced in repeated games with uncertainty. We illustrate this by analyzing the unexpected hanging paradox.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"28 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":"134341924","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 considers a general class of discounted Markov stochastic games characterized by multidimensional state and action spaces with an order structure, and one-period reward functions and state transition law satisfying some complementarity and monotonicity conditions. Existence of pure-strategy Markov (Markov-stationary) equilibria for the finite (infinite) horizon game, with nondecreasing -and possibly discontinuous - strategies and value functions, is proved. The analysis is based on lattice programming, and not on concavity assumptions. Selected economic applications that fit the underlying framework are described: dynamic search with learning, long-run competition with learning-by-doing or network effects, and resource extraction.
{"title":"Discounted stochastic games with strategic complementarities: theory and applications","authors":"R. Amir","doi":"10.1145/1807406.1807432","DOIUrl":"https://doi.org/10.1145/1807406.1807432","url":null,"abstract":"This paper considers a general class of discounted Markov stochastic games characterized by multidimensional state and action spaces with an order structure, and one-period reward functions and state transition law satisfying some complementarity and monotonicity conditions. Existence of pure-strategy Markov (Markov-stationary) equilibria for the finite (infinite) horizon game, with nondecreasing -and possibly discontinuous - strategies and value functions, is proved. The analysis is based on lattice programming, and not on concavity assumptions. Selected economic applications that fit the underlying framework are described: dynamic search with learning, long-run competition with learning-by-doing or network effects, and resource extraction.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"1 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":"130889447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In some situations, players have to start analyzing the game before they have formed their preferences over the outcomes of the game. However, strategic analysis naturally depends on preferences. This dilemma will be discussed and some ideas for resolving it will be presented.
{"title":"Formation of preferences and strategic analysis","authors":"N. Megiddo","doi":"10.1145/1807406.1807476","DOIUrl":"https://doi.org/10.1145/1807406.1807476","url":null,"abstract":"In some situations, players have to start analyzing the game before they have formed their preferences over the outcomes of the game. However, strategic analysis naturally depends on preferences. This dilemma will be discussed and some ideas for resolving it will be presented.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"6 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":"133824410","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}
It is well known that an equilibrium point of a zero-sum two-player game can be computed in polynomial time using linear programming while the computation of a Nash equilibrium in a general two-player game is PPAD complete. In parallel, an Arrow-Debreu equilibrium price of an exchange market of traders with linear utilities is polynomial-time computable using convex programming, while the computation of an equilibrium price of an exchange market with linearly separable piece-wise linear utilities is PPAD complete. This convexity based dichotomy is fascinating in my view. In this talk I would like to discuss some of our recent work about the mathematical and complexity structure of equilibria, both for fixed-point-based Nash and market equilibria and for potential-function-based network equilibria that can be found by any local search procedure. I would also like to touch on the questions such as "Is local search fundamentally easier than fixed point computation?"
{"title":"Beyond convexity: local search and equilibrium computation","authors":"S. Teng","doi":"10.1145/1807406.1807469","DOIUrl":"https://doi.org/10.1145/1807406.1807469","url":null,"abstract":"It is well known that an equilibrium point of a zero-sum two-player game can be computed in polynomial time using linear programming while the computation of a Nash equilibrium in a general two-player game is PPAD complete. In parallel, an Arrow-Debreu equilibrium price of an exchange market of traders with linear utilities is polynomial-time computable using convex programming, while the computation of an equilibrium price of an exchange market with linearly separable piece-wise linear utilities is PPAD complete. This convexity based dichotomy is fascinating in my view. In this talk I would like to discuss some of our recent work about the mathematical and complexity structure of equilibria, both for fixed-point-based Nash and market equilibria and for potential-function-based network equilibria that can be found by any local search procedure. I would also like to touch on the questions such as \"Is local search fundamentally easier than fixed point computation?\"","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"82 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":"134411491","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}
Privacy and trust affect our everyday thinking and, in particular, the way we approach a concrete game. Accordingly, we hope that a rigorous treatment of privacy and trust will become integral part of mechanism design. As of now, the field has been very successful in finding many ingenious mechanisms as solutions to a variety of problems. But these mechanisms are theoretical constructions and not enough attention has been devoted to their concrete implementation. Indeed, It should be appreciated that the outcome function of a simple normal-form mechanism does not spontaneously evaluate itself on the "messages" that the players have selected in "their own minds." To be practically useful in a real strategic setting, any mechanism M, whether of normal or extensive form, must be concretely implemented. But then, in such concrete implementations, issues of privacy and trust may arise so as to undermine the valuable theoretical properties of M.
{"title":"Perfect concrete implementation of arbitrary mechanisms: a quick summary of joint work with Sergei Izmalkov and Matt Lepinski","authors":"S. Micali","doi":"10.1145/1807406.1807494","DOIUrl":"https://doi.org/10.1145/1807406.1807494","url":null,"abstract":"Privacy and trust affect our everyday thinking and, in particular, the way we approach a concrete game. Accordingly, we hope that a rigorous treatment of privacy and trust will become integral part of mechanism design. As of now, the field has been very successful in finding many ingenious mechanisms as solutions to a variety of problems. But these mechanisms are theoretical constructions and not enough attention has been devoted to their concrete implementation. Indeed, It should be appreciated that the outcome function of a simple normal-form mechanism does not spontaneously evaluate itself on the \"messages\" that the players have selected in \"their own minds.\" To be practically useful in a real strategic setting, any mechanism M, whether of normal or extensive form, must be concretely implemented. But then, in such concrete implementations, issues of privacy and trust may arise so as to undermine the valuable theoretical properties of M.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"4 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":"130582939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In auctions with private information acquisition costs, we completely characterize efficient and optimal two-stage selling procedures, with the first stage being the prescreening or entry right allocation mechanism, and the second stage being the traditional private good provision mechanism. Both efficiency and optimality require the second stage mechanism to be ex post efficient. For the first stage of entry allocation, both efficient and optimal mechanisms admit the most efficient bidders (the bidders with the least information acquisition costs), while the optimal mechanism admits fewer entrants. The efficient entry right allocation rule maximizes the expected total surplus, while the optimal entry right allocation rule maximizes the expected "virtual" total surplus, which is the total surplus adjusted for the information rent. We show that both efficient and optimal entry right allocation rules can be truthfully implemented in dominant strategies. We also demonstrate that the optimal entry right allocation mechanism can be implemented through an all-pay auction.
{"title":"Efficient and optimal selling procedures with private information acquisition costs","authors":"Jingfeng Lu, Lixin Ye","doi":"10.1145/1807406.1807450","DOIUrl":"https://doi.org/10.1145/1807406.1807450","url":null,"abstract":"In auctions with private information acquisition costs, we completely characterize efficient and optimal two-stage selling procedures, with the first stage being the prescreening or entry right allocation mechanism, and the second stage being the traditional private good provision mechanism. Both efficiency and optimality require the second stage mechanism to be ex post efficient. For the first stage of entry allocation, both efficient and optimal mechanisms admit the most efficient bidders (the bidders with the least information acquisition costs), while the optimal mechanism admits fewer entrants. The efficient entry right allocation rule maximizes the expected total surplus, while the optimal entry right allocation rule maximizes the expected \"virtual\" total surplus, which is the total surplus adjusted for the information rent. We show that both efficient and optimal entry right allocation rules can be truthfully implemented in dominant strategies. We also demonstrate that the optimal entry right allocation mechanism can be implemented through an all-pay auction.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"34 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":"126853881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we investigate a two-tier supply chain in which there is a supplier offering price-only contracts to several retailers who face stochastic demand. Each retailer has to determine his price before taking pre -orders and his demand depends on the prices of all retailers in the market. We assume the expected demand function is affine. We analyze two scenarios when retailers compete with substitutes or complements. In contrast to most existing literature which typically assumes symmetric retailers with a homogeneous product, we study asymmetric price-setting retailers with differentiated products. We derive tight upper and lower bounds on the profit loss due to lack of coordination in the supply chain. Our results show that when retailers compete with substitutes, horizontal competition among retailers compensates the double marginalization effect and promotes efficiency. Furthermore, the loss of profit in the decentralized setting is no more than 25% of the optimal profit in the centralized setting. This implies that in a substitutable product market, there is limited room for improvement from more elaborate contracts, which are often costly to implement. The opposite happens for complements, where horizontal competition aggravates the double marginalization effect and further deteriorates the chain-wide efficiency. It suggests that large profit gains can be achieved through more complex contracts which coordinate the chain.
{"title":"Loss of coordination in a competitive supply chain with pre-orders and endogenous pricing","authors":"G. Perakis, Wei Sun","doi":"10.1145/1807406.1807501","DOIUrl":"https://doi.org/10.1145/1807406.1807501","url":null,"abstract":"In this work, we investigate a two-tier supply chain in which there is a supplier offering price-only contracts to several retailers who face stochastic demand. Each retailer has to determine his price before taking pre -orders and his demand depends on the prices of all retailers in the market. We assume the expected demand function is affine. We analyze two scenarios when retailers compete with substitutes or complements. In contrast to most existing literature which typically assumes symmetric retailers with a homogeneous product, we study asymmetric price-setting retailers with differentiated products. We derive tight upper and lower bounds on the profit loss due to lack of coordination in the supply chain. Our results show that when retailers compete with substitutes, horizontal competition among retailers compensates the double marginalization effect and promotes efficiency. Furthermore, the loss of profit in the decentralized setting is no more than 25% of the optimal profit in the centralized setting. This implies that in a substitutable product market, there is limited room for improvement from more elaborate contracts, which are often costly to implement. The opposite happens for complements, where horizontal competition aggravates the double marginalization effect and further deteriorates the chain-wide efficiency. It suggests that large profit gains can be achieved through more complex contracts which coordinate the chain.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"12 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":"121581222","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}
Revenue management is a large and growing practice in industry. It involves much of what economists, computer scientists and applied mathematicians know and love: statistics, optimization, demand modeling and algorithm design. And strategic behavior is clearly of central importance to many pricing decisions. Despite all this, game theory is rarely used in revenue management practice. In this talk, we look at the potential role of game theory in revenue management and what challenges must be overcome to make it viable in practice.
{"title":"Game theory and the practice of revenue management","authors":"G. V. Ryzin","doi":"10.1145/1807406.1807424","DOIUrl":"https://doi.org/10.1145/1807406.1807424","url":null,"abstract":"Revenue management is a large and growing practice in industry. It involves much of what economists, computer scientists and applied mathematicians know and love: statistics, optimization, demand modeling and algorithm design. And strategic behavior is clearly of central importance to many pricing decisions. Despite all this, game theory is rarely used in revenue management practice. In this talk, we look at the potential role of game theory in revenue management and what challenges must be overcome to make it viable in practice.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"91 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":"121802652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics coincide with the network's Wardrop equilibria and form a convex polytope whose dimension is determined by the network's redundancy (an important concept which measures the "linear dependence" of the users' paths). Despite this abundance of stationary points, we show that the long-term behaviour of the replicator dynamics is remarkably simple: every solution orbit converges to a Wardrop equilibrium. On the other hand, a major challenge occurs when the users' delays fluctuate unpredictably due to random external factors. In that case, interior equilibria are no longer stationary, but strict equilibria remain stochastically stable irrespective of the fluctuations' magnitude. In fact, if the network has no redundancy and the users are patient enough, we show that the long-term average of the users' traffic flows converges to the vicinity of an equilibrium, and we also estimate the corresponding invariant distribution.
{"title":"Balancing traffic in networks: redundancy, learning, and the effect of stochastic fluctuations","authors":"P. Mertikopoulos, A. L. Moustakas","doi":"10.1145/1807406.1807408","DOIUrl":"https://doi.org/10.1145/1807406.1807408","url":null,"abstract":"We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics coincide with the network's Wardrop equilibria and form a convex polytope whose dimension is determined by the network's redundancy (an important concept which measures the \"linear dependence\" of the users' paths). Despite this abundance of stationary points, we show that the long-term behaviour of the replicator dynamics is remarkably simple: every solution orbit converges to a Wardrop equilibrium. On the other hand, a major challenge occurs when the users' delays fluctuate unpredictably due to random external factors. In that case, interior equilibria are no longer stationary, but strict equilibria remain stochastically stable irrespective of the fluctuations' magnitude. In fact, if the network has no redundancy and the users are patient enough, we show that the long-term average of the users' traffic flows converges to the vicinity of an equilibrium, and we also estimate the corresponding invariant distribution.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131086284","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}
Peter Bro Miltersen, J. Nielsen, Nikos Triandopoulos
We consider enhancing with privacy concerns a large class of auctions, which include sealed-bid single-item auctions but also general multi-item multi-winner auctions, our assumption being that bidders primarily care about monetary payoff and secondarily worry about exposing information about their type to other players and learning information about other players' types, that is, bidders are greedy then paranoid. To treat privacy explicitly within the game theoretic context, we put forward a novel hybrid utility model that considers both monetary and privacy components in players' payoffs. We show how to use rational cryptography to approximately implement any given ex interim individually strictly rational equilibrium of such an auction without a trusted mediator through a cryptographic protocol that uses only point-to-point authenticated channels between the players. By "ex interim individually strictly rational" we mean that, given its type and before making its move, each player has a strictly positive expected utility. By "approximately implement" we mean that, under cryptographic assumptions, running the protocol is a computational Nash equilibrium with a payoff profile negligibly close to the original equilibrium.
{"title":"Privacy-enhancing auctions using rational cryptography","authors":"Peter Bro Miltersen, J. Nielsen, Nikos Triandopoulos","doi":"10.1145/1807406.1807496","DOIUrl":"https://doi.org/10.1145/1807406.1807496","url":null,"abstract":"We consider enhancing with privacy concerns a large class of auctions, which include sealed-bid single-item auctions but also general multi-item multi-winner auctions, our assumption being that bidders primarily care about monetary payoff and secondarily worry about exposing information about their type to other players and learning information about other players' types, that is, bidders are greedy then paranoid. To treat privacy explicitly within the game theoretic context, we put forward a novel hybrid utility model that considers both monetary and privacy components in players' payoffs. We show how to use rational cryptography to approximately implement any given ex interim individually strictly rational equilibrium of such an auction without a trusted mediator through a cryptographic protocol that uses only point-to-point authenticated channels between the players. By \"ex interim individually strictly rational\" we mean that, given its type and before making its move, each player has a strictly positive expected utility. By \"approximately implement\" we mean that, under cryptographic assumptions, running the protocol is a computational Nash equilibrium with a payoff profile negligibly close to the original equilibrium.","PeriodicalId":142982,"journal":{"name":"Behavioral and Quantitative Game Theory","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115088570","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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