计量经济分析 = Econometric analysis

A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

A Course in Game Theory

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Convex Analysisの二,三の進展について

Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

Learning by observing the past decisions of others can help explain some otherwise puzzling phenomena about human behavior. For example, why do people tend to converge on similar behavior? Why is mass behavior prone to error and fads? The authors argue that the theory of observational learning, and particularly of informational cascades, has much to offer economics, business strategy, political science, and the study of criminal behavior.

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Learning from the behavior of others : conformity, fads, and informational cascades

In Becker's (1973) neoclassical marriage market model, matching is positively assortative if types are complements: i.e., match output f(x, y) is suipermoddlar in x and y. We reprise this famous result assuming time-intensive partner search and transferable output. We prove existence of a search equilibrium with a continuum of types, and then characterize matching. After showing that Becker's conditions on match output no longer suffice for assortative matching, we find sufficient conditions valid for any search frictions and type distribution: supermodularity not only of output f, but also of log f, and log f Symmetric submodularity conditions imply negatively assortative matching. Examples show these conditions are necessary.

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Assortative Matching and Search

This paper explores how Bayes-rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type-specific ‘‘herds’’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type’s actions forever nontrivially split between two actions. To verify that our identified limit outcomes do arise, we exploit the Markov-martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.

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Pathological outcomes of observational learning

In his theory of marriage, Becker (1973) showed that assortative matching arises with either (i) supermodular productive interaction and transferable utility, or (ii)monotonic production with nontransferable utility (NTU). In an exploration of the latter NTU matching model, this paper shows how productive interaction again matters if finding partners requirestiming-consuming search. I show that the reason is that one must consider the value of everyone's time. Assume that type x earns f(x; y) when matched with y, with higher types preferred (fy 0). When f(x2; y2 )f(x1; y1 )f(x2; y1 )f(x1; y2 ), all von Neumann-Morgenstern preferences over matches coincide, and perfect segregation, or equivalence classes, arises. This observation then motivates my main proposition that in any search equilibrium and for all atomless type distributions, matching is positively assortative [i.e. the set of types with whom x matches is increasing in x] when f is log-supermodular: f(x2; y2 )f(x1; y1 )f(x2; y1 )f(x1; y2 ) for x2 x1; y2 y1.

The Marriage Model with Search Frictions

WE ARE CONCERNED here with perfect "folk theorems" for infinitely repeated games with complete information. Folk theorems assert that any feasible and individually rational payoff vector of the stage game is a (subgame perfect) equilibrium payoff in the associated infinitely repeated game with little or no discounting (where payoff streams are evaluated as average discounted or average values respectively). It is obvious that feasibility and individual rationality are necessary conditions for a payoff vector to be an equilibrium payoff. The surprising content of the folk theorems is that these conditions are also (almost) sufficient. Perhaps the first folk theorem type result is due to Friedman (1971) who showed that any feasible payoff which Pareto dominates a Nash equilibrium payoff of the stage game will be an equilibrium payoff in the associated repeated game with sufficiently patient players. This kind of result is sometimes termed a "Nash threats" folk theorem, a reference to its method of proof. For the more permissive kinds of folk theorems considered here, the seminal results are those of Aumann and Shapley (1976) and Rubinstein (1977, 1979). These authors assume that payoff streams are undiscounted.2 Fudenberg and Maskin (1986) establish an analogous result for discounted repeated games as the discount factor goes to 1. Their result uses techniques of proof rather different from those used by Aumann-Shapley and Rubinstein, respectively. See their paper for an insightful discussion of this point, and quite generally for more by way of background. It is a key reference for subsequent work in this area, including our own. For the two-player case, the result of Fudenberg and Maskin (1986) is a complete if and only if characterization (modulo the requirement of strict rather than weak individual rationality, which we retain in this note) and does not employ additional conditions. For three or more players Fudenberg and Maskin introduced a full dimensionality condition: The convex hull F, of the set of feasible payoff vectors of the stage game must have dimension n (where n is the number of players), or equivalently a nonempty interior. This condition has been widely adopted in proving folk theorems for related environments such as finitely repeated games (Benoit and Krishna (1985)), and overlapping generations games (Kandori (1992), Smith (1992)). Full dimensionality is a sufficient condition. Fudenberg and Maskin present an example of a three-player stage game in which the conclusion of the folk theorem is false. In this example all players receive the same payoffs in all contingencies; the (convex hull of the) set of feasible payoffs is one-dimensional. This example violates full dimensionality in a rather extreme way. Less extreme violations may also lead to

The folk theorem for repeated games: a neu condition'

Consider a heterogeneous agent matching model in which the payoff of each matched individual is a fixed function of both partners’ types. In a 1973 article, Becker showed that assortative matching arises in a frictionless setting simply if everyone prefers higher partners. This paper shows that if finding partners requires time‐consuming search and individuals are impatient, then productive interaction matters. Matching is positively assortative—higher types match with higher sets of types—when the proportionate gains from having better partners rise in one’s type. With multiplicatively separable payoffs, these proportionate gains are constant in one’s type, and “block segregation” arises, a common finding of the literature.

https://www.jstor.org/stable/10.1086/510440

Lones Smith

Papers

Assortative Matching and Search

Pathological outcomes of observational learning

The Marriage Model with Search Frictions

The folk theorem for repeated games: a neu condition'

The Marriage Model with Search Frictions