Distributional Strategies for Games with Incomplete Information

We study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game-theoretic models. Using the notion of “distributional” strategies, we prove four main theorems: (i) a mixed-strategy Nash equilibrium existence theorem, (ii) a pure-strategy equilibrium existence theorem, (iii) a pure-strategy (epsilon)-equilibrium existence theorem, and (iv) a theorem describing how the set of equilibria of a game varies with the parameters of the game.

[1]  P. Milgrom.  The Structure Of Information In Competitive Bidding , 1978 .

[2]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[3]  Paul R. Milgrom,et al.  Competitive Bidding and Proprietary Information , 1983 .

[4]  Robert J . Aumann,et al.  28. Mixed and Behavior Strategies in Infinite Extensive Games , 1964 .

[5]  Robert B. Wilson.  A Bidding Model of Perfect Competition , 1977 .

[6]  Roy Radner,et al.  Private Information and Pure-Strategy Equilibria , 1982, Math. Oper. Res..

[7]  R. Aumann.  Subjectivity and Correlation in Randomized Strategies , 1974 .

[8]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[9]  J. Wolfowitz,et al.  Elimination of Randomization in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games , 1951 .

[10]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[11]  Robert J. Weber,et al.  Topologies on Information and Strategies in Games with Incomplete Information , 1981 .

[12]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

[13]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[14]  Paul R. Milgrom,et al.  The value of information in a sealed-bid auction , 1982 .

[15]  R. Selten.  The chain store paradox , 1978 .

[16]  Paul R. Milgrom,et al.  LIMIT PRICING AND ENTRY UNDER INCOMPLETE INFORMATION: AN EQUILIBRIUM ANALYSIS' , 1982 .

[17]  Paul R. Milgrom,et al.  Rational Expectations, Information Acquisition, and Competitive Bidding , 1981 .

[18]  R BELLMAN,et al.  Some two person games involving bluffing. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Paul R. Milgrom,et al.  Predation, reputation, and entry deterrence☆ , 1982 .

[20]  J. M. Smith,et al.  The war of attrition with random rewards. , 1978, Journal of theoretical biology.

[21]  J. Wolfowitz,et al.  Relations among certain ranges of vector measures , 1951 .

[22]  David M. Kreps,et al.  Reputation and imperfect information , 1982 .

[23]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[24]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[25]  R. Selten.  Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[26]  J. Harsanyi.  Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points , 1973 .

[27]  I. Glicksberg.  A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS , 1952 .

[28]  K. Fan.  Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces. , 1952, Proceedings of the National Academy of Sciences of the United States of America.