Learning and Approximating the Optimal Strategy to Commit To

Computing optimal Stackelberg strategies in general two-player Bayesian games (not to be confused with Stackelberg strategies in routing games) is a topic that has recently been gaining attention, due to their application in various security and law enforcement scenarios. Earlier results consider the computation of optimal Stackelberg strategies, given that all the payoffs and the prior distribution over types are known. We extend these results in two different ways. First, we consider learning optimal Stackelberg strategies. Our results here are mostly positive. Second, we consider computing approximately optimal Stackelberg strategies. Our results here are mostly negative.

[1]  Michael Maschler,et al.  A price leadership method for solving the inspector's non-constant-sum game , 1966 .

[2]  Sarit Kraus,et al.  Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games , 2008, AAMAS.

[3]  Eitan Zemel,et al.  Nash and correlated equilibria: Some complexity considerations , 1989 .

[4]  Xiaotie Deng,et al.  Settling the Complexity of Two-Player Nash Equilibrium , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[5]  F. Scherer,et al.  Heinrich von Stackelberg’s Marktform und Gleichgewicht , 1996 .

[6]  B. Stengel,et al.  Leadership with commitment to mixed strategies , 2004 .

[7]  Tim Roughgarden,et al.  Stackelberg scheduling strategies , 2001, STOC '01.

[8]  Tim Roughgarden.  Stackelberg Scheduling Strategies , 2004, SIAM J. Comput..

[9]  Martin Shubik.  Antoine Augustin Cournot , 1989 .

[10]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[11]  A. Cournot.  Researches into the Mathematical Principles of the Theory of Wealth , 1898, Forerunners of Realizable Values Accounting in Financial Reporting.

[12]  Vincent Conitzer,et al.  New complexity results about Nash equilibria , 2008, Games Econ. Behav..

[13]  Paul W. Goldberg,et al.  The complexity of computing a Nash equilibrium , 2006, STOC '06.

[14]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[15]  David Zuckerman,et al.  Electronic Colloquium on Computational Complexity, Report No. 100 (2005) Linear Degree Extractors and the Inapproximability of MAX CLIQUE and CHROMATIC NUMBER , 2005 .

[16]  Sarit Kraus,et al.  Bayesian stackelberg games and their application for security at Los Angeles international airport , 2008, SECO.

[17]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[18]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Felix A. Fischer,et al.  Commitment and extortion , 2007, AAMAS '07.

[20]  Sarit Kraus,et al.  Using Game Theory for Los Angeles Airport Security , 2009, AI Mag..

[21]  David Zuckerman.  Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number , 2007, Theory Comput..