Computing optimal strategies to commit to in extensive-form games

Computing optimal strategies to commit to in general normal-form or Bayesian games is a topic that has recently been gaining attention, in part due to the application of such algorithms in various security and law enforcement scenarios. In this paper, we extend this line of work to the more general case of commitment in extensive-form games. We show that in some cases, the optimal strategy can be computed in polynomial time; in others, computing it is NP-hard.

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

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

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

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

[5]  H. W. Kuhn,et al.  11. Extensive Games and the Problem of Information , 1953 .

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

[7]  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).

[8]  Vincent Conitzer,et al.  Learning and Approximating the Optimal Strategy to Commit To , 2009, SAGT.

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

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

[11]  H PapadimitriouChristos,et al.  The complexity of computing a Nash equilibrium , 2009 .

[12]  Augustin M. Cournot.  Cournot, Antoine Augustin: Recherches sur les principes mathématiques de la théorie des richesses , 2019, Die 100 wichtigsten Werke der Ökonomie.

[13]  Milind Tambe,et al.  Security and Game Theory: IRIS – A Tool for Strategic Security Allocation in Transportation Networks , 2011, AAMAS 2011.

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

[15]  Manish Jain,et al.  Computing optimal randomized resource allocations for massive security games , 2009, AAMAS.

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

[17]  Bernhard von Stengel,et al.  Leadership games with convex strategy sets , 2010, Games Econ. Behav..

[18]  Vincent Conitzer,et al.  Complexity of Computing Optimal Stackelberg Strategies in Security Resource Allocation Games , 2010, AAAI.

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

[20]  D. Koller,et al.  Finding mixed strategies with small supports in extensive form games , 1996 .