Computing the optimal strategy to commit to

In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are selected simultaneously.The recent surge in interest in computing game-theoretic solutions has so far ignored leadership models (with the exception of the interest in mechanism design, where the designer is implicitly in a leadership position). In this paper, we study how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normal-form and Bayesian games. We give both positive results (efficient algorithms) and negative results (NP-hardness results).

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

[2]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .

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

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

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

[6]  Steven Vajda,et al.  Games and Decisions. By R. Duncan Luce and Howard Raiffa. Pp. xi, 509. 70s. 1957. (J Wiley & Sons) , 1959, Mathematical Gazette.

[7]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[8]  D. Knuth,et al.  A note on strategy elimination in bimatrix games , 1988 .

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

[10]  D. Koller,et al.  The complexity of two-person zero-sum games in extensive form , 1992 .

[11]  Eitan Zemel,et al.  The Complexity of Eliminating Dominated Strategies , 1993, Math. Oper. Res..

[12]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[13]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[14]  Michael L. Littman,et al.  Graphical Models for Game Theory , 2001, UAI.

[15]  Christos H. Papadimitriou,et al.  Algorithms, Games, and the Internet , 2001, ICALP.

[16]  Moshe Tennenholtz,et al.  Local-Effect Games , 2003, IJCAI.

[17]  Peter Stone,et al.  A polynomial-time nash equilibrium algorithm for repeated games , 2003, EC '03.

[18]  Aranyak Mehta,et al.  Playing large games using simple strategies , 2003, EC '03.

[19]  Vincent Conitzer,et al.  Complexity Results about Nash Equilibria , 2002, IJCAI.

[20]  A. Cournot.  Mathematical Principles of the Theory of Wealth , 2004 .

[21]  Kevin Leyton-Brown,et al.  Computing Nash Equilibria of Action-Graph Games , 2004, UAI.

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

[23]  Yoav Shoham,et al.  Run the GAMUT: a comprehensive approach to evaluating game-theoretic algorithms , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[24]  Vincent Conitzer,et al.  A Generalized Strategy Eliminability Criterion and Computational Methods for Applying It , 2005, AAAI.

[25]  Vincent Conitzer,et al.  Mixed-Integer Programming Methods for Finding Nash Equilibria , 2005, AAAI.

[26]  Vincent Conitzer,et al.  Complexity of (iterated) dominance , 2005, EC '05.

[27]  Yoav Shoham,et al.  Simple search methods for finding a Nash equilibrium , 2004, Games Econ. Behav..