Computation of Stackelberg Equilibria of Finite Sequential Games

The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player 1 (the leader) first commits to a strategy that is publicly announced, then Player 2 (the follower) plays a best response to the leader’s choice. We study the problem of computing Stackelberg equilibria in finite sequential (i.e., extensive-form) games and provide new exact algorithms, approximation algorithms, and hardness results for finding equilibria for several classes of such two-player games.

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

[2]  Federico Etro,et al.  Stackelberg Competition with Endogenous Entry , 2008 .

[3]  Haifeng Xu,et al.  Exploring Information Asymmetry in Two-Stage Security Games , 2015, AAAI.

[4]  J.P.M. Hurkens,et al.  Endogenous Stackelberg leadership , 1999 .

[5]  Christos H. Papadimitriou,et al.  The Game World Is Flat: The Complexity of Nash Equilibria in Succinct Games , 2006, ICALP.

[6]  Rabah Amir,et al.  Stackelberg versus Cournot Equilibrium , 1999 .

[7]  Vincent Conitzer,et al.  Commitment to Correlated Strategies , 2011, AAAI.

[8]  Vincent Conitzer,et al.  Computing Optimal Strategies to Commit to in Stochastic Games , 2012, AAAI.

[9]  Branislav Bosanský,et al.  Using Correlated Strategies for Computing Stackelberg Equilibria in Extensive-Form Games , 2016, AAAI.

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

[11]  MasumHassan Review of Computational Geometry: Algorithms and Applications (2nd ed.) by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf , 2000 .

[12]  Paul W. Goldberg,et al.  The Complexity of Computing a Nash Equilibrium , 2009, SIAM J. Comput..

[13]  Toshihiro Matsumura Stackelberg Mixed Duopoly with a Foreign Competitor , 2003 .

[14]  Xiaotie Deng,et al.  Settling the complexity of computing two-player Nash equilibria , 2007, JACM.

[15]  Sven Schewe,et al.  Making the Best of Limited Memory in Multi-Player Discounted Sum Games , 2014, GandALF.

[16]  Milind Tambe,et al.  Security and Game Theory - Algorithms, Deployed Systems, Lessons Learned , 2011 .

[17]  Peter Gritzmann,et al.  Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Basis , 1993, SIAM J. Discret. Math..

[18]  Bernhard von Stengel,et al.  Extensive-Form Correlated Equilibrium: Definition and Computational Complexity , 2008, Math. Oper. Res..

[19]  Jakub Černý,et al.  Stackelberg Extensive-Form Correlated Equilibrium with Multiple Followers , 2022 .

[20]  Joshua Letchford,et al.  Computational Aspects of Stackelberg Games , 2013 .

[21]  Hanif D. Sherali,et al.  A Multiple Leader Stackelberg Model and Analysis , 1984, Oper. Res..

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

[23]  Anshul Gupta,et al.  Equilibria in finite games , 2016 .

[24]  Noa Agmon,et al.  Making the Most of Our Regrets: Regret-Based Solutions to Handle Payoff Uncertainty and Elicitation in Green Security Games , 2015, GameSec.

[25]  Vincent Conitzer,et al.  Computing optimal strategies to commit to in extensive-form games , 2010, EC '10.

[26]  Jonathan H. Hamilton,et al.  Endogenous timing in duopoly games: Stackelberg or cournot equilibria , 1990 .

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

[28]  Branislav Bosanský,et al.  Sequence-Form Algorithm for Computing Stackelberg Equilibria in Extensive-Form Games , 2015, AAAI.