A Genetic Algorithm Approach to Compute Mixed Strategy Solutions for General Stackelberg Games

Stackelberg games have found a role in a number of applications including modeling market competition, identifying traffic equilibrium, developing practical security applications and many others. While a number of solution approaches have been developed for these games in a variety of contexts that use mathematical optimization, analytical analysis or heuristic based solutions, literature has been quite sparse on the usage of Genetic Algorithm (GA) based techniques. In this paper, we develop a GA based solution to compute high quality mixed strategy solution for the leader to commit to, in a General Stackelberg Game (GSG). Our experiments showcase that the GA solution developed here indeed performs well in terms of scalability and provides reasonably good solution quality in terms of the average reward obtained.

[1]  Fernando Ordóñez,et al.  Coordinating resources in Stackelberg Security Games , 2019, Eur. J. Oper. Res..

[2]  Elia Daniele,et al.  Equilibrium strategies via GA to stackelberg games under multiple follower's best reply , 2012, Int. J. Intell. Syst..

[3]  Patrice Marcotte,et al.  An overview of bilevel optimization , 2007, Ann. Oper. Res..

[4]  John Geraghty,et al.  Genetic Algorithm Performance with Different Selection Strategies in Solving TSP , 2011 .

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

[6]  M. Dufwenberg.  Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[7]  Sarit Kraus,et al.  An efficient heuristic approach for security against multiple adversaries , 2007, AAMAS '07.

[8]  Alexandre M. Bayen,et al.  Stackelberg Routing on Parallel Networks With Horizontal Queues , 2012, IEEE Transactions on Automatic Control.

[9]  Kenny Q. Zhu.  Population Diversity in Genetic Algorithm for Vehicle Routing Problem with Time Windows , 2022 .

[10]  Chyi Hwang,et al.  A real-coded genetic algorithm with a direction-based crossover operator , 2015, Inf. Sci..

[11]  Sarit Kraus,et al.  Deployed ARMOR protection: the application of a game theoretic model for security at the Los Angeles International Airport , 2008, AAMAS.

[12]  Kalyanmoy Deb,et al.  A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications , 2017, IEEE Transactions on Evolutionary Computation.

[13]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[14]  Milind Tambe,et al.  Trends and Applications in Stackelberg Security Games , 2018 .

[15]  Sui Ruan,et al.  Patrolling in a Stochastic Environment , 2005 .

[16]  Kalyanmoy Deb,et al.  Efficiently Solving: A Large-Scale Integer Linear Program Using a Customized Genetic Algorithm , 2004, GECCO.

[17]  Gerald G. Brown,et al.  Defending Critical Infrastructure , 2006, Interfaces.

[18]  Marc Parizeau,et al.  DEAP: a python framework for evolutionary algorithms , 2012, GECCO '12.

[19]  Heinrich von Stackelberg.  Market Structure and Equilibrium , 2010 .

[20]  Kalyanmoy Deb,et al.  Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems , 1995, Complex Syst..

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

[22]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[23]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

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

[25]  Timothy W. McLain,et al.  Multiple UAV cooperative search under collision avoidance and limited range communication constraints , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[26]  Pedro Pedroso.  Numerical solution of Nash and Stackelbergequilibria : an evolutionary approachJo , 1996 .

[27]  Martine Labbé,et al.  A study of general and security Stackelberg game formulations , 2019, Eur. J. Oper. Res..

[28]  Sibel Sirakaya,et al.  On-line computation of Stackelberg equilibria with synchronous parallel genetic algorithms , 2003 .