Representing and Reasoning with Large Games

In the last decade, there has been much research at the interface of computer science and game theory. One important class of problems at this interface is the computation of solution concepts (such as Nash equilibrium or correlated equilibrium) of a finite game. In order to take advantage of the highly-structured utility functions in games of practical interest, it is important to design compact representations of games as well as efficient algorithms for computing solution concepts on such representations. In this thesis I present several novel contributions in this direction: The design and analysis of Action-Graph Games (AGGs), a fully-expressive modeling language for representing simultaneous-move games. We propose a polynomial-time algorithm for computing expected utilities given arbitrary mixed strategy profiles, and leverage the algorithm to achieve exponential speedups of existing algorithms for computing Nash equilibria. Designing efficient algorithms for computing pure-strategy Nash equilibria in AGGs. For symmetric AGGs with bounded treewidth our algorithm runs in polynomial time. Extending the AGG framework beyond simultaneous-move games. We propose Temporal Action-Graph Games (TAGGs) for representing dynamic games and Bayesian Action-Graph Games (BAGGs) for representing Bayesian games. For certain subclasses of TAGGs and BAGGs we gave efficient algorithms for equilibria that achieve exponential speedups over existing approaches. Efficient computation of correlated equilibria. In a landmark paper, Papadim-