The Gambit Toolkit is a generic game theoretic model for solving extensive and normal form game theoretic models. analyzing general games in extensive or strategy form and computing Nash equilibria and other solution concepts in games.
Gambit is for finite games only. Because of the mathematical structure of finite games, it is possible to write many general- purpose routines for analyzing these games. Thus, Gambit can be used in a wide variety of applications of game theory. However, games that are not finite, that is, games in which players may choose from a continuum of actions, or in which players may have a continuum of types, do not admit the same general-purpose methods.
Gambit is for noncooperative game theory only. Gambit focuses on the branch of game theory in which the rules of the game are written down explicitly, and in which players choose their actions independently. Gambit’s analytical tools center primarily around Nash equilibrium, and related concepts of bounded rationality such as quantal response equilibrium. Gambit does not at this time provide any representations of, or methods for, analyzing games written in cooperative form. (It should be noted that some problems in cooperative game theory do not suffer from the computational complexity that the Nash equilibrium problem does, and thus cooperative concepts could be an interesting future direction of development.
Analyzing large games may become infeasible surprisingly quickly. While the specific formal complexity classes of computing Nash equilibria and related concepts are still an area of active research, it is clear that, in the typical case, the amount of time required to compute equilibria increases rapidly in the size of the game. In other words, it is quite easy to write down games which will take Gambit an unacceptably long amount time to compute the equilibria of. There are two ways to deal with this problem in practice. One way is to better identify good heuristic approaches for guiding the equilibrium computation process. Another way is to take advantage of known features of the game to guide the process. Both of these approaches are now becoming areas of active interest. While it will certainly not be possible to analyze every game that one would like to, it is hoped that Gambit will both contribute to these two areas of research, as well as make the resulting methods available to both students and practitioners.
