Vision

Here is the "vision" of what we want to achieve with the Gambit open source project:

Game theory is the formal study of interactive behaviour. It is central to economic theory, and applied across a variety of fields from political science to computing and biology. The long-term vision of this project is to build a web portal where users can with maximum ease create games - models of interactive decisions - with the tools of game theory, and obtain the theoretical predictions for the model "at a mouseclick".

The potential users of this portal should eventually include people who are not familiar with game theory. They would be introduced to the field with explanations, examples, and invited to "play" with games that they can create as models of interactive situations.

However, to get started, the portal is directed at people who are familiar with game theory, at least to some extent, such as researchers and students in economics, for example. They should not have to be experts in algorithms for solving games.

A game is a mathematical of an interactive situation. The most common models (of "non-cooperative" game theory) are games in extensive form, with a game tree and information sets representing possibly imperfect information of a player about the game state, and games in strategic (or "normal") form, which is a table listing each player's strategies and the resulting payoff to each player resulting from each strategy profile (a profile lists one strategy for each player).

The analysis of a game is given by a solution concept known as equilibrium, the most important of which is the Nash equilibrium (NE). An NE is a strategy profile so that no player can profit by "unilaterally deviating", that is, by changing their own strategy, assuming the other players play their strategies as prescribed by the profile. A game has always at least one NE if players are allowed to use mixed strategies, which are active randomizations over the given strategies. Finding one or all NE is not easy, and can take considerable time and effort.

A computer program for finding NE of a game is of particular interest for the applied or experimental economist who wants to find the theoretical prediction of her model in order to compare it with empirical or experimental results, and possibly vary the parameters of the model in order to improve it.

So, our typical "customer" is someone who knows what a game is, and wants to know its equilibria. The game should be easy to input, possibly by altering a previously used game, and the analysis - computing equilibria - should not be complicated to obtain.

A web interface with a nice GUI seems to offer the easiest entry route, which seems particularly suitable for entering and manipulating game trees. Alternatively, the input might be a table of payoffs that the user has generated, which might be copied as a whole into a suitable box on a web form. This would mean entering the strategic form of the game, and starting the computation with a mouseclick. An example of this is Rahul Savani's webpage Solve a Bimatrix Game.

The primary purpose of the portal is to provide useful tools for game-theoretic analysis. The outputs of this research tool should be scholarly valid in the sense that others can reproduce the computation. This requires retrieving the data and reproducing the computation. Moreover, researchers (including those that develop algorithms for solving games) may want to demonstrate their computational experiments on a larger number of examples, and so we want to offer interfaces to store their examples, and possibly the corresponding code, as well as testing the computations themselves which may take a long time on a single machine. The challenge here would be to use cloud computing to allow for these multiple computations, and suitable databases and their manipulation and representation to demonstrate the experiments themselves.

From this, several projects arise:

• Design of user-friendly portal as a webpage for the "customer" of our software for game manipulation and analysis. This should be separate from the development webpage under github, which is for coders, not users.

• Extending the existing code with a GUI for extensive games (gte, Game Theory Explorer).

• Improving Rahul's Nash equilibrium webpage for bimatrix games: Larger number of strategies, finding single equilibria by Lemke-Howson or other path-following methods which is typically much quicker than complete enumeration for larger games.

• For people who want to systematically generate various games, improving Gambit's capabilities in a downloadable version that also offers a "command language" for generating games.

• An integration between the downloadable Gambit version and the web input version, the latter of which has to be developed anyhow.