This page contains a few programs about Game Theory, written by students of Frank Thuijsman.
These programs are able to solve various types of games.
- This program, written by Max Buegler (2009), can be used to calculate value and optimal strategies from matrix games as well as equilibria in bimatrix games by means of the Lemke-Howson algorithm. Fictitious play and regret matching are implemented as well. The program can also be used to calculate the Shapley value for cooperative games and, using input form Robbert Harms, it is also possible to examine several types of solutions for bankruptcy problems.
- This program, written by Robbert Harms (2009), can be used to calculate “contested-garment-consistent” solutions to solve bankruptcy problems by means of the method of communicating vessels. A short explanation of this issue can be found in my booklets: “Spelen en Delen” (look here) and in the lecture notes “Introduction to Game Theory” (not yet published).
Relevant original publications on this topic are the following ones:
- B. O’Neill (1982): “a problem of rights arbitration from the Talmud”, Mathematical Social Sciences 2, 345-371.
- R.J. Aumann, M. Maschler (1985): “game theoretic analysis of a bankruptcy problem from the Talmud”, Journal of Economic Theory 36, 195-213.
- M.M. Kaminski (2000): “hydraulic’ rationing”, Mathematical Social Sciences 40, 131-155.