Game theory is a huge area of mathematical (and economical) research. We restrict ourselves mainly to two person zero-sum games, in which you make a decision and your opponent makes a decision (no cooperation allowed!), and your winnings equal your opponents loss. The main result is the so-called minimax theorem. Essentially, game theory is about playing against a (possibly) better player and e...

When a zero-sum game is played once, a risk-neutral player will want to maximize his expected outcome in that single play. However, if that single play instead only determines how much one player must pay to the other, and the same game must be played again, until either player runs out of money, optimal play may differ. Optimal play may require using different strategies depending on how much ...

In the case of two individuals in a competitive situation, or “game,” the game itself (i.e. the players, the rules, the equipment) can be considered to constitute a distributed cognitive system. However, the dominant model of competitive behavior is game theory (VonNeumann & Morgenstern, 1944), which has traditionally treated individuals as isolated units of cognition. By simulating game playin...

We provide a computable algorithm to calculate uniform ε-optimal strategies in two-player zero-sum stochastic games. Our approach can be used to construct algorithms that calculate uniform ε-equilibria and uniform correlated ε-equilibria in various classes of multi-player non-zero-sum stochastic games. JEL codes: C63, C73.

We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game.

We study collective choices from the revealed preference theory viewpoint. For every product set of individual actions, joint choices are called Nash-rationalizable if there exists a preference relation for each player such that the selected joint actions are Nash equilibria of the corresponding game. We characterize Nash-rationalizable joint choice behavior by zero-sum games, or games of confl...

In this paper, we consider an interval matrix game with interval valued payoffs, which is the generation of the traditional matrix game. The “saddle-points”of this interval matrix game are defined and characterized as equilibrium points of corresponding non-zero sum parametric games. Numerical examples are given to illustrate our idea. These results are extended to the fuzzy matrix games. Also,...