We have seen that Nash equilibria in two-player zero-sum games (and generalizations thereof) are polynomial-time tractable from a centralized computation perspective. We have also seen that the payoff matrix of a zero-sum game determines a unique value for the row player and a unique value for the column player (summing to zero), which specify their payoffs in all equilibria of the game. In thi...

Matching Pennies is a well-known example of a two player, zero-sum game. In this game, each of the players, the matcher and the mismatcher, flips a coin, and the payoffs are determined as follows. If the coins come up matching (i.e., both heads or both tails), then the matcher wins, so the mismatcher pays the matcher the sum of $1. If the coins do not match (i.e., one head and one tail), then t...

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,...

It is known that the value of a zero-sum infinitely repeated game with incomplete information on both sides need not exist [1]. It is proved that any number between the minmax and the maxmin of the zero-sum infinitely repeated game with incomplete information on both sides is the value of the long finitely repeated game where players’ information about the uncertain number of repetitions is asy...

In 1954, O.G. Haywood used game theory to analyze the military decisions used in the Battle of the Bismarck Sea, a battle fought during the World War II. Haywood analyzed the Battle of the Bismarck Sea by using a two-person zero-sum game [1]. This paper discusses the fundamental concepts of the two-person zero-sum game and some Nash Equilibrium dominance ideas as well as the strategies applied ...

Joyal’s categorical construction on (well-founded) Conway games and winning strategies provides a compact closed category, where tensor and linear implication are defined via Conway disjunctive sum (in combination with negation for linear implication). The equivalence induced on games by the morphisms coincides with the contextual closure of the equideterminacy relation w.r.t. the disjunctive s...

In 1951, Dantzig [3] showed the equivalence of linear programming and two-person zero-sum games. However, in the description of his reduction from linear programming to zero-sum games, he noted that there was one case in which his reduction does not work. This also led to incomplete proofs of the relationship between the Minmax Theorem of game theory and the Strong Duality Theorem of linear pro...