Consider a two-person general-sum game on n × n payoff random matrices A and B with iid continuous entries, for large n. It is shown that the probability that there exists a pure strategy Nash equilibrium that is not pure Pareto optimal remains bounded away from 0 and 1 as n increases. We also consider the number of mixed strategy Nash equilibria: It is shown that for a mixed strategy Nash equi...

In this paper we study the nonzero-sum Dynkin game in continuous time, which is a two-player noncooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.

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 ...