Difficulties in practical application of game theory and a partial solution

Abstract

Much effort has been devoted to development of game theory. However, nontrivial practical applications of discrete game theory are few. One reason may be difficulties in evaluating payoff matrices. Another reason may be the very limited extent of situations for which game solutions of a 'forcing' nature have been developed. That is, the solutions control what the players can do, according to some reasonable criterion (such as expected payoff received) rather than merely trying to predict what they will do. A third reason may be that very little has been developed for situations where the - numbers in a payoff matrix do not satisfy the arithmetic operations. As ah example, this occurs for the practically important case where the ranks of the payoff values are the numbers in a payoff matrix. These three restraints on game theory use are discussed here. Then, attention is directed to a new form of game theory, based on median (rather than expected value) considerations, that is much less sensitive to these restraints.