Description of median game theory with examples of competitive and median competitive games

Abstract

Random selection of strategies greatly extends the opportunity to develop optimum strategies for discrete two-person games, A consequence, however, is that the payoffs received by the players can have probability distributions, which complicates the determination of optimum strategies. This problem can be greatly simplified by only considering some reasonable type of « representative value » for a distribution. The expected-value approach uses the distribution mean. The distribution median is another reasonable possibility. For the common situation where the players behave competitively, a form of game theory is developed by applying the median approach to the payoffs for each player. This form of median game theory has very desirable properties with respect to effort needed for application and, compared to expected-value game theory, strong advantages with respect to generality of application, for example, the payoffs can be of a very general nature. A player has an optimum strategy when the game is one player median competitive (OPMC) for him. A game is median competitive when it is OPMC for both players. Competitive games are an important subclass of median competitive games wherein nondecreasing desirability of the payoffs for one player corresponds to nonincreasing desirability of the payoffs to the other player. This paper contains an introduction to median game theory and examples of competitive, OPMC for one player, and median competitive games.