MEDIAN TWO-PERSON GAME THEORY AND EXAMPLES OF ITS FLEXIBILITY IN APPLICATIONS.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Considered is discrete two-person game theory where the players choose their strategies independently. Use of mixed strategies introduces probabilistic aspects, so that the payoff to a player has a probability distribution. Determination of optimum strategies is simplified when only some reasonable representative value is considered for a distribution. The distribution mean is used for this purpose in expected-value game theory. Another reasonable choice is the distribution median, and this is the basis for median game theory. Median game theory has huge application advantages over expected-value game theory. Payoffs of a very general nature are allowable for median game theory some payoffs may not even be numbers. Also, optimum solutions are obtainable for virtually all games. These solutions are obtained through orderings of the outcomes of the game pairs of payoffs, one to each player according to desirability, with each player doing a separate ordering. The paper first provides an introduction to median game theory and then gives the generally applicable solution, which depends on choices of relative desirability functions by the two players to order the outcomes. Finally, to illustrate the flexibility of median game theory, there is a discussion including some examples about considerations in selection of relative desirability functions. Author
- Operations Research