GENERALLY APPLICABLE SOLUTIONS FOR TWO-PERSON MEDIAN GAME THEORY.
John Evangelist Walsh · NASA STI Repository (National Aeronautics and Space Administration) · 1969
Two-person median game theory has application advantages over expected-value game theory.For example, median game theory is usable when the values in one or both payoff matrices do not satisfy the arithmetical operations (but can be ranked within each matrix).Also, the class of games where the players have optimum solutions is huge compared to (and includes) this class for expected-value game theory.Moreover, there is a much larger class where one player, but not necessarily the other, has an optimum solution (no expected-value analogue occurs).The overwhelmingly large class of median games, however, is that where at least one player does not have an optimum solution.That is, for one or both players, no strategy exists (pure or mixed) such that the player can simultaneously be as protective as possible for himself and as vindictive as possible toward the other player.To reasonably resolve such situations a "relative desirability" function, suitably chosen, is used to order pairs of payoffs, a payoff to each player, that occur for some of the combinations of pure strategies (according to increasing desirability to the player considered).This provides the basis for a compromise "optimum" solution and identification of a corresponding "optimum" strategy.