Introduction to Game-theory Calculations

Abstract

Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent and rational decision makers (Myerson 1991). Game-theory concepts apply in economy, sociology, biology, and health care, and whenever the actions of several agents (individuals, groups, or any combination of these) are interdependent. We present a new command gamet to represent the extensive form (game tree) and the strategic form (payoff matrix) of a noncooperative game and to identify the solution of a nonzero and zero-sum game through dominant and dominated strategies, iterated elimination of dominated strategies, and Nash equilibrium in pure and fully mixed strategies. Further, gamet can identify the solution of a zero-sum game through maximin criterion and the solution of an extensive form game through backward induction.