Mathematical models and properties of games

Games are a decision process under competition where opponent players compete for the maximum gain or a success state in the same environment according to the same rules of the game. Games are conventionally dealt with payoff tables based on random strategies that are found inadequate to describe the dynamic behaviors of games and to rigorously predict the outcomes of games. This paper presents a formal treatment of games by a set of mathematical models for both the layouts and behaviors of games. A formal model of games is introduced, based on which the properties of games in terms of decision strategies and serial matches are described. A wide range of generic zero-sum and nonzero-sum games are formally modeled and analyzed using the mathematical models of games.