A game is a situation that involves two or more decision makers (called players), where (1) each player faces a choice between at least two behavioral options, (2) each player strives to maximize utility (i.e., to achieve the greatest payoff possible), and (3) the payoff obtained by a given player depends not only on the option that he or she chooses but also on the option(s) chosen by the other player(s). In virtually all games, some or all of the players have fully or partially opposing interests; this causes the behavior of players to be proactive and strategic.

The theory of games is a branch of applied mathematics that rigorously treats the topic of optimal behavior in two-person and n-person games. Its origins go back at least to 1710, when the German mathematician-philosopher Leibniz foresaw the need for a theory...