In non-cooperative games, players make decisions independently and are unable to make any collaboration contracts with other players in the game. Therefore, a family of non-cooperative games is presented in which players do not cooperate and selfishly select a strategy that maximizes their own utility. Initially, traditional applications of game theory developed from these games. There are various kinds of non-cooperative games.
Static Game
If all players select their strategy simultaneously, without knowledge of the other players’ strategies, these games are called static games. Sometimes, static games are also called strategic games, one-shot games, single stage games or simultaneous games. Traditionally, static games are represented by the normal form; if two players play a static game, it can be represented in a matrix format. Each element represents a pair of payoffs when a certain combination of strategies in used. Therefore, these games are called matrix games or coordination games.
One example of matrix games is the stag hunt game (Skyrms, 2004). In this game situation, two hunters go out on a hunt. Each can individually choose to hunt a stag or a hare. Each hunter must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation. Therefore, the stag hunt game is used to describe a conflict between safety and social cooperation. Formally, the payoff matrix for the stag hunt is pictured in Table 1, where A (a) > B (b) ≥ D (d) > C (c).
Table 1. Sample matrix for the prisoners' payoffs
| Stag | Hare |
| Stag | A, a (e.g., 2,2) | C, b (e.g., 0,1) |
| Hare | B, c (e.g., 1,0) | D, d (e.g., 1,1) |
A solution concept for static games is Nash equilibrium. In the stag hunt game, there are two Nash equilibria when both hunters hunt a stag and both hunters hunt a hare. Sometimes, like as the Prisoner's Dilemma, an equilibrium is not an efficient solution despite that players can get a Pareto efficient solution. Due to this reason, many researchers focus on how to drive a game where players have a non-cooperative behavior to an optimal outcome.