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In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory and/or computer assistance.
An important notion in combinatorial game theory is that of the solved game. For example, tic-tac-toe is considered a solved game, as it can be proven that any game will result in a draw if both players play optimally. Deriving similar results for games with rich combinatorial structures is difficult.
The Hobbesian trap (or Schelling's dilemma) is a theory that explains why preemptive strikes occur between two groups, out of bilateral fear of an imminent attack. Without outside influences, this situation will lead to a fear spiral (catch-22, vicious circle, Nash equilibrium) in which fear will lead to an arms race which in turn will lead to increasing fear.
The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well. [ 67 ] Although pre-twentieth-century naturalists such as Charles Darwin made game-theoretic kinds of statements, the use of game-theoretic analysis in biology began with Ronald Fisher 's ...
In game theory, trembling hand perfect equilibrium is a type of refinement of a Nash equilibrium that was first proposed by Reinhard Selten. [1] A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or tremble, may choose unintended strategies, albeit with negligible ...
The first game theory model of fighting is known as the hawk-dove game. This model pits a hawk strategy (always try to injure your opponent and only withdraw from the contest if an injury is received) against a dove strategy (always use a non-injurious display if the rival is another dove and always withdraw if the rival is a hawk).
The free money game is an example of a "special" game with an even number of equilibria. In it, two players have to both vote "yes" rather than "no" to get a reward and the votes are simultaneous. There are two pure-strategy Nash equilibria, (yes, yes) and (no, no), and no mixed strategy equilibria, because the strategy "yes" weakly dominates "no".