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Non-cooperative games are mathematical models of interactive strategic decision situations.In contrast to cooperative models, they build on the assumption that all possibilities for commitment and contract have been incorporated in the rules of the game.This contribution describes the main models (games in normal form, and games in extensive form), as well as the main concepts that have been proposed to solve these games.Solution concepts predict the outcomes that might arise when the game is played by "rational" individuals, or after learning processes have converged.Most of these solution concepts are variations of the equilibrium concept that was proposed by John Nash in the 1950s, a Nash equilibrium being a combination of strategies such that no player can improve his payoff by deviating unilaterally.The paper also discusses the justifications of these concepts and concludes with remarks about the applicability of game theory in contexts where players are less than fully rational.

We describe non-cooperative game models and discuss game theoretic solutionconcepts. Some applications are also noted. Conventional theory focuses on thequestion ‘how will rational players play?’, and has the Nash equilibrium at its core.We discuss this concept and its interpretations, as well as refinements (perfect andstable equilibria) and relaxations (rationalizability and correlated equilibria).Motivated by experiments that show systematic theory violations, behavioral gametheory aims to integrate insights from psychology to get better answers to thequestion ‘how do humans play?’. We provide an overview of the observedregularities and briefly sketch (beginnings of) theories of boundedly rational play.