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  2. Best response - Wikipedia

    en.wikipedia.org/wiki/Best_response

    In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given. [1] The concept of a best response is central to John Nash's best-known contribution, the Nash equilibrium, the point at which each player in a game has selected the best response (or one of the best responses) to the other players ...

  3. Outcome (game theory) - Wikipedia

    en.wikipedia.org/wiki/Outcome_(game_theory)

    In a Prisoner's Dilemma game between two players, player one and player two can choose the utilities that are the best response to maximise their outcomes. "A best response to a coplayer’s strategy is a strategy that yields the highest payoff against that particular strategy". [9] A matrix is used to present the payoff of both players in the ...

  4. Nash equilibrium - Wikipedia

    en.wikipedia.org/wiki/Nash_equilibrium

    In game theory, the Nash equilibrium is the most commonly-used solution concept for non-cooperative games.A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). [1]

  5. Game theory - Wikipedia

    en.wikipedia.org/wiki/Game_theory

    Game theory is the study of mathematical models of strategic interactions. [1] ... (and therefore the best response to any possible opponent strategy), ...

  6. Matching pennies - Wikipedia

    en.wikipedia.org/wiki/Matching_pennies

    In this way, each player makes the other indifferent between choosing heads or tails, so neither player has an incentive to try another strategy. The best-response functions for mixed strategies are depicted in Figure 1 below: Figure 1. Best response correspondences for players in the matching pennies game. The leftmost mapping is for the Even ...

  7. Strong Nash equilibrium - Wikipedia

    en.wikipedia.org/wiki/Strong_Nash_equilibrium

    If x is not an SNE, the condition requires that one can move to a different strategy-profile which is a social-welfare-best-response for all coalitions simultaneously. For example, consider a game with two players, with strategy spaces [1/3, 2] and [3/4, 2], which are clearly compact and convex. The utility functions are: u1(x) = - x1 2 + x2 + 1

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  9. Solution concept - Wikipedia

    en.wikipedia.org/wiki/Solution_concept

    A Nash equilibrium is a strategy profile (a strategy profile specifies a strategy for every player, e.g. in the above prisoners' dilemma game (cooperate, defect) specifies that prisoner 1 plays cooperate and prisoner 2 plays defect) in which every strategy played by every agent (agent i) is a best response to every other strategy played by all the other opponents (agents j for every j≠i) .