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• We focused on equilibrium in pure strategies, meaning actions were mapped to certain outcomes • We will now consider mixed strategies: probabilistic play • But first, we have to develop a notion of preferences over uncertain outcomes: expected utility theory. 2
mixed strategies for player i are Δ(S i). Idea: a player can randomize over pure strategies. Mixed strategies ... Any N-player game where all strategy spaces are finite has at least one Nash equilibrium. Notes:-The equilibrium may be mixed.-There is a generalization if strategy
Chapter summary. Given a game in strategic form we extend the strategy set of a player to the set of all probability distributions over his strategies. The elements of the new set are called mixed strategies, while the elements of the original strategy set are called pure strategies.
Instead of picking a deterministic action as in a pure strategy, a mixed strategy user tosses a coin to determine what action to play. Game theorists are interested in mixed strategies for at least two reasons: (i) mixed strategies correspond to how humans play certain games, such as rock-paper-scissors; (ii) the space of mixed strategies ...
19 de dic. de 2016 · A mixed strategy is a probability distribution one uses to randomly choose among available actions in order to avoid being predictable. In a mixed strategy equilibrium each player in a game is using a mixed strategy, one that is best for him against the strategies the other players are using.
5 de ago. de 2012 · Game Theory. Interactive Strategies in Economics and Management. , pp. 211 - 234. DOI: https://doi.org/10.1017/CBO9781139049344.018. Publisher: Cambridge University Press. Print publication year: 2012.
This game has two pure strategy equilibria: (Swerve, Don’t) and (Don’t, Swerve). In addition, it has a mixed strategy. Suppose that Column swerves with probability p.Then Row gets 0p + –1(1 – p) from swerving, 1p + (–4)(1 – p) from not swerving, and Row will randomize if these are equal, which requires p = ¾. That is, the probability that Column swerves in a mixed strategy ...
