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Denition dominant strategy a strategy si si is

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Unformatted text preview: matrix. ISP 1 / ISP 2 Hot potato Cooperate Hot potato (−4, −4) (−1, −5) Cooperate (−5, −1) (−2, −2) 16 Game Theory: Lecture 2 Dominant Strategies Dominant Strategy Equilibrium Compelling notion of equilibrium in games would be dominant strategy equilibrium, where each player plays a dominant strategy. Definition (Dominant Strategy) A strategy si ∈ Si is dominant for player i if ui (si , s−i ) ≥ ui (si� , s−i ) for all si� ∈ Si and for all s−i ∈ S−i . Definition (Dominant Strategy Equilibrium) A strategy profile s ∗ is the dominant strategy equilibrium if for each player i , si∗ is a dominant strategy. These notions could be defined for strictly dominant strategies as well. 17 Game Theory: Lecture 2 Dominant Strategies Dominant and Dominated Strategies Though compelling, dominant strategy equilibria do not always exist, for example, as illustrated by the partnership or the matching pennies games we have seen above. Nevertheless, in the prisoner’s dilemma game, “confess, confess” is a dominant strategy equilibrium. We can also introduce the converse of the notion of dominant strategy, which will be useful next. Definition (Strictly Dominated Strategy) A strategy si ∈ Si is strictly dominated for player i...
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This document was uploaded on 03/19/2014 for the course EECS 6.254 at MIT.

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