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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.
 Spring '10
 AsuOzdaglar

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