Persistent Nash equilibrium

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Notes for CS 8803 - Game Theory and Computer Science. Spring 2008

The persistent NE extends the intuition gleamed from the Strict Nash equilibrium. We want to define a refinement that excludes unstable equilibrium, while still always existing. Persistent Nash equilibrium achieves this goal.

Our game G = (N,A,u).

a retract is a set T_1 \times T_2 \times \cdots \times T_n where Ti is a convex closed subset of Δi.

a retract T is said to be absorbing if \exists open set S s.t. T\subseteq S \and \forall \sigma \in S, \exists best response to S in T.


N.E. σ is Persistent if \sigma \in T \and T is an absorbing retract and \not\exists T'\subset T s.t. T' is an absorbing retract.

Example: to be added...

Theorem: For any finite game there exists a persistent trembling hand perfect equilibrium. - not proved in class.

The production of this material was supported in part by NSF award SES-0734780.

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