Folk theorem

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

Given a finite game G=(N,A,u:A\rightarrow [-M,M]^N), let

\theta \in [-M,M]^N, \theta_i = \min_{\sigma_{-i} \in \Delta_{-i}} \max_{\sigma_i \in \Delta_i} u_i(\sigma).

This is called the min-max point or the threat point. It is the punishement payoff, if all opponents of i get together and decide to punish i

For simplicity, let us consider the two-player case. The N-player case is quite similar.

Theorem. For any G=(N,A,u:A\rightarrow [-M,M]^N) and any x in the individually rational region, 


See these excellent notes by Jim Ratliff.


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

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