Equilibrium Selection in Auctions and High Stakes Games∗

We introduce the test-set equilibrium refinement of Nash equilibrium and apply it to three well-known auction games, comparing our findings to similar ones previously obtained by ad hoc equilibrium selections. We also introduce a theory of high stakes versions of games, in which strategies are first proposed and then subjected to a potentially costly review-and-revise process. For finite games, when the cost of revising strategies is small, a Nash equilibrium is a test-set equilibrium if and only if those strategies are chosen for play in a quasi*-perfect equilibrium of the corresponding high stakes version.