Equilibrium Selection in Auctions and High Stakes Games

We introduce the test-set equilibrium refinement of Nash equilibrium to formalize the idea that players contemplate only deviations from equilibrium play in which a single competitor plays a non-equilibrium best response. We then apply this refinement to three well-known auction games, comparing our findings to similar ones previously obtained by specialized 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. We demonstrate a sense in which the test-set equilibria emerge from such processes when the cost of revision is small.