Equilibrium Selection in Auctions and High Stakes Games

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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.