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.