Analyzing Games with Ambiguous Player Types

6 In many common interactive scenarios, participants lack information 7 about other participants, and specifically about the preferences of other 8 participants. In this work, we model an extreme case of incomplete 9 information, which we term games with type ambiguity, where a participant 10 lacks even information enabling him to form a belief on the preferences of 11 others. Under type ambiguity, one cannot analyze the scenario using the 12 commonly used Bayesian framework, and therefore he needs to model the 13 participants using a different decision model. 14 In this work, we present the MINthenMAX decision model under 15 ambiguity. This model is a refinement of Wald’s MiniMax principle, which 16 we show to be too coarse for games with type ambiguity. We characterize 17 MINthenMAX as the finest refinement of the MiniMax principle that 18 satisfies three properties we claim are necessary for games with type 19 ambiguity. This prior-less approach we present her also follows the common 20 practice in computer science of worst-case analysis. 21 Finally, we define and analyze the corresponding equilibrium concept 22 assuming all players follow MINthenMAX. We demonstrate this equi23 librium by applying it to two common economic scenarios: coordination 24 games and bilateral trade. We show that in both scenarios, an equilibrium 25 in pure strategies always exists and we analyze the equilibria. 26