Analyzing games with ambiguous player types using the MIN then MAX decision model

In many common interactive scenarios, participants lack information about other participants, and specifically about the preferences of other participants. In this work, we model an extreme case of incomplete information, which we term games with type ambiguity, where a participant lacks even information enabling him to form a belief on the preferences of others. Under type ambiguity, one cannot analyze the scenario using the commonly used Bayesian framework, and therefore one needs to model the participants using a different decision model. To this end, we present the MINthenMAX decision model under ambiguity. This model is a refinement of Wald's Min- iMax principle, which we show to be too coarse for games with type ambiguity. We characterize MINthenMAX as the finest refinement of the MiniMax principle that satisfies three properties we claim are necessary for games with type ambiguity. This prior-less approach we present follows the common practice in computer science of worst-case analysis. Finally, we define and analyze the corresponding equilibrium concept, when all players follow MINthenMAX. We demonstrate this equilibrium by applying it to bilateral trade, which is a common economic scenario. We show that an equilibrium in pure strategies always exists, and we analyze the equilibria.