Mechanisms with costly knowledge

Abstract

We propose investigating the design and analysis of game theoretic mechanisms when the players have very unstructured initial knowledge about themselves, but can refine their own knowledge at a cost. We consider several set-theoretic models of "costly knowledge". Specifically, we consider auctions of a single good in which a player i's only knowledge about his own valuation, [theta]i, is that it lies in a given interval [a, b]. However, the player can pay a cost, depending on a and b (in several ways), and learn a possibly arbitrary but shorter (in several metrics) sub-interval, which is guaranteed to contain [theta]i. In light of the set-theoretic uncertainty they face, it is natural for the players to act so as to minimize their regret. As a first step, we analyze the performance of the second-price mechanism in regret-minimizing strategies, and show that, in all our models, it always returns an outcome of very high social welfare.