Private Equilibrium Computation Yields Truthful Mediators ( Part 2 ) 1 Introduction

Recall our goal from last class: we wanted to take a game that has nice properties when described as a game of complete information, and then augment it with an extremely weak “mediator”, such that in the new game, we can implement the equilibria of the original (complete information) game as simple ex-post equilibria, which do not require players to know anything about each other’s types. Some brief recapping is in order. Suppose G is a game with action set A, type set T , and cost function ci(a) ≡ c(ti, a). Definition 1 A mediator is given by an algorithm M : (T ∪ {⊥}) → (A ∪ {⊥}) mapping reported types (or ⊥, which denotes declining to report any type) to suggested actions (or ⊥, which denotes not suggesting any action).