This paper studies normal form games with multiple prior preferences. We develop a new measure of ambiguity based on the concept that a translation of a set of priors does not change the level of ambiguity. This is applied to non-cooperative games with ambiguity. We propose a solution concept for games where players have multiple prior preferences. The set of translations of a given set of priors is shown to be isomorphic to the simplex. This enable us to prove existence of equilibrium. Like conventional mixing, translations can convexify pure strategies.

In standard models of signaling and signal jamming, a sender with a varying degree of private information concerning her type chooses an action that serves as a signal of that type. However, this is not an accurate description of many real-world settings. That is, in many real-world situations where signaling is present, the sender chooses an unobservable action that influences the signal, but does not choose the signal directly. We investigate such environments under various assumptions concerning the determinants of sender productivity. We show that, when the unobservable action has no direct effect on sender productivity, then there is overinvestment similar to equilibrium behavior in standard signaling models. However, when the action directly affects sender productivity, underinvestment arises if the direct productivity return to the action is sufficiently high. We also relate our results to various real-world settings including which colleges students attend, performance in job interviews, and certification testing.

This paper presents an analytical characterization of the long run policies learned by algorithms that interact repeatedly. These algorithms update policies which are maps from observed states to actions. I show that the long run policies correspond to equilibria that are stable points of a tractable differential equation. As a running example, I consider a repeated Cournot game of quantity competition, for which learning the stage game Nash equilibrium serves as non-collusive benchmark. I give necessary and sufficient conditions for this Nash equilibrium not to be learned. These conditions are requirements on the state variables algorithms use to determine their actions, and on the stage game. When algorithms determine actions based only on the past period's price, the Nash equilibrium can be learned. However, conditioning actions on a richer type of information can preclude the Nash equilibrium from being reached. This type of information allows for the existence of a collusive equilibrium that will be learned with positive probability.

We prove the 2-player, generic extensive-form case of the conjecture of Govindan and Wilson (1997a,b) and Hauk and Hurkens (2002) stating that an equilibrium component is essential in every equivalent game if and only if the index of the component is nonzero. This provides an index-theoretic characterization of the concept of hyperstable components of equilibria in generic extensive-form games, first formulated by Kohlberg and Mertens (1986). We explore consequences of the result for the literature on refinements.