Stable Observable Behavior

Abstract

We study stable behavior when players are randomly matched to play a game, and before the game begins each player may observe how his partner behaved in a few interactions in the past. We present a novel modeling approach and we show that strict Nash equilibria are always stable in such environments. We apply the model to study the Prisoner's Dilemma.We show that if players only observe past actions, then defection is the unique stable outcome. However, if players are able to observe past action profiles, then cooperation is also stable. Finally, we present extensions that study endogenous observation probabilities and the evolution of preferences.

Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli

“…In a companion paper (Heller and Mohlin 2014) we study environments in which players are randomly matched, and make inferences about the opponent's type by observing her past behaviour (rather than observing the type directly as is standard in the "indirect evolutionary approach"). In future research, it would be interesting to combine both approaches and allow the observation of the past behaviour to be in ‡uenced by deception.…”

Simple Records Support Robust Indirect Reciprocity

“…We develop a new theoretical paradigm for modeling indirect reciprocity that supports positive social cooperation as a strict, stable equilibrium while relying only on simple, individualistic information: when two players meet, they observe each other's records and nothing else, and each individual's record depends only on their own past behavior. (Individualistic information is also called "first-order" [98,47,11,79]. )…”