We often talk about cooperating and defecting in general-sum games. This post proposes that we say that a player P has defected against a coalition C (that includes P) currently playing a strategy S when P deviates from the strategy S in a way that increases his or her own personal utility, but decreases the (weighted) average utility of the coalition. It shows that this definition has several nice intuitive properties: it implies that defection cannot exist in common-payoff games, uniformly weighted constant-sum games, or arbitrary games with a Nash equilibrium strategy. A Pareto improvement can also never be defection. It then goes on to show the opportunity for defection can exist in the Prisoner’s dilemma, Stag hunt, and Chicken (whether it exists depends on the specific payoff matrices).
Planned summary for the Alignment Newsletter: