Dependency Equilibria

This paper introduces a new equilibrium concept for normal form games called dependency equilibrium; it is defined, exemplified, and compared with Nash and correlated equilibria in Sections 2–4. Its philosophical motive is to rationalize cooperation in the one shot prisoners' dilemma. A brief discussion of its meaningfulness in Section 5 concludes the paper. 1. Introduction. In this note I would like to present and briefly discuss a new equilibrium concept for game theory that I call dependency equilibrium. When it occurred to me 24 years ago, I put it aside because it seemed to me of doubtful sense. I do not know whether anybody had the same idea; if so, he or she may have dismissed it for the same reason. In the meantime, I have changed my mind; I think it can be backed up by a meaningful story. Hence, I think the concept at least deserves a hearing, even though the longer story can at best be feebly indicated here. The driving force behind this concept is, once more, the great riddle posed by the Prisoners' Dilemma (PD). This has elicited a vast literature and a large number of astonishingly varied attempts to undermine de-fection as the only rational solution and establish cooperation as a rational possibility, at least in the iterated case. But the hard case, it seems to me, still stands unshaken. Under appropriate conditions backward induction is valid; 1 hence, given full rationality (instead of some form of 'bounded rationality') and sufficient common knowledge, continued defection is the only solution in the finitely iterated PD. The same conclusion is reached via the iterated elimination of weakly dominated strategies. 2 I find this