MBS 93-07
Deliberational Correlated Equilibria
Peter Vanderschraff and Brian Skyrms
The Nash equilibrium concept in noncooperative game theory assumes
that players' strategies are probabilistically independent. Recent theories
of equilibrium selection in noncooperative games (Harsanyi, Selten 1988,
Fudenberg, Kreps 1990, Skyrms 1990) also presuppose probabilistic independence
among the players' strategies. In this paper, we argue that the probabilistic
independence assumption is not well founded, and introduce a theory of
equilibrium selection that permits correlation in the players' beliefs
and strategies. This approach generalized the inductive deliberational
dynamics presented in Skyrms (1991a) by relaxing the probabilistic independence
assumption along lines Skyrms has suggested. The resulting inductive correlation-dynamics
enables even players who begin at an initial state of probabilistic independence
to converge to deliberational equilibria corresponding to two types of
correlated equilibria in noncooperative games. Inductive deliberators can
converge to an endogenous correlated equilibrium (Vanderschraaf 1992) simply
by dropping the assumption that their opponents' strategies are probabilistically
independent events. Relaxing the probabilistic independence assumption
this way permits correlation in beliefs to emerge as a result of the deliberation
itself. A second kind of correlation in strategies results from players
tying their strategies to an event which is external to the game. By extending
the model of inductive deliberation so that the deliberators incorporate
their strategies with such an exogenous event so as to achieve an Aumann
correlated equilibrium (Aumann 1974, 1987). We address the following questions:
(1) Do correlated equilibria correspond to fixed points of the dynamics?
(2) Can the dynamics "amplify" an initial weak correlation? (3) Can the
dynamics create correlation from an initial uncorrelated state? Although
we are very far from a complete treatment of these questions, we will be
able to show how they may have different answers for different kinds of
correlated equilibrium and different versions of the inductive dynamics.