# SFB 303 Discussion Paper No. B - 244

**Author**: Mailath, G., L. Samuelson, and A. Shaked

**Title**: Correlated Equilibria as Network Equilibria

**Abstract**: The main intuition this paper sets to explore is the analogy between Network equilibria and Correlated
equilibria. In a neighborhood system players face strategy profiles that are correlated but not identical. In a
network equilibrium each player will respond optimally to the strategy profile he sees. This seems to be
reminiscent of Correlated equilibrium where each player responds optimally to the strategy mix he observes.
Indeed, we show that this intuition can be made precise. By globally looking at the network system one finds that
when it is in equilibrium it imitates a correlated equilibrium, and that for each correlated equilibrium there is a
network and an equilibrium which is analogous to the given correlated equilibrium. In the second part of the
paper the network itself becomes the subject of evolution. It is no longer assumed that the network is given.
Players can choose their contacts and those evolve over time. Thus when the system settles down it will settle to
a correlated equilibrium which the system itself has chosen. The particular equilibrium the system selects is a
function of the technique chosen for establishing links between players.

**Keywords**: Network equilibria, Game theory, Correlated equilibria, Evolutionary
models of games, Connections between player

**JEL-Classification-Number**:

**Creation-Date**: March 1993

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