Title: On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences,
Abstract: It is known that the set of all correlated equilibria of an n-player
non-cooperative game is a convex polytope and includes all the Nash equilibria.
Further, the Nash equilibria all lie on the boundary of this polytope. We study
the geometry of both these equilibrium notions when the players have cumulative
prospect theoretic (CPT) preferences. The set of CPT correlated equilibria
includes all the CPT Nash equilibria but it need not be a convex polytope. We
show that it can, in fact, be disconnected. However, all the CPT Nash
equilibria continue to lie on its boundary. We also characterize the sets of
CPT correlated equilibria and CPT Nash equilibria for all 2x2 games.