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We consider risk-sensitive generalizations of Nash and correlated equilibria in noncooperative games. We prove that, except for a class of degenerate games, unless a two-player game has a pure Nash equilibrium, it does not have a risksensitive Nash equilibrium. We also show that every game has a risk-sensitive correlated equilibrium. The striking contrast between these existence results is due to the different sources of randomization in Nash (private randomization) and correlated equilibria (third-party randomization).
Brautbar, Michael; Kearns, Michael J.; and Syed, Umar, "Private and Third-Party Randomization in Risk-Sensitive Equilibrium Concepts" (2010). Departmental Papers (CIS). Paper 651.
Date Posted: 24 July 2012