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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).
Michael Brautbar, Michael J. Kearns, and Umar Syed, "Private and Third-Party Randomization in Risk-Sensitive Equilibrium Concepts", . July 2010.
Date Posted: 24 July 2012