Private and Third-Party Randomization in Risk-Sensitive Equilibrium Concepts - Brautbar, Mickey; Kearns, Michael; Syed, Umar (Proceedings of the AAAI Conference on Artificial Intelligence, 2010)
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 risk-sensitive 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).