Private and third-party randomization in risk-sensitive equilibrium concepts

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).

• Algorithms and theory