by Robert F. Nau (Fuqua School of Business Working Paper)

**Abstract: **A refinement of subjective correlated equilibrium is
proposed: "arbitrage-free equilibrium." This solution concept is derived
from the requirement that the outcome of a noncooperative game should not
present arbitrage opportunities to an outside observer when the players
publicly accept small side-gambles consistent with their preferences, whether
they are risk neutral or risk averse. An arbitrage-free equilibrium is
a correlated equilibrium in which the common prior assumption applies to
the players' risk neutral probabilities (products of probabilities and
relative marginal utilities for money) rather than their true probabilities.
The players' true probabilities may therefore be discordant, but nonetheless
they satisfy a strong consistency condition given the marginal utilities.
This reinterpretation of the common prior assumption guarantees that, when
the players are risk averse, their equilibrium expected payoffs are Pareto
efficient, a condition which is generally not satisfied by completely mixed
Nash or objective correlated equilibria among risk averse players. The
knowledge requirements for arbitrage-free correlated equilibria are also
weaker than those of Nash or objective correlated equilibria in the sense
that we need not observe the player's true probabilities or utilities for
outcomes: the parameters of the game which are common knowledge are merely
the small monetary side-gambles that the players are willing to accept.
These results generalize earlier work by Nau and McCardle
(1990) concerning the arbitrage-free properties of objective correlated
equilibria for risk neutral players.

**Key Words:** Correlated equilibrium, joint coherence, arbitrage,
common knowledge, common prior assumption, risk neutral probabilities,
separation of probability and utility