Rational coordination under risk: Coherence and the Nash bargain

The design of automated multiagent cooperative systems can be greatly facilitated by the use of conditional utilities, which provide each individual the capability of modulating its interests as a function of the interests of others. Perhaps the weakest possible requirement for meaningful coordination is that the group be coherent: no individual is required, under all circumstances, to sacrifice its own welfare to benefit the group. When the influence relationships among the members of a group can be expressed via a directed acyclic graph, a group is coherent if and only if its utilities are conditional mass functions. This structure permits the performance aspects to be merged with the random aspects to form a unified mathematical framework for decision problems under risk. The resulting solution may be interpreted as the Nash bargaining solution when the disagreement points of all agents are set to zero. Coherence is shown to be operationally equivalent to the concept of symmetry for a cooperative game. The resulting theory is designed to account for both individual and group-level preferences.