Threat Equilibria and Fair Settlements in Cooperative Games

The role of threats is studied in cooperative normal form games. A threats-game is constructed, in which every set of players selects a joint threat strategy and then a settlement function determines the final outcome. Threat equilibria and cooperative solutions are defined for any settlement function. Two axioms are introduced which determine a unique settlement function for games with transferable utility. This settlement function is closely related to the Shapley value, and has attractive Pareto-optimality and individual-rationality properties. A simple oligopoly problem is studied to illustrate these ideas.