Equilibrium Binding Agreements: A Comment

To construct their Equilibrium Binding Agreements, Ray and Vohra (J. Econ. Theory, 73 (1997) 30–78) define a concept of an equilibrium between coalitions and prove its existence for any coalition structure. We show that this result crucially depends on the quasi-concavity of the utility functions, which in turn depends on the type of mixed strategies used by the coalitions. When coalitions use uncorrelated mixed strategies utility functions may not be quasi-concave and an equilibrium may not exist. However, if coalitions use correlated strategies, an equilibrium always exist.