An Ordinal Bargaining Set for Games Without Side Payments

Billera (Billera, L. J. 1968. On cores and bargaining sets for N-person cooperative games without side payments. Ph.D. dissertation, The City University of New York, 1968; Billera, L. J. 1970. Existence of general bargaining sets for cooperative games without side payments. Bull. Amer. Math. Soc.76 375–379.] proposed a simple bargaining set for games without side payments, and announced it as an open question, whether his proposed bargaining set is never empty. An affirmative answer is given to Billera's question in this paper.