In cooperative Cournot oligopoly games, it is known that the β‐core is equal to the α‐core, and both are non‐empty if every individual profit function is continuous and concave (Zhao, 1999b). Following Chander and Tulkens (1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non‐emptiness of the induced core, the γ‐core, by two different approaches. The first establishes that the associated Cournot oligopoly Transferable Utility (TU)‐games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao’s core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU‐games with linear cost functions, provides a single‐valued allocation rule in the γ‐core called Nash Pro rata (NP)‐value. This result generalizes Funaki and Yamato’s (1999) core existence result from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity, and non‐cooperative fairness.
