Sequential vs Collusive Payoffs in Symmetric Duopoly Games

In many strategic settings comparing the payo¤s obtained by players under full cooperation to those obtainable at a sequential (Stackelberg) equilibrium can be crucial to determine the final outcome of the game. This happens, for instance, in repeated games in which players can break cooperation by acting sequentially, as well as in merger games in which rms are allowed to sequence their actions. Despite the relevance of these and other applications, no fully-edged comparisons betwen collusive and sequential payo¤s have been performed so far. In this paper we show that even in symmetric duopoly games the ranking of cooperative and sequential payo¤s can be extremely variable, particularly when the consuete linear demand assumption is relaxed. Not surprisingly, the degree of strategic complementarity and substitutability of players actions (and, hence, the slope of their best-replies) appears decisive to determine the ranking of collusive and sequential payo¤s. Some applications to endogenous timing are discussed.