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ISRN Economics
Volume 2013 (2013), Article ID 645481, 10 pages
Research Article

Lead, Follow or Cooperate? Sequential versus Collusive Payoffs in Symmetric Duopoly Games

Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy

Received 18 August 2013; Accepted 15 September 2013

Academic Editors: M. E. Kandil and M. Tsionas

Copyright © 2013 Marco A. Marini and Giorgio Rodano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In many strategic settings comparing the payoffs obtained by players under full cooperation to those obtainable at a sequential (Stackelberg) equilibrium can be crucial to determine the 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 firms are allowed to sequence their actions. Despite the relevance of these and other applications, no full-fledged comparisons between collusive and sequential payoffs have been performed so far. In this paper we show that even in symmetric duopoly games the ranking of cooperative and sequential payoffs can be extremely variable, particularly when the usual 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 payoffs. Some applications to endogenous timing are discussed.