Lead, Follow or Cooperate? Endogenous Timing & Cooperation in Symmetric Duopoly Games

17 Pages Posted: 1 Aug 2011 Last revised: 8 Aug 2011

See all articles by Marco A. Marini

Marco A. Marini

Marco A. Marini; University of Rome La Sapienza

Giorgio Rodano

SPES Development Studies at the University of Rome La Sapienza

Date Written: August 1, 2011

Abstract

The aim of this paper is to extend Hamilton and Slutsky's (1990) endogenous timing game by including the possibility for players to cooperate. At an initial stage players are assumed to announce both their purpose to play early or late a given duopoly game as well as their intention to cooperate or not with their rival. The cooperation and timing formation rule is rather simple: when both players agree to cooperate and play with a given timing, they end up playing their actions coordinately and simultaneously. Otherwise, they play as singletons with the timing as prescribed by their own announcement. We check for the existence of a subgame perfect Nash equilibrium (in pure strategies) of such a cooperation-timing duopoly game. Two main results on the emergence of cooperation are provided. If players' actions in the symmetric duopoly game are strategic substitutes and there is no discount, cooperating early (as a grand coalition) is a subgame perfect equilibrium of the extended timing-cooperation game. Conversely, cooperating late (at period two) represents an equilibrium when players' strategies are strategic complements. Other equilibria are also possible. Most importantly, our model shows that, in general, the success of cooperation is affected by the endogenous timing of the game. Moreover, the slope of players' best-replies appears crucial both for the success of cooperation as well as for the players' choice of sequencing their market actions.

Keywords: Endogenous Timing, Cooperation, Duopoly Games

JEL Classification: C70, C71, D23, D43

Suggested Citation

Marini, Marco A. and Rodano, Giorgio, Lead, Follow or Cooperate? Endogenous Timing & Cooperation in Symmetric Duopoly Games (August 1, 2011). Available at SSRN: https://ssrn.com/abstract=1899554 or http://dx.doi.org/10.2139/ssrn.1899554

Marco A. Marini (Contact Author)

Marco A. Marini ( email )

Piazzale Aldo Moro, 5
Roma, 00185
Italy

HOME PAGE: http://sites.google.com/a/uniroma1.it/marcomarini/

University of Rome La Sapienza ( email )

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Roma, 00185
Italy
+39 06 49910843 (Phone)

HOME PAGE: http://sites.google.com/a/uniroma1.it/marcomarini

Giorgio Rodano

SPES Development Studies at the University of Rome La Sapienza ( email )

Via del Castro Laurenziano, 9
Rome, RM I - 00183
Italy

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