Lead, Follow or Cooperate? Endogenous Timing & Cooperation in Symmetric Duopoly Games
AbstractThe 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 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 a¤ected 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.
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Bibliographic InfoPaper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 1112.
Length: 18 pages
Date of creation: 2011
Date of revision: 2011
Endogenous Timing; Cooperation;
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-15 (All new papers)
- NEP-BEC-2011-08-15 (Business Economics)
- NEP-COM-2011-08-15 (Industrial Competition)
- NEP-EVO-2011-08-15 (Evolutionary Economics)
- NEP-GTH-2011-08-15 (Game Theory)
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