This paper presents an analysis of cooperation in the context of a repeated rent-seeking game which can be thought of as modeling bilateral situations such as military/political conflict, labor/business lobbying, gang/illegal activities, or criminal/civil law suits. The potential for mutually advantageous agreements is explored using the repeated nature of the game as the mechanism which sustains the cooperation. The Nash bargaining solution is applied to symmetric as well as asymmetric rent-seeking situations. The asymmetries can derive from the players valuing the rent differently or choosing sequentially.
KeywordsNash Equilibrium Bargaining Solution Payoff Vector Stackelberg Game Equilibrium Payoff
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- 1.See Buchanan (1980) for an excellent introduction to this problem.Google Scholar
- 2.Aumann (1981) provides an excellent discussion of equilibria in repeated games.Google Scholar
- 3.Although the word “collusive” could easily be used here, these agreements will be called “cooperative” to avoid any negative connotations.Google Scholar
- 4.For more details and an excellent discussion of this, see Binmore (1992: 180–191).Google Scholar
- 5.A more detailed explanation of these bargaining solutions can be found in Shubik (1982: 194–200).Google Scholar
- 6.Linster (19936) shows how to find the Nash equilibrium in this game.Google Scholar
- 7.For a detailed description of how these curves are derived for both the Stackelberg and simultaneous-move games, see Linster (1993b).Google Scholar
- 8.To see this, notice U1 + U2 = (x1+x2)/(x1+x2) - (x1+x2) = 1 - (x1+x2) 333 1 as long as x1 + x2 111 0, and U1 + U2 = 1 if x1 + x2 = 0.Google Scholar
- 9.To see that this is true, let one of the players cheat by making a contribution of y 111 0 which is arbitrarily close to zero. Then he will have a payoff of 1— y, which is arbitrarily close to one.Google Scholar
- 10.For an excellent discussion of bargaining and the Nash Bargaining solution, see Binmore (1992).Google Scholar