Long-Term Competition in a Dynamic Game

The Cold Fish War

by Jonathan Cave

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In repeated games, simple forms of dependence on history have been used to characterize various kinds of equilibrium behavior. This paper extends the use of history-dependent strategies to an example of a more general class of games called dynamic games. The "Great Fish War" of D. Levhari and L. Mirman provides an example of a dynamic game in which several players jointly exploit a renewable resource. This paper describes the model, the recursive equilibrium, and the Pareto optima; defines and characterizes the recursively supported equilibria and gives conditions for their Pareto optimality; and presents and analyzes an appropriate definition of "renegotiation proof equilibrium" for this example. The paper generally concludes that the use of threat strategies can result in Pareto improvements, but that repeated or severe defections limit cooperative possibilities. The methods developed for this example suggest a general approach to the analysis of cooperative institutions.

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