We take a general model of externalities matching the Cooper & John framework with identical agents. If each agent's payoff depends on a parameter interpreted as the favourableness of the environment, we explore how the number of Nash equilibria varies with this parameter, especially in the cases in which the reaction curves are either concave or convex. In many examples the environmental conditions are themselves endogenous because either market or regulatory forces interact with agents' Nash equilibrium actions. This gives the idea of a simultaneous equilibrium in the environment and players' symmetric actions. We analyse how this generalised equilibrium behaves as a function of some additional parameters conditioning the environmental response to players actions. We show that generally there is a fold bifurcation in these equilibria. We illustrate the principles with two examples from industrial economics (cost spillovers between firms and demand spillovers under imperfect competition).
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Paper provided by Department of Economics, University of York in its series Discussion Papers with number
09/07.
Length: Date of creation: Mar 2009 Date of revision: Handle: RePEc:yor:yorken:09/07
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Find related papers by JEL classification: C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection D62 - Microeconomics - - Welfare Economics - - - Externalities
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