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On the endogeneity of Cournot–Nash and Stackelberg equilibria: games of accumulation. (English) Zbl 1122.91012

Summary: We characterize equilibria of games with two properties: (i) Agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur; but (ii) they can only add to their initial amounts. The equilibrium set consists of just the Cournot-Nash outcome, one or both Stackelberg outcomes, or a continuum of points including the Cournot-Nash outcome and one or both Stackelberg outcomes. A simple theorem that uses agents’ standard one-period reaction functions and the one-period Cournot-Nash and Stackelberg equilibria delineates the equilibrium set. Applications include contribution, oligopoly, and rent-seeking games.

MSC:

91A10 Noncooperative games
91A65 Hierarchical games (including Stackelberg games)
91A15 Stochastic games, stochastic differential games
91B18 Public goods
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