On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation

Abstract 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.

[1]  Avinash Dixit,et al.  Strategic Behavior in Contests , 1987 .

[2]  Bruce G. Linster.  Stackelberg rent-seeking , 1993 .

[3]  Jonathan H. Hamilton,et al.  Endogenizing the order of moves in matrix games , 1993 .

[4]  Garth Saloner,et al.  Cournot duopoly with two production periods , 1987 .

[5]  George Hendrikse,et al.  The Theory of Industrial Organization , 1989 .

[6]  X. Vives,et al.  Price and quantity competition in a differentiated duopoly , 1984 .

[7]  Wolfgang Leininger,et al.  More efficient rent-seeking — A Münchhausen solution , 1993 .

[8]  Debashis Pal,et al.  Cournot Duopoly with Two Production Periods and Cost Differentials , 1991 .

[9]  Giovanni Maggi,et al.  Endogenous Leadership in a New Market , 1996 .

[10]  Anat R. Admati,et al.  Joint Projects without Commitment , 1991 .

[11]  Huseyin Yildirim,et al.  Why charities announce donations: a positive perspective , 2001 .

[12]  Jonathan H. Hamilton,et al.  Endogenous timing in duopoly games: Stackelberg or cournot equilibria , 1990 .

[13]  H. Varian,et al.  On the private provision of public goods , 1986 .

[14]  J. Shogren,et al.  Strategic Behavior in Contests: Comment , 1992 .

[15]  Eric van Damme,et al.  Commitment Robust Equilibria and Endogenous Timing , 1996 .

[16]  R. Tollison,et al.  Toward a theory of the rent-seeking society , 1982 .

[17]  G. Tullock.  Efficient Rent Seeking , 2001 .

[18]  Joachim Henkel,et al.  The 1.5th Mover Advantage , 2002 .

[19]  Douglas Gale,et al.  Monotone Games with Positive Spillovers , 2001, Games Econ. Behav..

[20]  Leslie M. Marx,et al.  Dynamic Voluntary Contribution to a Public Project , 2000 .

[21]  Ben Lockwood,et al.  Gradualism and Irreversibility , 1999 .

[22]  Avinash Dixit,et al.  A MODEL OF DUOPOLY SUGGESTING A THEORY OF ENTRY BARRIERS , 1978 .

[23]  H. Varian.  Sequential contributions to public goods , 1994 .