Preempting versus Postponing: the Stealing Game

Gallice, Andrea (2008): Preempting versus Postponing: the Stealing Game.

Abstract

We present an endogenous timing game of action commitment in which players can steal from each other parts of a homogeneous and perfectly divisible pie (market). We show how the incentives to preempt or to follow the rivals radically change with the number of players involved in the game. In the course of the analysis we also introduce, discuss and apply the concept of pu-dominance, a generalization of the risk-dominance criterion to games with more than two players.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stealing, endogenous timing games, pu-dominance
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

Brunnermeier, M.K., Morgan, J., 2006. Clock games: theory and experiments. Competition Policy Center CPC07-072.

Bulow, J., Klemperer, P., 1999. The generalized war of attrition. Amer. Econ. Rev. 89, 175-189.

Hamilton, J.H., Slutsky, S.M., 1990. Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games Econ. Behav. 2, 29-46.

Harsanyi, J., Selten, R., 1988. A general theory of equilibrium selection in games, MIT Press, Cambridge, MA.

Kajii, A., Morris, S., 1997. The robustness of equilibria to incomplete information. Econometrica 65, 1283-1309.

Kilgour, D.M., 1972. The simultaneous truel. Int. J. Game Theory 1, 229-242.

Kilgour, D.M., Brams, S.J., 1997. The truel. Math. Mag. 70, 315-326.

Maynard Smith, J., 1974. Theory of games and the evolution of animal contests. J. Theor. Biol. 47, 209-221.

Myerson, R., 1978. Refinement of the Nash Equilibrium Concept. Int. J. Game Theory 7, 73-80.

Morris, S., Rob, R., Shin, H.S., 1995. p-Dominance and belief potential. Econometrica 63, 145-157.

Park, A., Smith, L., 2006. Caller number five: timing games that morph from one form to another. Cowles Foundation Discussion Paper 1554.

Rosenthal, R., 1981. Games of perfect information, predatory pricing, and the chain store paradox. J. Econ. Theory 25, 92-100.

Selten, R., 1975. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. Int. J. Game Theory 4, 25-55.

Van Damme, E., Hurkens, S., 1996. Commitment robust equilibria and endogenous timing. Games Econ. Behav. 15, 290-311.

Van Damme, E., Hurkens, S., 1999. Endogenous Stackelberg leadership. Games Econ. Behav. 28, 105-129.

Van Damme, E., Hurkens, S., 2004. Endogenous price leadership. Games Econ. Behav. 47, 404-420.

Yates, G.E., Broom, M., 2007. Stochastic models of kleptoparasitism. J. Theor. Biol. 248, 480-489.