Theory and Decision

, Volume 80, Issue 3, pp 451–462 | Cite as

Optimal stealing time

Article
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Abstract

We study a dynamic game in which players can steal parts of a homogeneous and perfectly divisible pie from each other. The effectiveness of a player’s theft is a random function which is stochastically increasing in the share of the pie the agent currently owns. We show how the incentives to preempt or to follow the rivals change with the number of players involved in the game and investigate the conditions that lead to the occurrence of symmetric or asymmetric equilibria.

Keywords

Stealing Stochastic games Optimal timing Pie allocation 

References

  1. Borel, E. (1921). La theorie du jeu les equations integrales a noyau symetrique. Comptes Rendus de l’Academie 173, 1304–1308. English translation by Savage, L., 1953. The theory of play and integral equations with Skew Symmetric Kernels. Econometrica, 21, 97–100.Google Scholar
  2. Brunnermeier, M. K., & Morgan, J. (2010). Clock games: Theory and experiments. Games and Economic Behavior, 68, 532–550.CrossRefGoogle Scholar
  3. Bulow, J., & Klemperer, P. (1999). The generalized war of attrition. American Economic Review, 89, 175–189.CrossRefGoogle Scholar
  4. Dubovik, A., & Parakhonyak, A. (2014). Drugs, guns, and targeted competition. Games and Economic Behavior, 87, 497–507.CrossRefGoogle Scholar
  5. Harsanyi, J., & Selten, R. (1988). A general theory of equilibrium selection in games. Cambridge: MIT Press.Google Scholar
  6. Konrad, K. A. (2009). Strategy and dynamics in contests. Oxford, UK: Oxford University Press.Google Scholar
  7. Maynard Smith, J. (1974). Theory of games and the evolution of animal contests. Journal of Theoretical Biology, 47, 209–221.CrossRefGoogle Scholar
  8. Maskin, E., & Tirole, J. (2001). Markov perfect equilibrium I. Observable actions. Journal of Economic Theory, 100, 191–219.CrossRefGoogle Scholar
  9. Park, A., & Smith, L. (2008). Caller number five and related timing games. Theoretical Economics, 3, 231–256.Google Scholar
  10. Rinott, Y., Scarsini, M., & Yu, Y. (2012). A Colonel Blotto gladiator game. Mathematics of Operations Research, 37, 574–590.CrossRefGoogle Scholar
  11. Rosenthal, R. (1981). Games of perfect information, predatory pricing, and the chain store paradox. Journal of Economic Theory, 25, 92–100.CrossRefGoogle Scholar
  12. Sela, A., & Erez, E. (2013). Dynamic contests with resource constraints. Social Choice and Welfare, 41, 863–882.CrossRefGoogle Scholar
  13. von Stackelberg, H. (1934). Marktform und Gleichgewicht. Vienna and Berlin: Springer Verlag.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Economics and StatisticsUniversity of Torino and Collegio Carlo AlbertoTorinoItaly

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