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Leadership Games with Convex Strategy Sets

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  • Bernhard von Stengel
  • Shmuel Zamir

Abstract

A basic model of commitment is to convert a two-player game in strategic form to a “leadership game†with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader’s payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.

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Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp525.

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Length: 21 pages
Date of creation: Nov 2009
Date of revision:
Handle: RePEc:huj:dispap:dp525

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  1. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199269181, October.
  2. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
  3. Reny, Philip J. & Robson, Arthur J., 2004. "Reinterpreting mixed strategy equilibria: a unification of the classical and Bayesian views," Games and Economic Behavior, Elsevier, vol. 48(2), pages 355-384, August.
  4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  5. Avenhaus, Rudolf & Von Stengel, Bernhard & Zamir, Shmuel, 2002. "Inspection games," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 51, pages 1947-1987 Elsevier.
  6. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
  7. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  8. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization, Elsevier, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414 Elsevier.
  9. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
  10. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
  11. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
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Cited by:
  1. Marco Marini & Giorgio Rodano, 2012. "Sequential vs Collusive Payoffs in Symmetric Duopoly Games," DIAG Technical Reports 2012-06, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
  2. Rabah Amir & Giuseppe De Feo, 2012. "Endougenous Timing in a Mixed Duopoly," Quaderni di Dipartimento 162, University of Pavia, Department of Economics and Quantitative Methods.
  3. Kuzmics, Christoph & Balkenborg, Dieter & Hofbauer, Josef, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(1), January.

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