Mixed Strategies in Combinatorial Agency

(Extended Abstract)
  • Moshe Babaioff
  • Michal Feldman
  • Noam Nisan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


We study a setting where a principal needs to motivate a team of agents whose combination of hidden efforts stochastically determines an outcome. In a companion paper we devise and study a basic “combinatorial agency” model for this setting, where the principal is restricted to inducing a pure Nash equilibrium. Here, we show that the principal may possibly gain from inducing a mixed equilibrium, but this gain can be bounded for various families of technologies (in particular if a technology has symmetric combinatorial structure). In addition, we present a sufficient condition under which mixed strategies yield no gain to the principal.


Nash Equilibrium Mixed Strategy Pure Strategy Success Function Optimal Contract 
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  1. 1.
    Aumann, R.: Acceptable Points in General Cooperative n-Person Games. In: Contributions to the Theory of Games, vol. 4 (1959)Google Scholar
  2. 2.
    Babaioff, M., Feldman, M., Nisan, N.: Combinatorial agency. In: The 7th ACM conference on Electronic Commerce, pp. 18–28 (2006)Google Scholar
  3. 3.
    Che, Y.K., Yoo, S.W.: Optimal Incentives in Teams. American Economic Review 91, 525–541 (2001)CrossRefGoogle Scholar
  4. 4.
    Feldman, M., Chuang, J., Stoica, I., Shenker, S.: Hidden-Action in Multi-Hop Routing. In: ACM EC 2005, pp. 117–126 (2005)Google Scholar
  5. 5.
    Holmstrom, B.: Moral Hazard in Teams. Bell Journal of Economics 13, 324–340 (1982)CrossRefGoogle Scholar
  6. 6.
    Itoh, H.: Incentives to Help Multi-Agent Situations. Econometrica 59, 611–636 (1991)MATHCrossRefGoogle Scholar
  7. 7.
    Mass-Colell, A., Whinston, M., Green, J.: Microeconomic Theory. Oxford University Press, Oxford (1995)Google Scholar
  8. 8.
    Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behaviour 35, 166–196 (2001); A preliminary version appeared in STOC 1999MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Strausz, R.: Moral hazard in sequential teams. Departmental Working Paper. Free University of Berlin (1996)Google Scholar
  10. 10.
    Winter, E.: Incentives and Discrimination. American Economic Review 94, 764–773 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Moshe Babaioff
    • 1
  • Michal Feldman
    • 2
  • Noam Nisan
    • 2
  1. 1.UC Berkeley School of Information 
  2. 2.School of Computer ScienceHebrew University of Jerusalem 

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