International Journal of Game Theory

, Volume 41, Issue 1, pp 91–129 | Cite as

Choosing fair lotteries to defeat the competition

  • Liad Wagman
  • Vincent Conitzer


We study the following game: each agent i chooses a lottery over nonnegative numbers whose expectation is equal to his budget b i . The agent with the highest realized outcome wins (and agents only care about winning). This game is motivated by various real-world settings where agents each choose a gamble and the primary goal is to come out ahead. Such settings include patent races, stock market competitions, and R&D tournaments. We show that there is a unique symmetric equilibrium when budgets are equal. We proceed to study and solve extensions, including settings where agents choose their budgets (at a cost) and where budgets are private information.


Strategic gambling Nash equilibrium Fair lotteries 

JEL Classifications

C70 C72 D81 L20 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Stuart School of BusinessIllinois Institute of TechnologyChicagoUSA
  2. 2.Departments of Computer Science and Economics, Levine Science Research CenterDuke UniversityDurhamUSA

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