Choosing Fair Lotteries to Defeat the Competition

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.

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