Through the lens of Tullock contests, we take a fresh look at the contest game for crowdsourcing reviews [11] as a Tullock contest game with discrete strategies: Each of n players, endowed with skills, strategically invests an effort for writing a review of some quality she chooses from a finite set [Q]; she is awarded a payment, out of a budget \(\beta \) , in proportion to her effort, and pays a player-specific cost, which is the product of effort and skill. So both the payment and the utility functions for a player are strictly concave in the player’s effort. Players are anonymous if skills are identical, and so is the game. We study the mixed Nash equilibria of the game, where no player could deviate to increase her expected utility; her support in a Nash equilibrium is the set of qualities she chooses with strictly positive probability. By strict concavity, mixed Nash equilibria have the Small&Consecutive-Supports property: their supports have size at most 2. We show:

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Mixed Nash Equilibria in Discrete Tullock Contests

  • Vittorio Bilò,
  • Marios Mavronicolas,
  • Paul G. Spirakis,
  • Daniel Windisch

摘要

Through the lens of Tullock contests, we take a fresh look at the contest game for crowdsourcing reviews [11] as a Tullock contest game with discrete strategies: Each of n players, endowed with skills, strategically invests an effort for writing a review of some quality she chooses from a finite set [Q]; she is awarded a payment, out of a budget \(\beta \) , in proportion to her effort, and pays a player-specific cost, which is the product of effort and skill. So both the payment and the utility functions for a player are strictly concave in the player’s effort. Players are anonymous if skills are identical, and so is the game. We study the mixed Nash equilibria of the game, where no player could deviate to increase her expected utility; her support in a Nash equilibrium is the set of qualities she chooses with strictly positive probability. By strict concavity, mixed Nash equilibria have the Small&Consecutive-Supports property: their supports have size at most 2. We show: