Abstract:

Arad and Rubinstein (2013) describe a challenge tournament where n players have a binary choice and play a round-robin tournament where they score against each other randomly for a stake that depends on their choices. The player with the highest total score wins, with ties resolved randomly. They conjecture that for n > 3 the only equilibrium is that all players take the riskier choice. We present work in progress on an elementary proof of this conjecture which is based on a simple dominance argument.