The second-tier trap: Theory and experimental evidence

Winner‐take‐all competitions can lead to the person in the second‐tier (middle‐tier) environment having the worst expected payoff when players exclusively choose their environment and exert effort before their random, heterogeneous environmental supports are realized. The tiers are defined by the ranks in pairwise competitions. The second‐tier trap (STT) is a situation in which a player from the second‐tier environment has the worst expected payoff even though his expected environmental support is strictly greater than that of the third‐tier player. A sufficient condition for the STT is that the ex‐ante advantages, the winning probabilities when all the players exert the same amount of effort regardless of their environment, are the same for those two environments. I claim that this sufficient condition for the STT is so weak that players can easily be tempted to choose the second‐tier environment, which is the wrong decision. Lab experiments strongly support this claim.