Allocation of resources in asymmetric competitions: How do the weak maintain a chance of winning?

To maintain a chance of occasionally beating a stronger player in a competition waged over several fields, a weaker player should give up on some of the fields and concentrate resources on the remaining ones. But when do weak players actually do this? And which fields do they give up when the fields differ in their likelihood of being assessed? We report an experimental study of resource allocation in which asymmetric pairs of players compete over asymmetric fields. Symmetric players and symmetric fields are used for control. We find that players behave as follows: (1) Average wins are the same in the symmetric and asymmetric fields conditions and correspond to relative player strength. (2) The proportion of fields given up on decreases with a player's greater relative strength, increases for asymmetric field likelihoods, and increases when competitions are framed in meaningful context; this proportion is related to wins. (3) When field likelihoods are asymmetric, players' resource allocation is correlated with likelihood. Wins generally increase with that correlation but the relation is different for players of different strength. (4) The proportion of fields given up on and the correlation with likelihood change with experience towards the values corresponding to higher wins.