Resource allocations in the best-of-k ( $$k=2,3$$ k = 2 , 3 ) contests

We study best-of-k ( $$k=2,3$$ k = 2 , 3 ) contests with two players who have heterogeneous resource budgets that decrease within the stages proportionally to the resource allocated in the previous stages such that for each resource unit that a player allocates, he loses $$\alpha$$ α (the fatigue parameter) units of resource from his budget. We first analyze the players’ resource allocations and show that if the resource budget is the same, although the recycled resource is larger in the best-of-three contest than in the best-of-two contest, the total resource allocation in the best-of-two contest with the optimal asymmetric tie-breaking rule might be larger than in the best-of-three contest.