We study best-of-k (\(k=2,3\)) 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 \(\alpha\) (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.

我们研究最好的k ( \(k=2,3\) ) 与两个具有异质资源预算的玩家的竞赛，这些资源预算在阶段内减少与前一阶段分配的资源成比例，这样对于每个资源单元，一个玩家分配，他从预算中损失了\(\alpha\)（疲劳参数）单位的资源。我们首先分析了玩家的资源分配，并表明如果资源预算相同，虽然三人两胜制的循环资源比二人三胜制的循环资源大，但最好的总资源分配具有最佳不对称平局规则的二人制比赛可能比三人制比赛中的最佳比赛更大。