A Resource Allocation Tournament

We introduce and analyze a round-robin simultaneous resource allocation contest, motivated by sports leagues and other competitive environments where agents must distribute limited resources across multiple encounters. Players allocate resources in advance to matches against all opponents, and match outcomes are determined by relative allocations. We study two payoff schemes: total points, where players accumulate rewards for each win, and winner-takes-all, where only the tournament winner is rewarded. For three players, we provide complete equilibrium characterizations under both schemes. For four or more players, we show that the total points payoff admits Blotto-type equilibria, while the winner-takes-all payoff requires numerical and algorithmic analysis. To address this, we develop a best-response dynamics algorithm with stochastic inertia and use it to approximate equilibria in games with four and five players.