Players allocate resources across matches in tournament contests
A Resource Allocation Tournament
Computer Science and Game Theory
Summary
Some competitions involve players spreading limited resources across many games against different opponents. This paper studies how players decide their investments and the resulting outcomes under two reward schemes: one where every win scores points, and one where only the overall winner gets rewarded. The authors fully worked out the best strategies when there are three players. For larger groups, they identified patterns for the point-scoring scheme and used computer methods to find approximate strategies when only the top winner counts. They also created a new algorithm to help find these strategies in bigger contests.
What this means in practice
- •For sports league managers: Optimize team resource distribution strategies across a season’s matches to enhance competitive performance under different scoring rules.
- •For online gaming platform designers: Design tournament formats and scoring methods that balance strategic resource allocation and player engagement across multiple simultaneous matches.
Authors
Adam Nathaniel, Refael Hassin
Abstract
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.