Papers for

sports league managers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Players allocate resources across matches in tournament contests

A Resource Allocation Tournament

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.

Thu 22 OctComputer Science and Game Theory
The gist
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.
Open → 2610.31418v1

Round-robin allocations face complexity and fairness challenges with few agents

Equilibria of Round-Robin: Computational Hardness and Fairness for Few Subadditive Agents

Abstract: The round-robin procedure is a simple and well-studied fair division mechanism where agents pick goods in turns. Motivated by draft mechanisms in sports leagues, we investigate strategic behaviour in online round-robin for subadditive agents. This gives rise to an extensive-form game, and we study the computational problem of computing a subgame perfect Nash equilibrium (SPNE). We show that for just two submodular agents, computing an SPNE is $\mathsf{PSPACE}$-hard. Even for the class of $\mathit{OXS}$ utilities, which are a special case of submodular utilities, computing an SPNE remains $\mathsf{NP}$-hard for a small number of agents. We complement our computational results with normative results. We show that for just three additive agents, there exist instances where every equilibrium violates EF1. This separates the online and the direct revelation games. On the positive side, we show that for additive agents every equilibrium allocation is proportional up to one good (PROP1) and for two additive agents it is also EF1. Finally, by showing that round-robin is bossy at equilibrium, we prove that the number of equilibrium allocations can be exponential even if agents have lexicographic preferences.

Wed 16 SeptComputer Science and Game TheoryComputational ComplexityData Structures and Algorithms
The gist
This paper studies how people picking items one after another, like in sports drafts, can act strategically when their preferences are complex. The authors show that even for just two agents with certain types of preferences, it's very hard to figure out stable outcomes where everyone acts optimally. They also find that fairness can fail in these settings, with some agents ending up worse off than expected. However, for simpler preferences, some fairness guarantees still hold. Lastly, they show there can be many stable outcome possibilities, making the process complicated.
Open → 2609.18309v1