Strategyproof Tournament Rules for Teams with a Constant Degree of Selfishness

2025-12-04

AI Summary

This paper addresses the design of strategyproof tournament mechanisms under mixed motives, where agents’ selfishness is quantified by a parameter λ. Specifically, given round-robin outcomes among n teams, we seek an elimination rule satisfying monotonicity and Condorcet consistency such that no team can increase its winning probability by intentionally losing matches. Prior strategyproof mechanisms required λ = Ω(n), imposing a fundamental theoretical barrier. We propose the first mechanism achieving strategyproofness with constant λ = 11. To quantify manipulation resistance, we introduce *multiplicative pairwise non-manipulability*, attaining a manipulation suppression bound δ = 3.5. Our approach combines probabilistic winner selection, game-theoretic modeling, and rigorous mathematical analysis. The mechanism preserves fairness while strictly improving upon existing lower bounds—marking the first tournament rule with constant-level selfish robustness. This advances the theoretical frontier of manipulation-resistant tournament design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among $n$ teams in a league. Such a mechanism should satisfy the natural properties of monotonicity and Condorcet consistency. Moreover, from the league's perspective, the winner-determination tournament rule should be strategyproof, meaning that no team can do better by losing a game on purpose. Past work considered settings in which each team is fully selfish, caring only about its own probability of winning, and settings in which each team is fully selfless, caring only about the total winning probability of itself and the team to which it deliberately loses. More recently, researchers considered a mixture of these two settings with a parameter $λ$. Intermediate selfishness $λ$ means that a team will not lose on purpose unless its pair gains at least $λs$ winning probability, where $s$ is the individual team's sacrifice from its own winning probability. All of the dozens of previously known tournament rules require $λ= Ω(n)$ to be strategyproof, and it has been an open problem to find such a rule with the smallest $λ$. In this work, we make significant progress by designing a tournament rule that is strategyproof with $λ= 11$. Along the way, we propose a new notion of multiplicative pairwise non-manipulability that ensures that two teams cannot manipulate the outcome of a game to increase the sum of their winning probabilities by more than a multiplicative factor $δ$ and provide a rule which is multiplicatively pairwise non-manipulable for $δ= 3.5$.

Problem

• Designing tournament rules that are strategyproof for teams with limited selfishness.
• Finding rules with minimal selfishness parameter λ to prevent deliberate losing.
• Ensuring fairness and manipulation resistance in probabilistic winner determination.

Innovation

• Strategyproof tournament rule with constant selfishness parameter
• Multiplicative pairwise non-manipulability for bounded manipulation
• Rule ensures monotonicity and Condorcet consistency properties