How to design a multi-stage tournament when some results are carried over?

TL;DR

This paper analyzes the incentive issues in multi-stage sports tournaments with carried-over results and proposes new designs to ensure teams are motivated to perform optimally, with simulations supporting the effectiveness of carrying over half of the points.

Contribution

It introduces a family of incentive compatible tournament designs addressing the incentive incompatibility in existing formats with carried-over results.

Findings

Carrying over half of the points improves incentive compatibility.

Existing formats can incentivize teams to underperform.

Simulations show proposed designs outperform traditional formats.

Abstract

The paper discusses the strategy-proofness of sports tournaments with multiple group stages, where the results of matches already played in the previous round against teams in the same group are carried over. These tournaments, widely used in handball and other sports, are shown to be incentive incompatible in the sense that a team can be strictly better off by not exerting full effort in a game. Historical examples are presented when a team was ex ante disinterested in winning by a high margin. We propose a family of incentive compatible designs. Their main characteristics are compared to the original format via simulations. Carrying over half of the points scored in the previous round turns out to be a promising policy.