On the Shapley value and the influence of weak players in big boss games

L. A. Guardiola Alcalá, A. Meca Martínez

Big Boss games are a class of cooperative games in which a single veto player, the Big Boss, plays a central role in resource allocation and coalition stability. We propose a new allocation scheme based on the Shapley value and the τ-value, selecting along a core diagonal, defined by the Big Boss’s maximum aspirations, the τ-value, and those of weaker players, the point closest to the Shapley value, called the Projected Shapley Value (PSV) allocation. This allocation is coalitionally stable and accounts for weaker players’ contributions. Our analysis identifies a new property of Big Boss games, namely the relationship between the discrepancies assigned by the τ-value and the Shapley value, with particular focus on the Big Boss and the remaining players, and provides a new characterization of convexity. Finally, we conduct a statistical analysis to assess the position of the PSV allocation within the core, especially when computing the Shapley value is computationally demanding.

Palabras clave: Big boss games, Shapley value, τ -value

GT Teoría de Juegos IV: aplicaciones
4 de septiembre de 2026  11:10
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