Author: Lining Han, Ruben Juarez, Miguel Vargas

Abstract: We study robust equilibria in tournaments, where agents endowed with power form coalitions, and the coalition formed with the highest power prevails. We introduce the No-Threat Equilibrium (NTE), a stable partition where if a coalition deviates, then a new coalition could counter by forming an even stronger coalition. The NTE exists for any power function and preferences if and only if the set of feasible coalitions is a ‘Helly’ family.

In contrast, the core is a partition in which no group of agents can profitably deviate by forming a feasible coalition, assuming that other agents do not react to such a deviation. The core is not empty for any power function and preferences if and only if the set of feasible coalitions has a ‘hierarchical-structure’.

The paper also adapts and characterizes other stability concepts to tournaments, including the α-core, β-core, farsighted core and bargaining set.

Keywords: Coalition formation；Robust equilibria；Tournament；Externalities

The article was published in November 2023 in issue 142 of "Games and Economic Behavior," which is a Level A reward journal in the academic journal ranking scheme of the Economics and Management School of Wuhan University.

Link：https://linkinghub.elsevier.com/retrieve/pii/S0899825623001318