Full characterization of core for nonlinear optimization games

TL;DR

This paper provides a comprehensive characterization of the core in nonlinear optimization games by introducing a relaxation approach, broadening analysis scope and solving previously intractable game models.

Contribution

It generalizes linear core frameworks to nonlinear games, enabling analysis of complex models like quadratic, ratio, and combinatorial games.

Findings

Characterization of the core for broad nonlinear games

Application to classical and new game models

Extension to approximate core analysis

Abstract

We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands the scope of cooperative games that can be analyzed and contributes to the literature on games induced from optimization models. We apply these insights to not only establish connections with and provide new insights on classical models but also solve new games untamed in the existing literature, including combinatorial quadratic and ratio games such as portfolio, maximum cut, matching, and assortment games. These results are further extended to more general models and also the approximate core.