A New Solution for Cooperative Game with Public Externalities

TL;DR

This paper introduces the w-value, a new solution concept for cooperative games with public externalities, ensuring fair, stable, and computationally efficient outcomes, with applications to climate negotiations.

Contribution

It proposes the w-value, establishing its axiomatic foundations, existence, uniqueness, stability, and practical computation, advancing cooperative game analysis under externalities.

Findings

The w-value is within the core, specifically the {}-core, ensuring stability.

The solution is computationally efficient for complex problems.

Application to climate negotiations illustrates practical relevance.

Abstract

This study proposes a novel solution concept--the w-value--for cooperative games with public externalities. The w-value is axiomatically founded on three principles: Pareto Optimality (PO), Market Equilibrium (ME), and Fiscal Balance (FB), which together ensure a fair and economically sound distribution of gains. We establish its existence, uniqueness, and an accompanying implementation mechanism. A key theoretical advantage is its strong stability: the w-value lies within the core, specifically the {\gamma}-core making it resistant to coalitional deviations. Moreover, its computational efficiency facilitates practical application to complex real-world problems, offering a clear advantage over more cumbersome alternatives. These properties make the w-value a superior framework for analyzing cooperation under public externalities. A numerical illustration demonstrates the step-by-step calculation process. Finally, we apply the concept to international climate negotiations, showing how it provides a theoretical rationale for the shift from rigid mandatory emission reduction systems toward the flexible structure of Nationally Determined Contributions.