TY - JOUR

T1 - Decision support for buying cooperation in Nash-stable coalition partitions for environmental differential games

AU - Zhou, Jiangjing

AU - Mazalov, Vladimir

PY - 2026/5/10

Y1 - 2026/5/10

N2 - We analyze Nash-stable coalition partitions in a differential game with heterogeneous player populations; as a leading application, we study an asymmetric game of pollution control. Type-I players are non-vulnerable to pollution and do not internalize damages in their production choices, whereas Type-II players fully internalize the damages. We characterize optimal feedback strategies under alternative coalition partitions, establish conditions for Nash-stable partitions for fixed numbers of Type-I and Type-II players, and identify when vulnerable players can incentivize non-vulnerable players to cooperate in emission control. We prove that, under a non-transferable payoff scheme, no Nash-stable coalition partition exists, whereas under a transferable scheme with the CIS value, a stable partition can be achieved. We also provide a compact compute-allocate-verify module that, given the model parameters and a feasible-partition set, computes feedback Nash equilibrium, allocates CIS values, and verifies unilateral deviations to identify Nash-stable coalition partitions.

AB - We analyze Nash-stable coalition partitions in a differential game with heterogeneous player populations; as a leading application, we study an asymmetric game of pollution control. Type-I players are non-vulnerable to pollution and do not internalize damages in their production choices, whereas Type-II players fully internalize the damages. We characterize optimal feedback strategies under alternative coalition partitions, establish conditions for Nash-stable partitions for fixed numbers of Type-I and Type-II players, and identify when vulnerable players can incentivize non-vulnerable players to cooperate in emission control. We prove that, under a non-transferable payoff scheme, no Nash-stable coalition partition exists, whereas under a transferable scheme with the CIS value, a stable partition can be achieved. We also provide a compact compute-allocate-verify module that, given the model parameters and a feasible-partition set, computes feedback Nash equilibrium, allocates CIS values, and verifies unilateral deviations to identify Nash-stable coalition partitions.

KW - Stable coalition partitions

KW - Decision support systems

KW - Emissions

KW - Feedback-Nash equilibrium

KW - Decision support systems

KW - Emissions

KW - Feedback-Nash equilibrium

KW - Stable coalition partitions

UR - https://www.mendeley.com/catalogue/32673f03-694c-3213-9f26-2e12ff2b5cff/

UR - https://www.scopus.com/pages/publications/105034462669

U2 - 10.1016/j.eswa.2026.131322

DO - 10.1016/j.eswa.2026.131322

M3 - статья

VL - 310

JO - Expert Systems with Applications

JF - Expert Systems with Applications

SN - 0957-4174

M1 - 131322

ER -