Solving Cooperative Reliability Games

TL;DR

This paper introduces the reliability extension of cooperative games, accounting for agent failures, and explores solution concepts like the Shapley value and core stability, with methods for approximation and conditions for stability enhancement.

Contribution

It proposes the reliability extension model for cooperative games, providing algorithms for approximating the Shapley value and computing the core, and shows how reliability can stabilize the game.

Findings

Approximate Shapley value in reliability games

Core computation for few agent types

Reliability extension can stabilize games

Abstract

Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only "survives" with a certain probability, and a coalition's value is the probability that its surviving members would be a winning coalition in the base game. We study prominent solution concepts in such games, showing how to approximate the Shapley value and how to compute the core in games with few agent types. We also show that applying the reliability extension may stabilize the game, making the core non-empty even when the base game has an empty core.