The Expected Shapley value on a class of probabilistic games

TL;DR

This paper introduces the Expected Shapley value for probabilistic cooperative games, extending classical concepts to account for known realization probabilities and providing axiomatic characterizations.

Contribution

It defines and characterizes the Expected Shapley value for a new class of probabilistic cooperative games with known realization probabilities.

Findings

Provides three axiomatic characterizations of the Expected Shapley value.

Extends classical Shapley value to probabilistic settings with known probabilities.

Offers a method to allocate expected worth in probabilistic cooperative scenarios.

Abstract

We study a class of probabilistic cooperative games which can be treated as an extension of the classical cooperative games with transferable utilities. The coalitions have an exogenous probability of being realized. This probability distribution is known beforehand and the distribution of the expected worth needs to be done before the realization of the state. We obtain a value for this class of games and present three characterizations of this value using natural extensions of the axioms used in the seminal axiomatization of the Shapley value. The value, which we call the Expected Shapley value, allocates the players their expected worth with respect to a probability distribution.