On the Core of Dynamic Cooperative Games

TL;DR

This paper introduces a framework for dynamic cooperative games where coalition worths evolve over time, allowing for deviations and reformation of the game, and defines three types of core solutions with theoretical characterizations.

Contribution

It develops a novel theoretical framework for dynamic cooperative games with coalition deviations and characterizes three core solution concepts.

Findings

Characterization of fair and stable cores when instantaneous game depends on last allocation.

Definition and analysis of credible core in general dynamic setting.

Resemblance to non-cooperative dynamic game theory.

Abstract

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games.