Coalitional stability under myopic expectations and externalities

TL;DR

This paper investigates coalition stability with externalities under myopic expectations, providing conditions for core non-emptiness, characterizations of core partitions, and establishing links between different preference settings.

Contribution

It introduces a sufficient condition for core non-emptiness in externality-laden coalition problems and connects order-preserving preferences with externalities.

Findings

Sufficient condition for non-empty core and stable set

Characterization of all core partitions under this condition

Equivalence of core and stable set in order-preserving preferences

Abstract

We study coalition formation problems in the presence of externalities, focusing on settings where agents exhibit myopic expectations, that is, they evaluate potential deviations based solely on the immediate outcome, assuming no further reactions or reorganization by others. First, we establish a sufficient condition for the non-emptiness of both the core and the stable set. In the case of the core, our condition for ensuring non-emptiness also provides a characterization of all core partitions. We then turn our attention to problems with order-preserving preferences. Under our sufficient condition, the core and the stable set not only exist but also coincide, and convergence to a stable outcome is guaranteed. Furthermore, using the notion of absorbing set, we draw a connection between problems with order-preserving preferences and those without externalities. This allows us to lift known core non-emptiness results from the latter setting to the former, thereby establishing a novel bridge between these two classes of problems.