Power, Sharing Rules, and Stability in Coalition Formation: Theory and Experiment

Abstract

The chapters included in this dissertation represents an attempt to incorporate the notion of power in examining stability in coalition formation games. Power can emanate from different sources: wealth, military might, or political influence. Whatever the source, power is used by agents to impose their preferences on the rest of society. In the coalition formation games presented in this study, agents who are endowed with power compete for a divisible resource by forming coalitions with other agents. The coalition with the greatest power wins the resource and divides it among its members. Over time, coalitions form and disintegrate and different coalitions yield different payoffs for agents. Which coalitions will ultimately form when agents have heterogenous power? Can we find rules to select coalitions that are stable once formed and at the same time gives its members their highest payoff? The chapters in this study employ an axiomatic approach of searching for these rules that satisfy two main desirable properties: self-enforcement, which requires that no further deviation happens after a coalition has formed, and rationality, which requires that agents pick the coalition that gives them their highest payoff. The existence of these rules may be sensitive to the different features introduced in our coalition formation game. This dissertation and its key results are organized as follows. Chapter 1 enumerates the various applications of coalition formation in some key areas such as industrial organization, trade and international economics, public economics, environmental and resource economics, and political economy. It also introduces the two main approaches that is used in modelling how agents form coalitions. Chapter 2 investigates the implication of power dynamics, where power changes according to the resource share. The main findings show that self-enforcement may not be satisfied in some specific cases, and restrictions on the domain of power or the types of coalitions that can form are needed to satisfy self-enforcement and rationality simultaneously. Chapter 3 disallows power accumulation and investigates the sensitivity of these rules to different ways of dividing the prize (sharing rules). The main findings reveal that, in general, sharing rules may cause disagreements among agents on which coalitions should form. The chapter provides the sufficient and necessary conditions of the sharing rule parameter under which these disagreements can be ruled out. Chapter 4 conducts an economic experiment using a simplified version of a coalition formation game to investigate possible behavioral factors that may explain deviations from theoretical predictions. The main findings show that agents display rational behavior when forming coalitions, especially when they know that a large proportion of their opponents play myopic strategies in the beginning. Over time, however, agents learn to behave more strategically and even more rationally, and thus enables agents to display more of the behavior predicted by our model. Chapter 5 summarizes the key findings of the previous chapters and provides possible further directions for research on coalition formation. The models presented in this dissertation illustrate how power accumulation, the sharing rule, and possible behavioral factors, shape the way coalitions will be stable throughout time.