Essays on Blocking Mechanisms in Economies with Club Goods

Abstract

The thesis intends to investigate blocking mechanisms in club economies by analyzing the notion of core and bargaining sets. We adapt the framework of Ellickson et al. (1999) in this regard. Clubs in this framework are treated in a parallel fashion to private goods as articles of choice. Each club is composed of two components: (i) the profile of the club and (iii) the club project. Thus, clubs are identified through their member characteristics and the local public project they undertake. The competitive equilibria notion in our setup is known as club equilibrium, where each agent maximizes their utility through their choice of states, which depict a combination of private goods and club memberships in our framework. It should be noted that for any state of the economy, given the club profiles, the “consistency” condition for club memberships reveals the optimal number of clubs that need to be formed for each type to satisfy the membership demand in that state. To begin with, we try to answer one of the more nascent questions in the literature on general equilibrium theory by investigating the equivalence between the set of equilibrium states and the bargaining set for a club economy. We introduce the bargaining set for such an economy in line with Aumann and Maschler (1961) and define a two-step veto mechanism. We establish that non-club-equilibrium states are those against which there exists a set of agents and a price vector at which they are willing to trade amongst themselves rather than consume the non-club-equilibrium state assigned to them, and all other agents (weakly) prefer the non-club-equilibrium state to trade at that particular price vector. In other words, there is a Walrasian objection to non-club-equilibrium states. We further show that Walrasian objections are also justified, which helps us to establish our bargaining -equilibrium equivalence. As a second main contribution, we follow along the lines of the first contribution to introduce the bargaining set as a solution concept to talk about the repercussions of the objection mechanism from agents. In this regard, we adapt the concept of global bargaining set introduced by Vind (1992) for our club economy and provide characterizations of it in terms of the size of the (counter-) objecting coalitions, thereby extending the works of Schjødt and Sloth (1994) and Herves-Estevez and Moreno-Garcıa (2015). In the process, we obtain Schmeidler’s (1972) and Vind’s (1972) theorem for atomless club economies as simple corollaries. We provide further interpretations of the global bargaining set in terms of approximately robustly efficient states, a notion familiarised by Bhowmik and Kaur (2023) for club economies. The final contribution of the thesis aims to study some classical results concerning the equivalence between the core and equilibrium states in a mixed club economy. We begin with an atomless club economy as in Ellickson et al. (1999) and then allow for some agents to form cartels. The economy thus formed is characterized by the presence of both negligible and non-negligible agents to consider an oligopolistic setting as in Shitovitz (1973). Clubs in such an economy are interpreted to have no market power, as the amount of inputs required to form them is insignificant compared to the aggregate endowment resources of the economy. We follow a kind of similar approach to Greenberg and Shitovitz (1986) and establish the equivalence between the core (resp. club equilibria) of an atomless economy with the core (resp. club equilibria) of its associated mixed club economy, which generalizes the core-equivalence theorem of Ellickson et al. (1999) to the case of a mixed club economy.