Essays in Microeconomic Theory

Abstract

If the number of individuals is odd, Campbell and Kelly (2003) show that majority rule is the only non-dictatorial strategy-proof social choice rule on the domain of linear orders that admit a Condorcet winner, an alternative that is preferred to every other by a majority of individuals in pairwise majority voting. This paper shows that the claim is false when the number of individuals is even, and provides a characterization of non-dictatorial strategy-proof social choice rules on this domain. Two examples illustrate the primary reason that the result does not translate to the even case: when the number of individuals is even, no single individual can change her reported preference ordering in a manner that changes the Condorcet winner while remaining within the preference domain. Introducing two new definitions to account for this partitioning of the preference domain, the chapter concludes with a counterpart to the characterization of Campbell and Kelly (2003) for the even case. Adapting the models of Laibson (1994) and O’Donogue and Rabin (2001), a learning–naıve agent is presented who is endowed with beliefs about the value of the quasi–hyperbolic discount factor that enters into the utility calculations of her future–selves. Facing an infinite–horizon decision problem in which the payoff to a particular action varies stochastically, the agent updates her beliefs over time. Conditions are given under which the behavior of a learning–na¨ıve agent is eventually indistinguishable from that of a sophisticated agent, contributing to the efforts of Ali (2011) to justify the use of sophistication as a modeling assumption. Building upon the literature on one–to–one matching pioneered by Gale and Shapley (1962), this paper introduces a social network to the standard marriage model, embodying informational limitations of the agents. Motivated by the restrictive nature of stability in large markets, two new network–stability concepts are introduced that reflect informational limitations; in particular, two agents cannot form a blocking pair if they are not acquainted. Following Roth and Sotomayor (1990), key properties of the sets of network–stable matchings are derived, and concludes by introducing a network–formation game whose set of complete–information Nash equilibria correspond to the set of stable matchings