Essays on Collective Contests and Bargaining/ Dhritiman Gupta

Thesis (Ph.D) - Indian Statistical Institute, 2020

Introduction -- Prize Sharing Rule in Collective Contests: Towards Strategic Foundations -- Prize Sharing Rules in Collective Contests: When Does Group Size Matter? -- Bargaining for Assembly

Guided by Prof. Guided by Prabal Roy Chowdhury

This thesis consists of three theoretical essays in Microeconomics. The first two essays analyze
the properties of a particular class of prize sharing rules groups may employ in a situation of a
collective contest with another group, over a private good. The third essay studies a situation
of multi-lateral bargaining, where a buyer wants to successfully bargain with multiple sellers,
who own an input each, so that he can implement a grand project. The main focus of the
thesis is to theorize about and generate hypotheses of the situations summarized above.
In the first chapter, we consider a situation of a collective contest between two groups
of different sizes and pick for analysis a prize sharing rule groups may employ to share the
prize within the group in case of success. The rule being analyzed was introduced in Nitzan
(1991) and subsequently became the standard in the collective contests literature. Despite its
popularity the rule is ad hoc. In this chapter, we provide a robust strategic basis to these
prize sharing rules.
In the second chapter once again we deal with the same context as the first chapter, i.e.,
a collective contest over a private prize between two differently sized groups. We analyze
in depth the prize sharing rules introduced in Nitzan (1991). We posit a restriction on the
rule which can be interpreted as a group specific norm of competitiveness. We then go on to
analyze how the posited social norms affect the outcomes of the contest. In particular, we
analyze how these social norms affect the welfare of the groups participating in the contest.
In the third chapter we consider a situation of multi-lateral bargaining between a buyer and multiple sellers, who own and input each. The buyer needs to successfully bargain with
multiple sellers in order to implement a project. We embed the sellers in a graph and study
how the underlying structure of the graph, which determines the locations of the sellers,
affects the outcomes of the ensuing bargaining game. Specifically, we show how the presence
of indispensable sellers turns out to be crucial to the way the surplus is divided in equilibrium.
In the following sections we take up one chapter at a time and provide a brief description
outlining the research questions, the theoretical approach taken and the main findings.