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Three essays in microeconomics

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Title: Three essays in microeconomics
Author(s): Rong, Kang
Director of Research: Williams, Steven
Doctoral Committee Chair(s): Williams, Steven
Doctoral Committee Member(s): Bernhardt, Dan; Taub, Bart; Polborn, Mittias
Department / Program: Economics
Discipline: Economics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Alternating-offer game Final-offer arbitration Splitting-the-difference Delay in bargaining Arbitration problem Kalai-Smorodinsky solution Public goods alpha proportional individual rationality Asymptotic efficiency Asymptotic inefficiency Convergence rates.
Abstract: This dissertation consists of three essays in microeconomics. The first essay studies a finite-horizon alternating-offer model that integrates the common practice of having an arbitrator determine the outcomes if both players' offers are rejected. We find that if the arbitrator uses final-offer arbitration (as in professional baseball), and the arbitrator does not excessively favor one player, then the unique subgame-perfect equilibrium always coincides with the subgame-perfect equilibrium outcome in Rubinstein's infinite-horizon alternating-offer game. However, if the arbitrator sufficiently favors the player making the initial offer, then delay occurs in equilibrium. If, instead, the arbitrator uses the split-the-difference arbitration rule, then the unique subgame-perfect equilibrium can feature immediate agreement, delayed agreement, or no agreement, depending on the discount factor. The second essay studies the arbitration problem using the axiomatic approach. In particular, we define an arbitration problem as the triplet of a bargaining set and the offers submitted by two players. We characterize the solution to a class of arbitration problems using the axiomatic approach. The axioms we impose on the arbitration solution are ``Symmetry in Offers,'' ``Invariance'' and ``Pareto Optimality.'' The key axiom, ``Symmetry in Offers,'' requires that whenever players' offers are symmetric, the arbitrated outcome should also be symmetric. We find that there exists a unique arbitration solution, called the symmetric arbitration solution, that satisfies all three axioms. We then analyze a simultaneous-offer game and an alternating-offer game. In both games, the symmetric arbitration solution is used to decide the outcome whenever players cannot reach agreement by themselves. We find that in both games, if the discount factor of players is close to 1, then the unique subgame perfect equilibrium outcome coincides with the Kalai-Smorodinsky solution outcome. The third essay studies the public good provision problem in which a public good can be provided and payments can be collected from agents only if the proportion of agents who obtain nonnegative expected utilities from the public good provision mechanism weakly exceeds a prespecified ratio alpha. We call this requirement ``alpha proportional individual rationality''. We identify a key threshold such that if alpha is less than this threshold, then efficiency obtains asymptotically. If alpha is greater than the threshold, then inefficiency obtains asymptotically. In addition, we obtain the convergence rate of the probability of provision to its efficient/inefficient level.
Issue Date: 2012-09-18
URI: http://hdl.handle.net/2142/34457
Rights Information: Copyright 2012 Kang Rong
Date Available in IDEALS: 2012-09-18
Date Deposited: 2012-08
 

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