Essays on Correlated Equilibrium and Voter Turnout

This thesis consists of three essays in the areas of political economy and game theory, unified by their focus on the effects of pre-play communication on equilibrium outcomes.

Communication is fundamental to elections. Chapter 2 extends canonical voter turnout models, where citizens, divided into two competing parties, choose between costly voting and abstaining, to include any form of communication, and characterizes the resulting set of Aumann's correlated equilibria. In contrast to previous research, high-turnout equilibria exist in large electorates and uncertain environments. This difference arises because communication can coordinate behavior in such a way that citizens find it incentive compatible to follow their correlated signals to vote more. The equilibria have expected turnout of at least twice the size of the minority for a wide range of positive voting costs.

In Chapter 3 I introduce a new equilibrium concept, called subcorrelated equilibrium, which fills the gap between Nash and correlated equilibrium, extending the latter to multiple mediators. Subcommunication equilibrium similarly extends communication equilibrium for incomplete information games. I explore the properties of these solutions and establish an equivalence between a subset of subcommunication equilibria and Myerson's quasi-principals' equilibria. I characterize an upper bound on expected turnout supported by subcorrelated equilibrium in the turnout game.

Chapter 4, co-authored with Thomas Palfrey, reports a new study of the effect of communication on voter turnout using a laboratory experiment. Before voting occurs, subjects may engage in various kinds of pre-play communication through computers. We study three communication treatments: No Communication, a control; Public Communication, where voters exchange public messages with all other voters, and Party Communication, where messages are exchanged only within one's own party. Our results point to a strong interaction effect between the form of communication and the voting cost. With a low voting cost, party communication increases turnout, while public communication decreases turnout. The data are consistent with correlated equilibrium play. With a high voting cost, public communication increases turnout. With communication, we find essentially no support for the standard Nash equilibrium turnout predictions.

Efficient registration of nonrigid 3-D bodies

We present a novel method to perform an accurate registration of 3-D nonrigid bodies by using phase-shift properties of the dual-tree complex wavelet transform (DT-CWT). Since the phases of DT-\BBCWT coefficients change approximately linearly with the amount of feature displacement in the spatial domain, motion can be estimated using the phase information from these coefficients. The motion estimation is performed iteratively: first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field. We use a parametric affine model to describe the motion, where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations. From the estimated affine parameters, the motion field between the sensed and the reference data sets can be generated, and the sensed data set then can be shifted and interpolated spatially to align with the reference data set. © 2011 IEEE.