The University of Southampton
University of Southampton Institutional Repository

Applied game theory and optimal mechanism design

Applied game theory and optimal mechanism design
Applied game theory and optimal mechanism design
This thesis applies game theory to study optimal toehold bidding strategies during takeover competition, the problem of optimal design of voting rules and the design of package bidding mechanism to implement the core allocations. It documents three different research questions that are all related to auction theory. Chapter 2 develops a two-stage takeover game to explain toehold puzzle in the context of takeover. Potential bidders are allowed to acquire target shares in the open market, subject to some limitations. This pre-bid ownership is known as a toehold. Purchasing a toehold prior to making any takeover offer looks like a profitable strategy given substantial takeover premiums. However actual toehold bidding has decreased since 1980s and now is not common. Its time-series patter is centred on either zero or a large value.

Chapter 2 develops a two-stage takeover game. In the first stage of this two-stage game, each bidder simultaneously acquires a toehold. In the second stage, bidders observe acquired toehold sizes, and process this information to update their beliefs about rival's private valuation. Then each bidder competes to win the target under a sealed-bid second-price auction. Different from previous toehold puzzle literature focusing on toehold bidding costs in the form of target managerial entrenchment, this chapter develops a two-stage takeover game and points another possible toehold bidding cost - the opportunity loss of a profitable resale. Chapter 2 finds that, under some conditions, there exists a partial pooling Bayesian equilibrium, in which low-value bidders optimally avoid any toehold, while high-value bidders pool their decisions at one size. The equilibrium toehold acquisition strategies coincide with the bimodal distribution of the actual toehold purchasing behaviour.

Chapter 3 studies the problem of optimal design of voting rules when each agent faces binary choice. The designer is allowed to use any type of non-transferable penalty on individuals in order to elicit agents' private valuations. And each agent's private valuation is assumed to be independently distributed. Early work showed that the simple majority rule has good normative properties in the situation of binary choice. However, their results relay on the assumption that agents' preferences have equal intensities. Chapter 3 shows that, under reasonable assumptions, the simple majority is the best voting mechanism in terms of utilitarian efficiency, even if voters' preferences are comparable and may have varying intensities. At equilibrium, the mechanism optimally assigns zero penalty to every voter. In other words, the designer does not extract private information from any agent in the society, because the expected penalty cost of eliciting private information to select the better alternative is too high.

Chapter 4 presents a package bidding mechanism whose subgame perfect equilibrium outcomes coincide with the core of an underlying strictly convex transferable utility game. It adopts the concept of core as a competitive standard, which enables the mechanism to avoid the well-known weaknesses of VCG mechanism. In this mechanism, only core allocations generate subgame perfect equilibrium payoffs, because non-core allocations provide arbitrage opportunities for some players. By the strict convexity assumption, the implementation of the core is achieved in terms of expectation.
Zhang, Qi
4cf8741a-d55e-4712-b7f3-bdf4f144cb09
Zhang, Qi
4cf8741a-d55e-4712-b7f3-bdf4f144cb09
Kwiek, Maksymilian
84ba7dab-b54b-4d22-8cf3-817b2a2077cf
Ianni, Antonella
35024f65-34cd-4e20-9b2a-554600d739f3

Zhang, Qi (2014) Applied game theory and optimal mechanism design. University of Southampton, School of Economics, Doctoral Thesis, 105pp.

Record type: Thesis (Doctoral)

Abstract

This thesis applies game theory to study optimal toehold bidding strategies during takeover competition, the problem of optimal design of voting rules and the design of package bidding mechanism to implement the core allocations. It documents three different research questions that are all related to auction theory. Chapter 2 develops a two-stage takeover game to explain toehold puzzle in the context of takeover. Potential bidders are allowed to acquire target shares in the open market, subject to some limitations. This pre-bid ownership is known as a toehold. Purchasing a toehold prior to making any takeover offer looks like a profitable strategy given substantial takeover premiums. However actual toehold bidding has decreased since 1980s and now is not common. Its time-series patter is centred on either zero or a large value.

Chapter 2 develops a two-stage takeover game. In the first stage of this two-stage game, each bidder simultaneously acquires a toehold. In the second stage, bidders observe acquired toehold sizes, and process this information to update their beliefs about rival's private valuation. Then each bidder competes to win the target under a sealed-bid second-price auction. Different from previous toehold puzzle literature focusing on toehold bidding costs in the form of target managerial entrenchment, this chapter develops a two-stage takeover game and points another possible toehold bidding cost - the opportunity loss of a profitable resale. Chapter 2 finds that, under some conditions, there exists a partial pooling Bayesian equilibrium, in which low-value bidders optimally avoid any toehold, while high-value bidders pool their decisions at one size. The equilibrium toehold acquisition strategies coincide with the bimodal distribution of the actual toehold purchasing behaviour.

Chapter 3 studies the problem of optimal design of voting rules when each agent faces binary choice. The designer is allowed to use any type of non-transferable penalty on individuals in order to elicit agents' private valuations. And each agent's private valuation is assumed to be independently distributed. Early work showed that the simple majority rule has good normative properties in the situation of binary choice. However, their results relay on the assumption that agents' preferences have equal intensities. Chapter 3 shows that, under reasonable assumptions, the simple majority is the best voting mechanism in terms of utilitarian efficiency, even if voters' preferences are comparable and may have varying intensities. At equilibrium, the mechanism optimally assigns zero penalty to every voter. In other words, the designer does not extract private information from any agent in the society, because the expected penalty cost of eliciting private information to select the better alternative is too high.

Chapter 4 presents a package bidding mechanism whose subgame perfect equilibrium outcomes coincide with the core of an underlying strictly convex transferable utility game. It adopts the concept of core as a competitive standard, which enables the mechanism to avoid the well-known weaknesses of VCG mechanism. In this mechanism, only core allocations generate subgame perfect equilibrium payoffs, because non-core allocations provide arbitrage opportunities for some players. By the strict convexity assumption, the implementation of the core is achieved in terms of expectation.

PDF
Qi thesis final copy.pdf - Other
Download (763kB)

More information

Published date: March 2014
Organisations: University of Southampton, Economics

Identifiers

Local EPrints ID: 370438
URI: http://eprints.soton.ac.uk/id/eprint/370438
PURE UUID: 25f0ac99-bd2f-425c-a7a8-55a12dc75640
ORCID for Antonella Ianni: ORCID iD orcid.org/0000-0002-5003-4482

Catalogue record

Date deposited: 27 Oct 2014 13:09
Last modified: 03 Oct 2018 00:35

Export record

Contributors

Author: Qi Zhang
Thesis advisor: Maksymilian Kwiek
Thesis advisor: Antonella Ianni ORCID iD

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×