Applied game theory and optimal mechanism design

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.

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Identifiers

ORCID for Antonella Ianni: orcid.org/0000-0002-5003-4482

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