Selection, Learning, and Nomination: Essays on Supermodular Games, Design, and Political Theory

Citation

Mathevet, Laurent Alexandre (2008) Selection, Learning, and Nomination: Essays on Supermodular Games, Design, and Political Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/BQAQ-KV91. https://resolver.caltech.edu/CaltechETD:etd-05282008-122413

Abstract

Games with strategic complementarities (GSC) possess nice properties in terms of learning and structure of the equilibria. Two major concerns in the theory of GSC and mechanism design are addressed. Firstly, complementarities often result in multiple equilibria, which requires a theory of equilibrium selection for GSC to have predictive power. Chapter 2 deals with global games, a selection paradigm for GSC. I provide a new proof of equilibrium uniqueness in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction principle. Furthermore, the contraction-mapping approach provides an intuition for why uniqueness arises: complementarities generate multiple equilibria, but the global-games structure dampens complementarities until one equilibrium survives. Secondly, there is a concern in mechanism design about the assumption of equilibrium play. Chapter 3 examines the problem of designing mechanisms that induce supermodular games, thereby guiding agents to play desired equilibrium strategies via learning. In quasilinear environments, I prove that if a scf can be implemented by a mechanism that generates bounded substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the scf. If the scf also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances budget. Then I provide general sufficient conditions for a scf to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. I also give conditions for the equilibrium to be unique. Finally, a supermodular revelation principle is provided for general preferences. The final chapter is an independent chapter on political economics. It provides three different processes by which two political parties nominate candidates for a general election: Nominations by party leaders, by a vote of party members, and by a spending competition. It is shown that more extreme outcomes can emerge from spending competition and that non-median outcomes can result via any process. Under endogenous party membership, median outcomes ensue when nominations are decided by a vote but not with spending competition.

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