Three essays on game theory and its applications

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Copyright: Shen, Jianfei
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Abstract
This thesis consists of three papers. The first paper is about voluntary provision of public goods, and the second paper studies elections when candidates are asymmetric and voting is costly. Finally, I discusses the equivalence between quasi-perfect equilibrium and sequential equilibria in the last paper. Chapter 1 considers the problem of collective actions. In an environment of voluntarily provision of public goods, we show that if the players are grouped according to their contributions and if their abilities to contribute are different, then there exist two positive contribution equilibria: one is fully efficient in the sense that all individuals contribute fully, and the other is near fully efficient in the sense that almost all individuals contribute fully. We consider the election problem in Chapter 2. Consider the following environment: An advantaged candidate and a disadvantaged candidate compete in a large election. Candidates exert effort to improve their valences, and voters cast their votes costly. This paper characterizes the pure strategy equilibria in this kind of election games, and gives sufficient conditions for the existence of pure strategy equilibria. We show that for most instances, there exists at least one and at most two pure strategy equilibria. On average a low voting cost causes high campaign efforts, but there also exists an interval of voting costs such that candidates' campaign efforts are strictly increasing on this interval. Moreover, when candidates become similar in terms of their productivity, their equilibrium valence choices also become similar. In Chapter 3 we prove the generic equivalence between quasi-perfect equilibrium and sequential equilibrium. Combining this result with Blume and Zame (1994) shows that perfect, quasi-perfect and sequential equilibrium coincide in generic games. Roughly speaking, this result tells us that if we pick an extensive-form game randomly, then the perfect, quasi-perfect and sequential equilibrium are equivalent for this game.
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Author(s)
Shen, Jianfei
Supervisor(s)
Pimienta, Carlos
Gunnthorsdottir, Anna
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Publication Year
2012
Resource Type
Thesis
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PhD Doctorate
UNSW Faculty
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