Author: Mr. Songzi Du

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Published: 2012

Total Pages:

ISBN-13:

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This dissertation consists of three essays on the foundation and applications of game theory. In Chapter 1 we study a refinement of correlated equilibrium in which players' actions are driven by their beliefs and higher order beliefs about the play of the game (beliefs over what other players will do, over what other players believe others will do, etc.). For any finite, complete-information game, we characterize the behavioral implications of this refinement with and without a common prior, and up to any a priori fixed depth of reasoning. In every finite game "most" correlated equilibrium distributions are consistent with this refinement; as a consequence, this refinement gives a classification of "most" correlated equilibrium distributions based on the maximum order of beliefs used by players in the equilibrium. On the other hand, in a generic two-player game any non-degenerate mixed-strategy Nash equilibrium is not consistent with this refinement. In the next two chapters we turn to the applications of game theory. In Chapter 2 we show that without flexible transfers, the timing of transactions is difficult to coordinate in large matching markets. In our model, some agents have the option of matching early before others arrive. We compare two regimes. In the first regime, transfers which divide surpluses created between the two sides of the market are exogenously fixed, perhaps due to some institutional constraints. Then even with a centralized mechanism that implements a stable matching after all agents arrive, some agents have incentives to match early. We prove that in this setting, as the market gets large, on average approximately one quarter of all agents have strict incentives to match early. Moreover, as the market gets large, with probability tending to 1 there is no early matching scheme that is dynamically stable. On the other hand, in the second regime in which agents can freely negotiate transfers, a stable matching after all agents arrive eliminates all incentives to match early and is dynamically stable. In Chapter 3 we study settlement auctions for credit default swaps (CDS). We find that the one-sided design of CDS auctions used in practice gives CDS buyers and sellers strong incentives to distort the final auction price, in order to maximize payoffs from existing CDS positions. Consequently, these auctions tend to overprice defaulted bonds conditional on an excess supply and underprice defaulted bonds conditional on an excess demand. In our model bidders have a commonly-known bond value but privately-known CDS positions. We prove that with a one-sided auction in every Bayesian-Nash equilibrium the final auction price is strictly greater than the common bond value given an excess supply of bonds, and strictly less than the common bond value given an excess demand of bonds. We propose a double auction to mitigate this price bias. Finally, we find the predictions of our model on bidding behavior to be consistent with data on CDS auctions.

Download or read book Essays in Game Theory written by Mr. Songzi Du and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three essays on the foundation and applications of game theory. In Chapter 1 we study a refinement of correlated equilibrium in which players' actions are driven by their beliefs and higher order beliefs about the play of the game (beliefs over what other players will do, over what other players believe others will do, etc.). For any finite, complete-information game, we characterize the behavioral implications of this refinement with and without a common prior, and up to any a priori fixed depth of reasoning. In every finite game "most" correlated equilibrium distributions are consistent with this refinement; as a consequence, this refinement gives a classification of "most" correlated equilibrium distributions based on the maximum order of beliefs used by players in the equilibrium. On the other hand, in a generic two-player game any non-degenerate mixed-strategy Nash equilibrium is not consistent with this refinement. In the next two chapters we turn to the applications of game theory. In Chapter 2 we show that without flexible transfers, the timing of transactions is difficult to coordinate in large matching markets. In our model, some agents have the option of matching early before others arrive. We compare two regimes. In the first regime, transfers which divide surpluses created between the two sides of the market are exogenously fixed, perhaps due to some institutional constraints. Then even with a centralized mechanism that implements a stable matching after all agents arrive, some agents have incentives to match early. We prove that in this setting, as the market gets large, on average approximately one quarter of all agents have strict incentives to match early. Moreover, as the market gets large, with probability tending to 1 there is no early matching scheme that is dynamically stable. On the other hand, in the second regime in which agents can freely negotiate transfers, a stable matching after all agents arrive eliminates all incentives to match early and is dynamically stable. In Chapter 3 we study settlement auctions for credit default swaps (CDS). We find that the one-sided design of CDS auctions used in practice gives CDS buyers and sellers strong incentives to distort the final auction price, in order to maximize payoffs from existing CDS positions. Consequently, these auctions tend to overprice defaulted bonds conditional on an excess supply and underprice defaulted bonds conditional on an excess demand. In our model bidders have a commonly-known bond value but privately-known CDS positions. We prove that with a one-sided auction in every Bayesian-Nash equilibrium the final auction price is strictly greater than the common bond value given an excess supply of bonds, and strictly less than the common bond value given an excess demand of bonds. We propose a double auction to mitigate this price bias. Finally, we find the predictions of our model on bidding behavior to be consistent with data on CDS auctions.