Game theory studies strategic decision making among multiple rational players. Since 1950 Nash’s famous paper, it has wide applications to many fields: political science, financial market, cooperate finance, industrial organization and etc. Researchers are not only interested in the applications of game theory but also focus on the mechanism design that considers the structure of game forms. In this dissertation, I explore both areas: the first two chapters consider the games played by multiple players in industrial organization and the third chapter considers the mechanism design problem for the assignment problem.
Continued government support of public good programs (e.g. assistance to less developed countries, or to university researchers for work on a multistage project, or to communities for environmental improvement programs) often depends on grant recipients making adequate progress toward their goals. Chapter 1 studies a prisoner’s dilemma with positive payoffs that will repeat a given known number of times or until there is evidence of cheating, whichever comes first. Our discussion focuses precisely on how much cooperation is possible (i.e., for how many periods cooperation lasts). When the termination rule is based on perfect information about the players’ behavior and players are motivated to cooperate for at least one period, early termination of the game never occurs, i.e. cooperation continues until the last possible period. Cooperation may end sooner when the termination rule is based on imperfect information about the players’ behavior. For the case of imperfect information, I show how much cooperation can occur as a function of the model parameters and under the assumption that players are able to engage in mutual monitoring.
Chapter 2 investigates the motivation of mutual recommendations. It seems irrational for people to refer customers to the other stores without having any profit. But such examples are around us, for example, a mechanical shop may refer customers to another one when it cannot fix the issues. In this chapter, I consider a two-player infinitely repeated game. Players, in each period, can either choose recommendation or not-recommendation that depends on the history of a public signal. A new mechanism, k + 1 punishment scheme, is proposed in which two players stop recommending when k consecutive bag signals occur. Among all possible k + 1 punishment schemes, there exists a unique optimal k* to maximize the player’s payoff. Thus, mutual recommendations between players can increase their overall profits even if such action incurs cost.
Chapter 3 investigates a typical class of assignment problems, which relaxes the assumption of the completeness of bipartite graphs but enforces balance conditions. When the domain is 2-connectivity (each agent has at most 2 available tasks), I find there exist mechanisms satisfying ordinal-efficiency, equal treatment of equals, and strategy-proof. This result does not restrict the number of players in the game. Since a strong negative result exists in the standard assignment problem, I propose a new mechanism, hybrid mechanism, to find a more relaxed domain to simultaneously satisfy all previous three conditions.
The last chapter of my dissertation explores the portfolio management. It compares the results of the decay model with various DCC-GARCH models in risk parity strategy. 16 commodity futures data ranging from 1990.1.1 to 2013.12.31 are implemented to construct portfolio weights. The performance measures are risk attribution, Sharpe Ratio, total return, loss functions and rolling volatilities. I find the decay model and DCC-GARCH model have the similar performances under risk-parity strategy, even if they have different assumptions about the covariance matrix.