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In this paper, we study a passenger–taxi matching queue system. The system is modeled as a birth-and-death process. Since the system is so complex, we mainly focus on numerical analysis. A centralized system and a decentralized one are considered. In the centralized system, the government sets thresholds for both passengers and taxis to maximize the social welfare. We analyze the performance measures of this model, discuss the range of two thresholds that ensures positive social welfare, and numerically give the upper bound of threshold. In the decentralized system, passengers and taxis determine whether to join the system or balk based on their individual utility functions. Further, we consider the government’s tax and subsidy to the taxi drivers. Numerical results show that the social welfare function in the centralized system is concave with respect to the thresholds and the government central planning benefits the society. In the decentralized system, no matter what the passenger and taxi arrival rates are, the social welfare is concave with respect to the taxi fare. Moreover, we analyze the effect of the arrival rates and the benefits of the tax and subsidy.

There exists a widely held belief that informed investors manipulate stock prices prior to seasoned equity offerings (SEO). Contrary to this assertion, a model is developed, which demonstrates there is significant evidence that informed investors not to manipulate trading prior to a SEO. Furthermore, there is an arguement that informed investors to trade the stock in the same direction indicated by their private information. In addition, the model is consistent with previous empirical evidence. Previous literature heavily relies on the Gerard and Nanda (1993) model. The model allows for more than one informed investors, whereas Gerard and Nanda de facto allows for only one. This model setting is not only more realistic to the real world, but also dramatically reverses its conclusion that there exists manipulative trading. It also indicated that following Securities and Exchange Commission (SEC) Rule 10b-21 and Rule 105, whose intention is to curb this manipulation, the SEO discount will change in either direction. Thus previous literature delineating methodology of utilizing the SEO discount change to test for the existence of manipulative trading is not well grounded. The model also predicts that undervalued firms tend to disclose more information in order to improve the stock price informativeness, whereas overvalued firms tend to do the contrary.

The properties of Cournot mixed oligopoly consisting of one public firm and one or more than one private firms have mostly been analyzed for simple cases on the basis of numerical calculations of the equilibrium values for a linear market demand function and linear or quadratic cost functions. In this chapter, after proving the existence of a unique equilibrium in Cournot mixed oligopoly under general conditions on the market demand and each firm’s cost function, we derive conditions ensuring the existence of a unique Nash equilibrium for the mixed oligopoly where one public firm and at least one of the private firms are active in a general model of Cournot mixed oligopoly with one public firm and several private firms.

We consider jamming in wireless networks in the framework of zero-sum games with linearized Shannon capacity utility function. The base station has to distribute the power fairly among the users in the presence of a jammer. The jammer in turn tries to distribute its power among the channels to produce as much harm as possible. This game can also be viewed as a minimax problem against the nature. We show that the game has the unique equilibrium and investigate its properties and also we developed an efficient algorithm which allows to find the optimal strategies in finite number of steps.

Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe — about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the part of other players, as to what a player will do. Common knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures implies that the conjectures form a Nash equilibrium. When n ≥ 3 and there is a common prior, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures, imply that the conjectures form a Nash equilibrium. Examples show the results to be tight.