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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 41188 (02)
- University: Sharif University of Technology
- Department: Mathematical Science
- Advisor(s): Mahmoodian, Ebadollah; Safari, Mohammad Ali
- Abstract:
- In this research, we study a new model for market on population games; two competing companies sell two comparable products within a social network. Like the classic treatments of this problem, we model the social network by a graph whose edges represent the interaction between people. The main difference, however, is that nodes of the graph represent communities in the society instead of individuals. Each community consists of a continuum of potential small agents which interact anonymously. In our model, the two companies first announce their prices and, then, agents within communities choose which company to buy from.An agent’s utility basically depends on the fraction of neighbours that are buying the same product as that agent. The goal is to study the behaviour of both agents (as consumers) and the two competing companies in this game. We consider the noisy best-response, logit-response, dynamics for the evolution of the market. In this setting, agents revise their strategies asynchronously. Each agent plays the strategy with the best payoff with probability close to 1; hence, allowing a slight probability of making mistakes. This may happens in reality when agents’ information about the environment is incomplete, when agents make mistakes in their computations, or when agents are not fully rational.The noisy best-response dynamics have been studied as a base model for the interaction of technologies and social norms. We have considered two separate games in our model. The first one is between agents who choose between the two products and the second one is between the two companies that choose their prices. For the first game we show that with the logit-response dynamic, the market always converges to an equilibrium point and provide a polynomial time algorithm for computing such an equilibrium. We show that the game will be a full potential game and its equilibrium point is the global maximum of some potential function. We also prove that agents within same community buy same product in the equilibrium. As for the second game, we study the behaviour of the two companies and obtain several results. After studying the best response behaviour of the companies, we will show that the game has either no pure Nash equilibrium or has a unique one. Furthermore, the noisy best-response dynamic between agents converge to this unique equilibrium
- Keywords:
- Population Games ; Noisy-Best-Response Dynamics ; Logit-Response Dynamics ; Full Potential Games ; Market Pricing
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