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Monopoly Pricing in the Presence of Social Learning
, 2011
"... To be submitted on November 2011 A monopolist offers a product to a market of consumers with heterogeneous quality preferences. Although initially uninformed about the product quality, they learn by observing past purchase decisions and reviews of other consumers. Our goal is to analyze the social l ..."
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To be submitted on November 2011 A monopolist offers a product to a market of consumers with heterogeneous quality preferences. Although initially uninformed about the product quality, they learn by observing past purchase decisions and reviews of other consumers. Our goal is to analyze the social learning mechanism and its effect on the seller’s pricing decision. This analysis borrows from the literature on social learning and on pricing and revenue management. Consumers follow a naive decision rule and, under some conditions, eventually learn the product’s quality. Using meanfield approximation, the dynamics of this learning process are characterized for markets with high demand intensity. The relationship between the price and the speed of learning depends on the heterogeneity of quality preferences. Two pricing strategies are studied: a static price and a single price change. Properties of the optimal prices are derived. Numerical experiments suggest that pricing strategies that account for social learning may increase revenues considerably relative to strategies that do not.
Decentralized Dynamics for Finite Opinion Games ⋆
"... Abstract. Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations. In the spirit of the field, we study the computat ..."
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Abstract. Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations. In the spirit of the field, we study the computation of solution concepts by means of decentralized dynamics. These are algorithms in which players move in turns to improve their own utility and the hope is that the system reaches an “equilibrium” quickly. We study these dynamics for the class of opinion games, recently introduced by [1]. These are games, important in economics and sociology, that model the formation of an opinion in a social network. We study bestresponse dynamics and show that the convergence to Nash equilibria is polynomial in the number of players. We also study a noisy version of bestresponse dynamics, called logit dynamics, and prove a host of results about its convergence rate as the noise in the system varies. To get these results, we use a variety of techniques developed to bound the mixing time of Markov chains, including coupling, spectral characterizations and bottleneck ratio. 1
Eulerian Opinion Dynamics with Bounded Confidence and Exogenous Inputs ⋆
"... Abstract: The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated with nonBayesian ”rule of thumb” methods. This pape ..."
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Abstract: The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated with nonBayesian ”rule of thumb” methods. This paper focuses on an Eulerian boundedconfidence model of opinion dynamics with a potential timevarying input. First, we prove some properties of this system’s dynamics with timevarying input. Second, we derive a simple sufficient condition for opinion consensus, and prove the convergence of the population’s distribution with no input to a sum of Dirac Delta functions. Finally, we define an input’s attraction range, and for a normally distributed input and uniformly distributed initial population, we conjecture that the length of attraction range is an increasing affine function of population’s confidence bound and input’s variance.
Trust and manipulation in social networks
, 2013
"... We investigate the role of manipulation in a model of opinion formation where agents have opinions about some common question of interest. Agents repeatedly communicate with their neighbors in the social network, can exert some effort to manipulate the trust of others, and update their opinions taki ..."
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We investigate the role of manipulation in a model of opinion formation where agents have opinions about some common question of interest. Agents repeatedly communicate with their neighbors in the social network, can exert some effort to manipulate the trust of others, and update their opinions taking weighted averages of neighbors ’ opinions. The incentives to manipulate are given by the agents’ preferences. We show that manipulation can modify the trust structure and lead to a connected society, and thus, make the society reaching a consensus. Manipulation fosters opinion leadership, but the manipulated agent may even gain influence on the longrun opinions. In sufficiently homophilic societies, manipulation accelerates (slows down) convergence if it decreases (increases) homophily. Finally, we investigate the tension between information aggregation and spread of misinformation. We find that if the ability of the manipulating agent is weak and the agents underselling (overselling) their information gain (lose) overall influence, then manipulation reduces misinformation and agents
Chinese Restaurant Game
"... Abstract—In this letter, by introducing the strategic decision making into the Chinese restaurant process, we propose a new game, called Chinese Restaurant Game, as a new general framework for analyzing the individual decision problem in a network with negative network externality. Our analysis show ..."
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Abstract—In this letter, by introducing the strategic decision making into the Chinese restaurant process, we propose a new game, called Chinese Restaurant Game, as a new general framework for analyzing the individual decision problem in a network with negative network externality. Our analysis shows that a balance in utilities among the customers in the game will eventually be achieved under the strategic decision making process. The equilibrium grouping is defined to describe the predicted outcome of the proposed game, which can be found by a simple algorithm. The simulation results confirm that the rational customers in Chinese restaurant game automatically achieve a balance in loading in order to reduce the impact from the negative network externality. Index Terms—Chinese restaurant game, game theory, Nash equilibrium, network externality. I.