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Mandyam S.,Ecometrix Research | Sridhar U.,Ecometrix Research
Proceedings of the 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2012 | Year: 2012

We model the persuasive effect of external information sources such as media on social networks using a new endogenous social learning framework. The agents are thought to hold uninformative probabilistic prior beliefs about an issue that concerns them and learn about this state of the world through a non-Bayesian myopic DeGroot-style update process applied on the priors using social influence 'mixtures'. We model external information sources in this framework as entities that can bring to the attention of agents 'global' beliefs that are potentially from beyond the confines of a community, and may well be in conflict among themselves. In our model agents score these information sources on the basis of how closely the beliefs propounded by the sources match their own beliefs, but determine how to assimilate such beliefs on the basis of the views of their community of connected neighbors. This form of social learning of external information allows local social influences to carry shared views resulting in the potential emergence of modified homophyllic structures, for example to capture the notion that those who view external information sources in a similar manner might be inclined to demonstrate higher affinities among themselves. We show that this form of social learning of externally expounded beliefs has a learnable dynamic which achieves convergence, and can mirror scenarios where external sources can bring about consensus among opposed cliques, or break emerging consensus. We illustrate the working of the learning model on a simple example. © 2012 IEEE. Source


Sridhar U.,Ecometrix Research | Mandyam S.,Ecometrix Research
Proceedings of the 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2012 | Year: 2012

In this paper we study network games where agents with different skills come together to cooperate and yet competitively pursue individual goals. We propose a multi-agent based utilitarian approach to model the payoff allocation problem for a class of such games where the capabilities of the agents and the payoffs are not known with certainty. The primary objective is to maximize a linear sum of the expected utilities of risk-averse agents; and we consider constant riskaversion with exponential utility functions. We pose the problem as a stochastic cooperative game which is solved in two phases. In the first phase we apply a learning mechanism on this 'social' network of fully connected agents to arrive at a consensus on the capability of every agent in the coalition thus resolving uncertainty in capabilities. Agents initially start with a social influence matrix reflecting the influence agents have on each other and prior subjective beliefs of the capabilities of the others and these beliefs evolve through a process of interaction. We use a variant of the DeGroot algorithm to show that over time learning results in a dynamic update of the beliefs and the social influence matrix leading to a consensus. We provide theoretical convergence proofs for the algorithm. The second phase involves optimizing a capability-weighted sum of the expected utilities of the agents to achieve a group Pareto optimal solution. In this paper we propose a new framework called the Capability Weighted Group Utility Maximizer developed around Borch's theorem borrowed from the actuarial world of insurance to obtain a fair distribution of the stochastic payoffs once a consensus is reached on the capabilities of the agents in the coalition. © 2012 IEEE. Source


Sridhar U.,Ecometrix Research | Mandyam S.,Ecometrix Research
Proceedings of the 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2012 | Year: 2012

A fully connected network of multiple interacting agents modeled as a cooperative game to attain a common objective has found wide applications in the real world. Competitors frequently come together to work in coalitions that are mutually beneficial to them all, though the allocation of the mutual gains achieved is seldom easy. Shapley value is a popular way to compute payoffs in cooperative games where the agents are assumed to have deterministic, risk-neutral (linear) utilities. This paper explores a class of Multi-agent constant-sum cooperative games where the payoffs are random variables. We introduce a new model based on Borch's Theorem from the actuarial world of re-insurance, to obtain a Pareto optimal allocation for agents with risk-averse exponential utilities. This allocation problem seeks to maximize a linear sum of the expected utilities of a set of agents and the solution obtained at this optimal value naturally maximizes the social welfare of the grand coalition. The four main axioms of the Shapely Value, namely, nullity, additivity, symmetry and efficiency are satisfied by this solution. We show the correspondence of our solution to the Shapley value. As a result we can directly obtain the Shapley value from the allocation values obtained at the Pareto optimum as the individual utility achievements of the grand coalition. © 2012 IEEE. Source


Sridhar U.,Ecometrix Research | Mandyam S.,Ecometrix Research
Social Network Analysis and Mining | Year: 2012

Belief learning in social networks is thought to occur through an update process that aggregates dispersed information on the beliefs of connected neighbors through social influences. We explore mechanisms to apply persuasive biases to beliefs at the individual and group level, using the popular DeGroot update as the basic network-learning scheme, to achieve purposeful control on belief learning. We show that linear control of belief learning results in the possibility of shaping the beliefs of individual agents. We prove convergence of the control and show that external persuasive biases, which are our linear control parameters, are not only learnt by the agents just as they learn beliefs, but they can even swamp out the original beliefs. We establish the theoretical foundation for linear dynamic control of belief learning in this paper and illustrate the key results with examples of small networks which show how emerging consensus can be amplified or even destroyed. © 2011, Springer-Verlag. Source


Mandyam S.,Ecometrix Research | Sridhar U.,Ecometrix Research
Social Network Analysis and Mining | Year: 2013

Our focus in this paper is to study a specific type of imitative behavior in the framework of non-Bayesian models, and to endow it with an endogenous control mechanism aimed at modeling a leader-following behavior. We show how an agent’s assertion of endogenous control in a social network is learned dynamically by the other agents in the course of their interactions. We develop variants of the DeGroot algorithm which we call BLIFT to illustrate two scenarios which lead to completely different situations. We illustrate how control could be related to changes in the social influence weights and how its manipulation could lead to a general consensus or homophily in a network. We show the convergence of the two algorithms and analyze their theoretical properties. We construct synthetic examples to illustrate our two methods. © 2013, Springer-Verlag Wien. Source

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