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9340[1] - A dynamic model of social network formation Brian...

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A dynamic model of social network formation Brian Skyrms* and Robin Pemantle *School of Social Sciences, University of California, Irvine, CA 92607; and Department of Mathematics, Ohio State University, Columbus, OH 43210 This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on April 27, 1999. Contributed by Brian Skyrms, May 9, 2000 We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolv- ing social network. Individual agents begin to interact at random, with the interactions modeled as games. The game payoffs deter- mine which interactions are reinforced, and the network structure emerges as a consequence of the dynamics of the agents’ learning behavior. We study this in a variety of game-theoretic conditions and show that the behavior is complex and sometimes dissimilar to behavior in the absence of structural dynamics. We argue that modeling network structure as dynamic increases realism without rendering the problem of analysis intractable. P airs from among a population of 10 individuals interact re- peatedly. Perhaps they are cooperating to hunt stags and rabbits, or coordinating on which concert to attend together; perhaps they are involved in the somewhat more antagonistic situation of bargaining to split a fixed payoff, or attempting to escape the undesirable but compelling equilibrium of a Pris- oner’s Dilemma. As time progresses, the players adapt their strategies, perhaps incorporating randomness in their decision rules, to suit their environment. But they may also exert con- trol over their environment. The players may have choice over the pairings but not perfect information about the other play- ers. They may improve their lot in two different ways. A child who is being bullied learns either to fight better or to run away. Similarly, a player who obtains unsatisfactory results may choose either to change strategies or to change associates. Regardless of whether the interactions are mostly cooperative or mostly an- tagonistic, it is natural and desirable to allow evolution of the social network (the propensity for each pair to interact) as well as the individuals’ strategies. We build a model that incorporates both of these modes of evolution. The idea is simple. (*) Individual agents begin to interact at random. The in- teractions are modeled as games. The game payoffs determine which interactions are reinforced, and the social network structure emerges as a consequence of the dynamics of the agents’ learning behavior. As the details of the specific game and the reinforcement dy- namics vary, we then obtain a class of models. In this paper, we treat some simple reinforcement dynamics, which may serve as a base for future investigation.
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