Summary
The paper studies network formation in undirected graphs. We assume a two-stage game: agents propose connections that if realized have a fixed cost; then, given the obtained graph and its exogenous surplus (the value function), they bargain on the split. We claim that, when the surplus from connections is super-additive, the bargaining process can be solved with the Myerson Value allocation rule, an adaptation of Shapley’s to graphs. This will lead to an (only theoretically, not in computations) easy characterisation of equilibria, refining the notion of pairwise stability.
We then focus our attention on the heuristical analysis of a tractable case. We run simulations, starting from different initial conditions, in order to qualitatively characterize alternative possible equilibria. For part of this last purpose we are using the simulated annealing approach, with theoretical justification for its adoption.
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Pin, P. (2006). A Model of Myerson-Nash Equilibria in Networks. In: Beckmann, M., et al. Artificial Economics. Lecture Notes in Economics and Mathematical Systems, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28547-4_15
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DOI: https://doi.org/10.1007/3-540-28547-4_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28578-6
Online ISBN: 978-3-540-28547-2
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