Social Networks: Equilibrium Selection and Friendliness

Given their importance in determining the outcome of many economic interactions, different models have been proposed to determine how social networks form and which structures are stable. In Bala and Goyal (2000), the one-sided link formation model has been considered, which is based on a noncooperative game of network formation. They found out that the empty networks, the wheel in the one-way flow of benefits case and the center sponsored star in the two-way flow case play a fundamental role, since they are strict Nash equilibria of the corresponding games for certain classes of payoff functions. In this paper, firstly we prove that all these network structures are in weakly dominated strategies whenever there are no strict Nash equilibria. Then, we exhibit a more accurate selection device between these network architectures by considering ‘altruistic behavior’ refinements. Such refinements, that we investigate here in the framework of finite strategy sets games, have been introduced by the authors in previous papers.