Co-author: Philippe Bich
We introduce a new concept of stability in network formation, perfect pairwise stability, and prove that a perfect pairwise stable network exists. Perfect pairwise stability strictly refines pairwise stability concept of Jackson and Wolinsky (1996), by transposing the idea of “trembling hand” perfection from non-cooperative games to the framework of cooperative, pairwise network formation. The existence result extends that of Bich and Morhaim (2020).
We prove that our concept is distinct from the concept of strongly stable networks introduced by Jackson and Van den Nouweland (2005), and perfect Nash equilibria of the Myerson’s network formation game studied by Calvó-Armengol and İlkılıç (2009). We also apply perfect pairwise stability to sequential network formation and prove that it allows refining sequential pairwise stability, a natural analogue of subgame perfection in a setting with cooperative, pairwise link formation.