On Perfect Pairwise Stable Networks (extra Seminar - Tuesday 16:30)
Title: "On Perfect Pairwise Stable Networks" (by Philippe Bich and Teteryatnikova Mariya )
Abstract: In this paper we introduce a refinement methodology from non-cooperative game theory to a cooperative framework of network formation theory. We define a new concept of network stability, perfect pairwise stability, that strictly refines the 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. We prove that a perfect pairwise stable network exists, at least as long as the payoff functions are quasiconcave, continuous and monotonic, which extends the existence result of Bich and Morhaim (2020). We further show 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 network formation game studied by Calvo-Armengol and Ilkilic (2009). Finally, we apply perfect pairwise stability to sequential network formation and prove that it facilitates a refinement of sequential pairwise stability, a natural analogue of subgame perfection in a setting with cooperative, pairwise link formation.