Maximality in the Farsighted Stable Set

Abstract

Harsanyi (1974) and Ray and Vohra (2015) extended the stable set of von Neumann and Morgenstern to impose farsighted credibility on coalitional deviations. But the resulting farsighted stable set suffers from a conceptual drawback: while coalitional moves improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable and easily verifiable properties is unaffected by the imposition of these stringent maximality constraints. The properties we describe are satisfied by many, but not all, farsighted stable sets.

Corrigendum to “Maximality in the Farsighted Stable Set”

“…It should be noted that the alternative condition given here and the weaker conditions in Newton (2020) are wholly consistent with the discussion of the remainder problem in the earlier work of Ray and Vohra (2015):…”

“…Furthermore, the new payoffs for T \ S depend on neither the coalitions and payoffs of players outside of T before the breakup, nor the coalitions and payoffs of players outside of T \ S after the breakup, nor the identities of players in S who are not members of T . Note that, concordant with the motivation given in Ray and Vohra (2019), a moving coalition S must take the resulting behavior of players outside of S as given.…”

Do Stable Outcomes Survive in Marriage Problems with Myopic and Farsighted Players?

“…The equivalence between vNM farsightedly stable sets and singleton core elements actually holds quite generally in characteristic function games as shown in Ray and Vohra (2015). Such results are also robust to the incorporation of various forms of maximality in the indirect dominance relation, like the strong rational expectations farsighted stable set in Dutta and Vohra (2017) and absolute maximality as in Ray and Vohra (2019). 2 However, the concepts studied so far in the literature do not allow for heterogeneity regarding the degree of farsightedness of the players in the market.…”

Network Stability under Limited Foresight

“…Ray and Vohra (2015) develop farsighted stability in this context by building on previous work by Von Neumann and Morgenstern (1944), Harsanyi (1974), and Chwe (1994). Ray and Vohra (2019) develop this further by focusing on deviations that embody the principle of absolute maximality, whereby it is not sufficient that coalitions should merely make deviations that lead to an improvement but rather the deviations should not be Pareto-dominated by other feasible deviations. Dutta and Vohra (2017) examine farsighted stability in the context of abstract games and take maximality into account in their notion of the rational expectation stable set.…”