In network theory, Jackson and Wolinsky introduced a now widely used notion of stability for unweighted network formation called pairwise stability. We prove the existence of pairwise stable weighted networks under assumptions on payoffs that are similar to those in Nash's and Glicksberg’s existence theorem (continuity and quasi concavity). Then, we extend our result, allowing payoffs to depend not only on the network, but also on some game-theoretic strategies. The proof is not a standard application of tools from game theory, the difficulty coming from the fact that the pairwise stability notion has both cooperative and noncooperative features. Last, some examples are given and illustrate how our results may open new paths in the literature on network formation.

This paper studies the existence of equilibrium solution concepts in a large class of economic models with discontinuous payoff functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition (Reny 1999) and its recent improvements (Barelli and Meneghel 2013, McLennan et al. 2011, Reny 2009. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of approximate equilibria and of sharing rule solutions in pure and mixed strategies (Simon and Zame 1990). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that many competition models have a sharing rule solution.We thank Panayotis Mertikopoulos and Christina Pawlowitsch for their useful comments. We thank the anonymous reviewers and the associated editor for many insightful comments and suggestions. We thank many participants of the following seminars or conferences for their valuable comments: Conference on

This paper proposes dynamic programming tools for payoffs based on aggregating functions that depend on the current action and the future expected payoff. Some regularity properties are provided on the aggregator to establish existence, uniqueness and computation of the solution to the Bellman equation. Our setting allows to encompass and generalize many previous results based upon additive or non-additive payoff functions.