We introduce a new solution concept for models of coalition formation, called the myopic stable set. The myopic stable set is defined for a very general class of social environments and allows for an infinite state space. We show that the myopic stable set exists and is non-empty. Under minor continuity conditions, we also demonstrate uniqueness. Furthermore, the myopic stable set is a superset of the core and of the set of pure strategy Nash equilibria in noncooperative games.Additionally, the myopic stable set generalizes and unifies various results from more specific environments. In particular, the myopic stable set coincides with the coalition structure core in coalition function form games if the coalition structure core is nonempty; with the set of stable matchings in the standard one-to-one matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria in finite supermodular games, finite potential games, and aggregative games. We illustrate the versatility of our concept by characterizing the myopic stable set in a model of Bertrand competition with asymmetric costs, for which the literature so far has not been able to fully characterize the set of all (mixed) Nash equilibria.
We introduce a new solution concept for models of coalition formation, called the myopic stable set (MSS). The MSS is defined for a general class of social environments and allows for an infinite state space. An MSS exists and, under minor continuity assumptions, it is also unique.The MSS generalizes and unifies various results from more specific applications. It coincides with the coalition structure core in coalition function form games when this set is nonempty; with the set of stable matchings in the Gale-Shapley matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria in pseudo-potential games and finite supermodular games. We also characterize the MSS for the class of proper simple games.
Research on collusion in vertically di §erentiated markets is conducted under one or two potentially restrictive assumptions. Either there is a single industry-wide cartel or costs are assumed to be independent of quality or quantity. We explore the extent to which these assumptions are indeed restrictive by relaxing both. For a wide range of coalition structures, proÖt-maximizing cartels of any size price most of their lower quality products out of the market as long as production costs do not increase too much with quality. If these costs rise su¢ciently, however, then market share is maintained for all product variants. All cartel sizes may emerge in equilibrium when exclusively considering individual deviations, but the industry-wide cartel is the only one immune to deviations by coalitions of members. Overall, our Öndings suggest that Örms have a strong incentive to coordinate prices when the products involved are vertically di §erentiated.
We consider two versions of a Bertrand duopoly with asymmetric costs and homogeneous goods. They differ in whether predatory pricing is allowed. For each version, we derive the Myopic Stable Set in pure strategies as introduced by Demuynck, Herings, Saulle, and Seel (2017). We contrast our prediction to the prediction of Nash Equilibrium in mixed strategies.
This paper studies coalition formation among individuals who differ in productivity. We consider egalitarian societies in which coalitions split their surplus equally and individualistic societies in which coalitions split their surplus according to productivity. Preferences of coalition members depend on their material payoffs, but are also influenced by relative payoff concerns. The stable partitions in both egalitarian and individualistic societies are segregated, i.e., individuals with adjacent productivities form coalitions. If some individuals are not part of a productive coalition, then these are the least productive ones for egalitarian societies and the most productive ones for individualistic societies.
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