Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games

We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network from each basin of attraction. We refer to any such von Neumann-Morgenstern stable set as a farsighted basis. (4) The core of the farsighted network formation game is constructed by selecting one network from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists at least one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis, and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that the farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitive contracting networks and highlight how the analysis of these networks requires the new features of our network formation model.Basins of attraction, Network formation, Supernetworks, Farsighted core, Nash networks

Farsighted House Allocation

In this note we study von Neumann-Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2008) shows that the set of competitive allocations coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., Wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of strong dominance (cf., Roth and Postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else.housing markets, indivisible goods, farsightedness, von Neumann-Morgenstern stable sets, top trading cycles, competitive allocations

Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market

While most of the literature starting with Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. Moreover, we show that even when only pairwise exchanges between two traders are allowed, the strictly stable allocations are attained eventually if traders are sufficiently farsighted.Indivisible Goods Market, Dynamics, Competitive Allocation, Strict Core, Foresight, Stable Set

Strategic basins of attraction, the farsighted core, and network formation games

We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network from each basin of attraction. We refer to any such von Neumann-Morgebstern stable set as farsighted basis. (4) The core of the farsighted network formation games is constructed by selecting one network from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that a farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitative contracting networks and highlight how the analysis of these networks requires the new features of our network formation model

Farsighted house allocation

In this note we study von Neumann-Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2008) shows that the set of competitive allocations coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., Wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of strong dominance (cf., Roth and Postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else

Von Neuman-Morgenstern farsightedly stable sets in two-sided matching

We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict with matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets : a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the von Neumann-Morgenstern (myopically) stable sets, von Neumann-Morgenstern farsightedly stable sets cannot include matchings thar are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences.matching problem, von Neumann-Morgenstern stable sets, farsightedly stability

Von Neumann-Morgenstern farsightedly stable sets in two-sided matching.

We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the von Neumann-Morgenstern (myopically) stable sets, von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences.matching problem, von Neumann-Morgenstern stable sets, farsighted stability

Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games

Given the preferences of players and the rules governing network formation, what networks are likely to emerge and persist? And how do individuals and coalitions evaluate possible consequences of their actions in forming networks? To address these questions we introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, the rules of network formation, and a dominance relation on feasible networks. The rules of network formation may range from non-cooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates not only player preferences and the rules of network formation but also assumptions concerning the degree of farsightedness of players. A specification of the primitives induces an abstract game consisting of (i) a feasible set of networks, and (ii) a path dominance relation defined on the feasible set of networks. Using this induced game we characterize sets of network outcomes that are likely to emerge and persist. Finally, we apply our approach and results to characterize the equilibrium of well known models and their rules of network formation, such as those of Jackson and Wolinsky (1996) and Jackson and van den Nouweland (2005).basins of attraction, network formation games, stable sets, path dominance core, Nash networks

Dynamic Effects on the Stability of International Environmental Agreements

In terms of the number of signatories, one observes both large and small international environmental agreements. The theoretical literature, based on game theory, discusses different concepts and mechanisms for the stability of coalitions and has reached the conclusion that, under farsightedness, both large and small stable coalitions can occur. In the context of a repeated game, this implies that large stable coalitions can also be sustained over time by a simple trigger mechanism, for large enough discount factors. However, if changes in time implement changes in state, this conclusion does not hold anymore: only small stable coalitions can be sustained.IEA’s, Coalitional stability, Dynamics

Voice and Bargaining Power

We propose a formal concept of the power of voice in the context of a simple model where individuals form groups and trade in competitive markets. Individuals use outside options in two different ways. Actual outside options reflect the possibility to exit or to join other existing groups. Hypothetical outside options refer to hypothetical groups that are ultimately not formed. Articulation of hypothetical outside options in the bargaining process determines the relative bargaining power of the members of a group, which constitutes an instance of the power of voice. The adopted equilibrium concept endogenizes the outside options as well as the power of voice. In our illustrative example, there exists an equilibrium that uniquely determines the power of voice and the allocation of commodities.Power of Voice, competitive equilibria, group formation, bargaining, articulation of outside options