Efficiency vs. Stability in a Mixed Network Formation Model

Documentos de Trabajo

Unilateral vs. Bilateral link-formation: Bridging the gap

We provide a model that bridges the gap between two benchmark models of strategic network formation: Jackson and Wolinsky' s model based on bilateral formation of links, and Bala and Goyal's two-way fl ow model, where links can be unilaterally formed. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the fl ow through the link suffers a certain decay, but when it is supported by both the fl ow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky 's connections model without decay, while when flow in such links is perfect we have Bala and Goyal' s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Efficiency and dynamics are also examined.

From bilateral two-way to unilateral one-way flow link-formation

Documento de trabajo

Expected Fair Allocation in Farsighted Network Formation

I consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called expected fair if for every link in the network both participants gain, marginally, and in discounted, expected terms, the same from it; and it is called a pairwise network formation procedure if the probability that a link is created (or eliminated) is positive if the discounted, expected gains to its two participants are positive too. The main result is the existence, for the discount factor small enough, of an expected fair and pairwise network formation procedure where the allocation rule is component balanced, meaning it distributes the total value of any maximal connected subnetwork among its participants. This existence result holds for all discount factors when the pairwise network formation procedure is restricted. I finally provide some comparison with previous models of farsighted network formation.

Forward-looking Pairwise Stability in Networks with Externalities

We consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called a forward-looking network formation scheme if, first, the probability that a link is created is positive if the discounted, expected gains to its two participants are positive, and if, second, the probability that a link is eliminated is positive if the discounted, expected gains to at least one of its two participants are positive. The main result is the existence, for all discount factors and all value functions, of a forward-looking network formation scheme. Furthermore, we can always nd a forward-looking network formation scheme such that (i) the allocation rule is component balanced and (ii) the transition probabilities increase in the di erence in payo s for the corresponding players responsible for the transition. We use this dynamic solution concept to explore the tension between e ciency and stability.

A Unifying model of strategic network formation

Documento de trabajo

The impact of liberalizing cost-saharing on basic models of network formation

This paper studies the impact of "liberalizing " the cost-sharing of links on some basic models of network formation. This is done in a setting where both doubly supported and singly supported links are possible, and which includes the two seminal models of network formation by Jackson and Wolinsky and Bala and Goyal as extreme cases. In this setting, the notion of pairwise stability is extended and it is proved that liberalizing cost-sharing for doubly supported links widens the range of values of the parameters where the efficient networks formed by such type of links are pairwise stable, while the range of values of the parameters where the efficient networks formed by singly supported links are pairwise stable shrinks, but the region where the latter are e¢ cient and pairwise stable remains the same.