Connections Among Farsighted Agents

Abstract

We study the stability of social and economic networks when players are farsighted. In particular, we examine whether the networks formed by farsighted players are different from those formed by myopic players. We adopt the notion of pairwise farsightedly stable sets (Herings, Mauleon, and Vannetelbosch 2009). We first show that under the componentwise egalitarian allocation rule, the set of strongly efficient networks and the set of pairwise (myopically) stable networks that are immune to coalitional deviations are the unique pairwise farsightedly stable set if and only if the value function is top convex. We then investigate in some classical models of social and economic networks whether the pairwise farsightedly stable sets of networks

Equilibrium coalitional behavior

“…Jackson and van den Nouweland () show that the set of strongly efficient networks is the set of strongly stable networks under the componentwise egalitarian allocation rule if v is top convex. In addition, Grandjean et al () show that the set of strongly efficient networks is also the unique farsightedly stable set under the componentwise egalitarian allocation rule if v is top convex. Together with Proposition , we see that when v is strictly top convex, the set of strongly stable networks, the farsighted stable set, and the (C)ECB all predict the same network structures, which are the efficient networks…”

Competition and networks of collaboration

“…Several papers in this literature follow a cooperative approach and use farsighted stability concepts as solutions. This strand of the literature includes Greenberg (), Chwe (), Ray and Vohra (), Diamantoudi and Xue (), Herings et al (), Page et al (), Grandjean et al (, ), and Mauleon et al (). The version of the farsighted stable set used in this paper differs from the versions defined in the above papers in a few aspects.…”

“…First, I allow for arbitrary acting coalitions ( Herings et al 2009 and Mauleon et al 2011 restrict the acting coalition to be a singleton or a pair). Second, I allow agents to choose all of their actions (i.e., the intensity of collaboration and the sizes of transfers) in a cooperative manner ( Herings et al 2009 , Page et al 2005 , Grandjean et al 2010 , , and Mauleon et al 2011 focus on pure network formation).…”

Allocating value among farsighted players in network formation

“…5 Mutuswami and Winter (2002) have proposed subscription mechanisms for network formation when the costs from linking are publicly known but the bene…ts from linking are not known to the social planner. Their mechanism is similar to Currarini and Morelli (2000) sequential network formation game 6 and leads to the formation of an e¢ cient network. 7 The payo¤s in Currarini and Morelli (2000) and Mutuswami and Winter (2002) are endogenously generated but are highly asymmetric and sensitive to the order in which players make proposals.…”

“…They have investigated whether di¤erent forms of transfers (direct transfers, indirect transfers or contingent transfers) can solve the con ‡ict between stability and e¢ ciency when there are network externalities that usually lead to the emergence of ine¢ cient networks when trans- 5 However, if the network formation process is simultaneous, then there are value functions that satisfy size monotonicity for which ine¢ cient equilibria can arise. 6 Each player, when it is her turn, proposes the set of links she wants to form and her cost contribution. Once all proposals have been made, the social planner selects the network to be formed and the cost contributions of the players.…”