Search

In this note we introduce different levels of decay in the Goyal, Galeotti and Kamphorst (GGK) insider-outsider model of network formation. First, we deal with situations where the amount of decay is sufficiently low to avoid superfluous connections in strict Nash networks and we examine the architectures of strict Nash networks. We show that centrality and small diameter are robust features of strict Nash networks. Then, we study the Nash and efficient networks when the decay vanishes. [ABSTRACT FROM AUTHOR]

Abstract: We consider two different approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider a network-based approach; in particular Jackson–Wolinsky’s concept of pairwise stability. Next, we discuss a non-cooperative game-theoretic approach, through a refinement of the Nash equilibria of Myerson’s consent game. This refinement, denoted as monadic stability, describes myopically forward looking behavior of the players. We show through an equivalence that the class of monadically stable networks is a strict subset of the class of pairwise stable networks that can be characterized fully by modifications of the properties defining pairwise stability. [ABSTRACT FROM AUTHOR]

We study message credibility in social networks with biased and unbiased agents. Biased agents prefer a specific outcome while unbiased agents prefer the true state of the world. Each agent who receives a message knows the identity (but not type) of the message creator and only the identity and types of their immediate neighbors. We characterize the perfect Bayesian equilibria of this game and demonstrate filtering by the network: the posterior beliefs of agents depend on the distance a message travels. Unbiased agents, who receive a message from a biased agent, are more likely to assign a higher credibility and transmit it further when they are further away from the source. For a given network, we compute the probability that it will always support the communication of messages by unbiased agents. Finally, we establish that under certain parameters, this probability increases when agents are uncertain about their network location. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we pursue the line of research initiated by . We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by  in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the payoff function to find conditions under which Nash networks always exist. We provide two properties—increasing differences and convexity in the first argument of the payoff function that ensure the existence of Nash networks. Note that the commonly used linear payoff function satisfies these two properties. [Copyright &y& Elsevier]

Abstract: We investigate the Nash equilibria of game theoretic models of network formation based on explicit consent in link formation. These so-called “consent models” explicitly take account of link formation costs. We provide characterizations of Nash equilibria of such consent models under both one-sided and two-sided costs of link formation. We relate these equilibrium concepts to link-based stability concepts, in particular strong link deletion proofness. [Copyright &y& Elsevier]

Abstract: We examine the fundamental tension between efficiency and stability in social network formation. Jackson and Wolinsky (JET, 1996) showed that the component-wise egalitarian payoff rule supports an efficient network as being pairwise stable if and only if the network benefit function is critical link monotone. We extend this insight to strong pairwise stability and derive that the critical link monotonicity condition has to be strengthened to a condition on individuals occupying critical positions in the network. [Copyright &y& Elsevier]

We study network formation in a situation where the network allows players to obtain information (signals) about other players. This information is important for making a payoff relevant decision. However, not all information is reliable and so players may have an incentive to check it. By obtaining multiple messages about the same player through the network, a player learns whether his information is reliable for making the payoff relevant decision. We study the existence and architecture of strict Nash networks. We find that players who are involved in at least three links sponsor all links they are involved in. These players are similar to the central players in center sponsored stars. We show that strict Nash networks can be over-connected as well as under-connected as compared to efficient networks. Finally, we extend the basic model to study heterogeneous populations. In the first scenario, we allow for the co-existence of players who only value checked information and players who also value information with unknown reliability. In the second scenario, players who do not care about checking their information co-exist with players who do. Our results are robust to both types of heterogeneity, with one exception: the presence of a single player who cares only about checked information is enough to ensure that center sponsored stars are no longer stable. [ABSTRACT FROM AUTHOR]