Nash equilibria of network formation games under consent

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.

Identity and Link Reliability in Social Networks

This paper considers a non-cooperative network formation game where identity is introduced as a single dimension to capture the characteristics of a player in the network. Players access to the benefits from the link through direct and indirect connections. We consider cases where cost of link formation paid by the initiator. Each player is allowed to choose their commitment level to their identities. The cost of link formation decreases as the players forming the link share the same identity and higher commitment levels. We then introduce link imperfections to the model. We characterize the Nash networks and we find that the set of Nash networks are either singletons with no links formed or separated blocks or components with mixed blocks or connected.

Endogenous Two-Sided Markets with Repeated Transactions

We consider homogeneous two-sided markets, in which connected buyer-seller pairs bargain and trade repeatedly. In this infinite market game with exogenous matching probabilities and a common discount factor, we prove the existence of equilibria in stationary strategies. The equilibrium payoffs are given implicitly as a solution to a system of linear equations. Then, we endogenize the matching mechanism in a link formation stage that precedes the market game. When agents are sufficiently patient and link costs are low, we provide an algorithm to construct minimally connected networks that are pairwise stable with respect to the expected payoffs in the trading stage. The constructed networks are essentially efficient and consist of components with a constant buyer-seller ratio. The latter ratio increases (decreases) for a buyer (seller) that deletes one of her links in a pairwise stable component.

Changes in fos expression in the rat brain after unilateral lesions of the anterior thalamic nuclei

Activity of the immediate early gene c-fos was compared across hemispheres in rats with unilateral anterior thalamic lesions. Fos protein was quantified after rats performed a spatial working memory test in the radial-arm maze, a task that is sensitive to bilateral lesions of the anterior thalamic nuclei. Unilateral anterior thalamic lesions produced evidence of a widespread hippocampal hypoactivity, as there were significant reductions in Fos counts in a range of regions within the ipsilateral hippocampal formation (rostral CA1, rostral dentate gyrus, 'dorsal' hippocampus, presubiculum and postsubiculum). A decrease in Fos levels was also found in the rostral and caudal retrosplenial cortex but not in the parahippocampal cortices or anterior cingulate cortices. The Fos changes seem most closely linked to sites that are also required for successful task performance, supporting the notion that the anterior thalamus, retrosplenial cortex and hippocampus form key components of an interdependent neuronal network involved in spatial mnemonic processing.