The Role of Trust in Costly Network Formation

We investigate game theoretic models of entwork formation that are based on individual actions only. Our approach is grounded in three simple and realistic principles. (1) Link formation should be a binary process of consent. (2) Link formation should be costly. (3) The class of network payoff functions should be as general as possible. We provide charecterizations of stable networks under the hypothesis of mutual consent for the case of two-sided and one-sided link formation costs. Furthermore, we introduce a new eqilibrium concept based on a limited, realistic form of farsightedness or (myopic) ''trust'' in network formation. We provide comparisons of the resulting networks with networks satisfying well known stability concepts developed in the literatureSocial networks, individual stability, pairwsie stability, trust

Stable Networks and Convex Payoffs

Recently a variety of link-based stability concepts have emerged in the literature on game theoretic models of social network formation. We investigate two basic formation properties that establish equivalence between some well known types of stable networks and their natural extensions. These properties can be identified as convexity conditions on the network payoff structures.

A Belief-based Approach to Network Formation

In this paper we consider four different game-theoretic approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider Jackson-Wolinsky’s concept of pairwise stability. Next, we introduce a stronger version of this concept based on linking decisions by nodes, denoted as strict pairwise stability. Third, we consider Myerson’s consent game and its Nash equilibria. Fourth, within the context of Myerson’s consent game, we consider self-confirming equilibria based on simple myopic belief systems. We provide an exhaustive comparison of the classes of equilibrium networks that result from each of these four approaches. We determine the conditions under which there is equivalence of pairwise stability and strict pairwise stability. Second, we show that the Nash equilibria of Myerson’s consent game form a super set of the class of pairwise stable networks, while strict pairwise stability and monadic stability are fully equivalent.

The Role of Beliefs and Confidence in Building Social Networks

We examine the process of building social relationships in a non-cooperative game where such link formation is costly and requires mutual consent. We provide a noncooperative foundation for several link-based network stability concepts that have been studied in the literature on network formation. In our model players form myopic beliefs about the feasibility of building direct relationships with their acquaintances. These beliefs represent how each neighbor of a player is expected to respond to the initiation of a link by that player. We introduce a stability concept called “monadic stability” where agents play a best response to their formed myopic beliefs such that these beliefs are self-confirming. The resulting equilibrium networks form a class of networks that are shown to have some very appealing properties.

Equipartition of Current in Parallel Conductors on Cooling Through the Superconducting Transition

Our experiments show that for two or more pieces of a wire, of different lengths in general, combined in parallel and connected to a dc source, the current ratio evolves towards unity as the combination is cooled to the superconducting transition temperature Tc, and remains pinned at that value below it. This re-distribution of the total current towards equipartition without external fine tuning is a surprise. It can be physically understood in terms of a mechanism that involves the flux-flow resistance associated with the transport current in a wire of type-II superconducting material. It is the fact that the flux-flow resistance increases with current that drives the current division towards equipartition.Comment: Revised version of J.Phys. Condens.Matter; vol. 18(2006) L143-L147 14 pages including 3 figures; provided an explanation in terms of the physical mechanism of flux flow induced resistance that is proportional to the impressed current. We are adding a simple, physically robust derivation of our equipartition without taking resort to the minimum dissipation principl

Stable Networks and Convex Payoffs

Recently a variety of link-based stability concepts have emerged in the literature on game theoretic models of social network formation. We investigate two basic formation properties that establish equivalence between some well known types of stable networks and their natural extensions. These properties can be identified as convexity conditions on the network payoff structures