Two-sided Network Research Articles

Bargaining and Network Structure: An Experiment

We consider bargaining in a bipartite network of buyers and sellers, who can only trade with the limited number of people with whom they are connected. Such networks could arise due to proximity issues or restricted communication flows, as with information transmission of job openings, business opportunities, and transactions not easily regulated by external authorities. We perform an experimental test of a graph-theoretic model that allows us to decompose any two-sided network into simple networks of three types, with unique predictions about equilibrium prices for the networks in our sessions. We begin with two separate simple networks, which are then joined by an additional link. Participants appear to quickly grasp important characteristics of the networks. The results diverge sharply depending on how this connection is made, typically conforming to the theoretical directional predictions. Payoffs can be systematically affected even for agents who are not connected by the new link. We find evidence of a form of social learning - the shares (publicly) allocated to others in the past affect what one is willing to accept.

Two-sided networks for completely simple semigroups

Let S be a completely simple semigroup represented as a Rees matrix semigroup M(I,G,P) with normalized sandwich matrix P. On the congruence lattice C(S) of S we consider the relations T i, K and T r which identify congruences with the same left trace, kernel and right trace, respectively. These are equivalences whose classes are intervals. The upper and lower ends of these intervals induce the following operators on C(S) Tl, K, Tr, tl, k and tr .We construct here the semigroup generated by these operators as a homomorphic image of a semigroup given by generators and relations and demonstrate the minimality of the latter.

Bank Interchange of Transactional Paper: Legal and Economic Perspectives

Bank Interchange of Transactional Paper: Legal and Economic Perspectives

Blocking States in Connecting Networks Made of Square Switches Arranged in Stages

Since the probability of blocking is a principal measure of the performance of a network, this paper examines the blocking states of a network. For two-sided connecting networks made of square switches arranged in stages, a parallel pair (PP) is a pair of paths through the network that meet at no switch. The blocking states of the network are closely related to those that have a busy PP. In particular, a routing algorithm can avoid all the blocking states if and only if it avoids all the states with busy PPS.

Permutation Groups, Complexes, and Rearrangeable Connecting Networks

In the interest of providing good telephone service with efficient connecting networks, it is desirable to have at hand a knowledge of some of the combinatorial properties of such networks. One of these properties is rearrangeability: a connecting network is rearrangeable if its permitted states realize every assignment of inlets to outlets, or alternatively, if given any state x of the network, any inlet idle in x, and any outlet idle in x, there is a way of assigning new routes (if necessary) to the calls in progress in x so that the idle inlet can be connected to the idle outlet. A natural algebraic and combinatorial approach to the study of rearrangeable networks is described, with attention centered principally on two-sided networks built of stages of square crossbar switches, each stage having N inlets and N outlets. The approach is based in part on the elementary theory of permutation groups. The principal problem posed (and partly answered) is this: What connecting networks built of stages are rearrangeable? Sufficient conditions, including all previously known results, are formulated and exemplified.

Markov Processes Representing Traffic in Connecting Networks

A class of Markov stochastic processes x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> , suitable as models for random traffic in connecting networks with blocked calls cleared, is described and analyzed. These models take into account the structure of the connecting network, the set S of its permitted states, the random epochs at which new calls are attempted and calls in progress are ended, and the method used for routing calls. The probability of blocking, or the fraction of blocked attempts, is defined in a rigorous way as the stochastic limit of a ratio of counter readings, and a formula for it is given in terms of the stationary probability vector p of x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> . This formula is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${(p, \beta) \over (p, \alpha)}, \quad {\rm or} \quad {\sum\limits_{x \epsilon S}P_{x}\beta_{x} \over \sum\limits_{x \epsilon S}P_{x}\alpha_{x},$</tex> where β <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> is the number of blocked idle inlet-outlet pairs in state x, and α <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> is the number of idle inlet-outlet pairs in state x. On the basis of this formula, it is shown that in some cases a simple algebraic relationship exists between the blocking probability b, the traffic parameter λ (the calling rate per idle inlet-outlet pair), the mean m of the load carried, and the variance σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of the load carried. For a one-sided connecting network of T inlets (= outlets), this relation is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-b={1 \over \lambda}{2_{m} \over (t-2_{m}^{2}- (T-2m)+4\sigma^{2}};$</tex> for a two-sided network with N inlets on one side and M outlets on the other, it is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-b= {m \over (N-m)(M-m)+ \sigma^{2}}.$</tex> The problem of calculating the vector p of stationary state provabilities is fully resolved in principle by three explicit formulas for the components of p: a determinant formula, a sum of products along paths on S, and an expansion in a power series around any point \lambda ≧ 0. The formulas all indicate how these state probabilities depend on the structure of the connecting network, the traffic parameter λ, and the method of routing.