Gathering information in a graph
Suppose each vertex in a graph G has a unit of information and that all the units must be collected at a vertex u in G. Assuming that a vertex can receive (from its neighbours) an unlimited number of units at each discrete moment but can only send one at a time, find the shortest collection time, col u(G), needed to collect all the information at u and an optimal protocol that achieves this. We derive lower and upper bounds for the problem, give a polynomial time algorithm in the general case, and a linear time algorithm for hypercubes.
We consider a game equilibrium in a network in each node of which an economy is described by the simple two-period model of endogenous growth with production and knowledge externalities. Each node of the network obtains an externality produced by the sum of knowledge in neighbor nodes. Uniqueness of the inner equilibrium is proved. Three ways of behavior of each agent are distinguished: active, passive, hyperactive. Behavior of agents in dependence on received externalities is studied. It is shown that the equilibrium depends on the network structure. We study the role of passive agents; in particular, possibilities of connection of components of active agents through components of passive agents. A notion of type of node is introduced and classification of networks based on this notion is provided. It is shown that the inner equilibrium depends not on the size of network but on its structure in terms of the types of nodes, and in similar networks of different size agents of the same type behave in similar way.
In this paper, we consider the following problem - what affects the amount of investment in knowledge when one of the network firms enters another innovation network. The solution of this problem will allow us to understand exactly how innovative companies will behave when deciding whether to enter the innovation network of another country or region, what conditions affect it and how the level of future investments in knowledge can be predicted.
We consider a network model of production with externalities which describes a situationtypical for many economic, social, and political systems. In the first period of time each of the agents in the network receives endowment and distributes it between consumption and investment. In the second period the agent’s consumption depends on its own investment as well as on investments of its neighbors. The agent’s benefit is determined by its consumption in the two periods. We introduce adjustment dynamics into this model and study the problem of stability of the game equilibrium. An important factwhich we have discovered in our research is the special role of the conditions of the presence and the absence of productivity both in a static and in a dynamic framework. The specifics of the dynamics and the nature of the resulting equilibrium depend on the parameters of the model and on the character of the initial disturbance. We have found the instability of the inner equilibrium and have studied the convergence to a new corner equilibrium and the stability of the latter. The instability of the inner equilibria, which we found and the sources of which we study, is the property typical for social and economic systems. The presence of many social institutions can be explained by the wish of the members of the society to preserve the existing equilibria under the dynamic instability which would take place without such stabilizing institutions.
The core problem considered in the article is dedicated to the revealing of project system elements, where the network modeling can be adopted to management. Using of Web of Science and ProQuest databases provided with the opportunity of publication activity statistics research and with the definite articles and other types of publications’ analysis for the search of basic directions of network theory adoption for project management. The identification of the most demanded and actual directions of network approach and social network analysis application to management of project system elements was fulfilled.
By the end of the 20th century, conflicts of a new type, came to the forefront. Subjects of conflicts have changed and this influences their dynamics directly. The article is aimed at revelation of the interaction between the conflicts of "network" and "hierarchy" and expansion of the information background of their presentation.
In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when one of the complete graph enters another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions and externalities affect it and how the level of future equilibrium amount of investments in knowledge can be predicted.
In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when some agents of the complete graph enter another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions and externalities affect it and how the level of future equilibrium amount of investments in knowledge can be predicted.