Равновесия в игре на сети с производством и экстерналиями
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.
In the rational choice problem Zutler (2011) proposed a model of choice by continuous Markov random walk on a set of alternatives to find the best. In this paper we investigate the optimal properties of obtained solutions.
It is shown that the result of this choice is the maximal element on a set of lotteries with respect to relation for special function that has a natural interpretation as flow of probability from one to another lottery.
It is shown the relationship between the problems of choosing the best alternative and non-cooperative games solution. It is proved that Nash equilibrium is a stationary point of a dynamical system of the continuous random walk of players on the set of available strategies. The intensity transition of the player from one strategy to another is equal to his assessment of increase of payoff in the alleged current rival’s strategies.
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.
We consider a dependence of the growth rate on the elasticity of factor substitution in a framework of a model of mutual dependence of n agents. This model is interpreted as a network structure and can be used to analyze agglomerations. The development is modeled as an increase in values of the agents in a dynamic system with CES functions. We investigate the cases of high and low complementarity of activities. In particular, we receive conditions allowing the identification of the cases when the elasticity of factor substitution has a positive effect on the growth rate under high complementarity of activities, and when the elasticity of factor substitution has a negative effect on the growth rate under low complementarity of activities.