Оптимальность выбора марковским блужданием
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.
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 design the elements of an automated tool for thequantitative analysis of the future regional power supply system based on the opinion of regional authorities on the current and future availability of power supply services in the industry and in the domestic sector. A mathematical model is suggested to estimate the return of investment into new power station and storage construction. The model includes a non-cooperative game on polyhedra, where the first player’s payoff function adds up from the bilinear and the linear function of vector arguments, whereas the the payoff function of the second player is a bilinear function of the same arguments. We prove that equilibria in this game can be found by solving a dual pair of linear programming problems. These equilibria determine, in particular, the volume of investment for generators and the electricity price for consumers, which are mutually acceptable to both parties.
We consider a model of location-price competition between two firms, located on the circle. Nash equilibrium, equilibrium in secure strategies, and Nash-2 equilibrium are compared. We demonstrate that Nash-2 equilibrium exists for any locations of firms. The set of Nash-2 equilibria is treated as tacit collusion.
Smoking is a problem, bringing signifi cant social and economic costs to Russiansociety. However, ratifi cation of the World health organization Framework conventionon tobacco control makes it possible to improve Russian legislation accordingto the international standards. So, I describe some measures that should be taken bythe Russian authorities in the nearest future, and I examine their effi ciency. By studyingthe international evidence I analyze the impact of the smoke-free areas, advertisementand sponsorship bans, tax increases, etc. on the prevalence of smoking, cigaretteconsumption and some other indicators. I also investigate the obstacles confrontingthe Russian authorities when they introduce new policy measures and the public attitudetowards these measures. I conclude that there is a number of easy-to-implementanti-smoking activities that need no fi nancial resources but only a political will.
One of the most important indicators of company's success is the increase of its value. The article investigates traditional methods of company's value assessment and the evidence that the application of these methods is incorrect in the new stage of economy. So it is necessary to create a new method of valuation based on the new main sources of company's success that is its intellectual capital.