Contributions to game theory and management / Ed. by L. A. Petrosyan, N. A. Zenkevich. Issue 8. St. Petersburg : Graduate School of Management, St. Petersburg University, 2015.
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 investigate the vertical differentiation model in the insurance market taking into account fixed costs (the costs of quality improvement) of different structure. The subgame perfect equilibrium in a two-stage game is constructed for the case of compulsory insurance when firms use Bertrand-Nash or Stakelberg equilibria at the stage of price competition. For the case of optional insurance we explore and compare the firms optimal behavior in monopoly and duopoly settings.