##### Sesión Aplicaciones de la Matemática y Física Matemática

Diciembre 14, 15:30 ~ 15:50

## A NOTE ON THE CORE, THE SYMMETRICAL CORE and SHAPLEY VALUE OF A GAME OF INFORMATION TRANSFERAL

### Galdeano, Patricia

We study some properties and we characterize the Symmetrical Core. We analize the relation of the Symmetrical Core with the Shapley value of a game modelling information transferal in a cooperative environment. This type of game was introduced by Galdeano, Oviedo and Quintas (2010) and it was also studied by Hou and Driessen (2012). It consists of an information market game involving n identical firms and an innovator having relevant information for the firms (e.g. a new technology). We consider a market with n firms (n >1) and an innovator who posses a patent or an information. The set of agents 1,2,...,n+1, where 1 (the innovator) is the agent having a new information and 2,...,n+1 (the users) are firms who could be willing to obtain the new information. The n users or firms interact in the same market, producing or performing the same activity with the same technology or the same information. Thus, all the users have the same incentives for the acquisition of the new information or technology. We will make the following assumptions about the problem we want to study: S.1: The n information users are the same before and after the information holder offers the new technology. This indicates that there are no exits or incoming agents in the market. S.2: All the players that acquire the new information make use of it. S.3: In order to compute the utilities of the players we use a conservative criteria, assuming that the uninformed agents make the right choice. We will take into account these conditions in order to define an (n+1)- person cooperative game. We analyze the Core and how the symmetrical part of the Core varies according with the initial information level of the firms and the value of the information. We also present conditions in order that the Shapley value belongs to the Core and the Symmetrical Core. Key Words: Cooperative game theory -Core- Symmetrical Core - Shapley value - Information transferal.

Autores: Galdeano, Patricia.