Shapley value in a model of information transferal

Abstract

In this paper we analyze the value of the information in a cooperative model. There is an agent (the innovator), having relevant information which can be sold to some potential buyers. The n potential users of the information share a market. The expected utility of each of them can be improved by obtaining the information. The whole situation is modelled as a (n + 1)–person cooperative game. We study the properties of the characteristic function of this game. It fulfills a weak version of the superadditivity property, namely 0-monotonicity. The game is proved to be monotonic. We compute the Shapley value and we prove it is an imputation for the game. We compare the Shapley value with the equilibrium studied in a noncooperative model by Quintas (1995). We also study some limit cases when the potential buyers are completely informed or uninformed. It includes Big Boss Games (Muto et al. (1988)) and other limit cases. We conclude that in a cooperative environment the buyers avoid being exploited by the innovator. Conversely the innovator obtains a higher utility in a noncooperative game.