Reward Functions and Cooperative Games: Characterization and Economic Application

In this paper we study network structures in which the possibilities for cooperation are restricted and the benefits of a group of players depend on how these players are 17 internally connected. One way to represent this type of situations is the so-called reward function, which represents the profits obtainable by the total coalition if links can be used 19 to coordinate agents’ actions. For any cooperative game, a reward function is associated. Given a reward function, our aim is to analyze under which conditions it is possible to 21 associate a cooperative game to it. We characterize the reward function by means of two conditions, component permanence and component additivity, in order to determine 23 whether there exists or not a cooperative game associated to it. An economic application is shown to illustrate the main theoretical result. Data from Catalan firms is used to 25 compute the reward function on the set of communication networks determined by firms, customers, distributors and suppliers. 27