Fixed tree games with multilocated players

This article introduces fixed tree games with multilocated players (FMP games), which are a generalization of standard fixed tree games. This generalization consists of allowing players to be located in more than one vertex. As a consequence, these players can choose among several ways of connection to the root. In this article we show that FMP games are balanced. Moreover, we prove that the core of an FMP game coincides with the core of a related submodular standard fixed tree game. We show how to find the nucleolus and we characterize the orders that provide marginal vectors in the core of an FMP game. Finally, we study the Shapley value and the average of the extreme points of the core.