Centralizing information in networks

In the dynamic game we analyze, players are the members of a fixed network. Everyone is initially endowed with an information item that he is the only player to hold. Players are offered a finite number of periods to centralize the initially dispersed items in the hands of any one member of the network. In every period, each agent strategically chooses whether or not to transmit the items he holds to his neighbors in the network. The sooner all the items are gathered by any individual, the better it is for the group of players as a whole. Besides, the agent who first centralizes all the items is offered an additional reward that he keeps for himself. In this framework where information transmission is strategic and physically restricted, we provide a necessary and sufficient condition for a group to pool information items in every equilibrium. This condition is independent of the network structure. The architecture of links however affects the time needed before items are centralized in equilibrium.