Power in Non-negotiated Exchange Networks
Phillip Bonacich
Bonacich@soc.ucla.edu


    Research on how power develops within exchange networks is a lively and exciting topic within sociological social psychology.  Almost all the work has involved the power imbalances that develop when actors are in unequal bargaining positions within networks of bargaining opportunities.  Models (one of which is mine) have been developed to predict exactly which positions will have power.  Only one researcher, Linda Molm, has experimented with networks in which actors do not negotiate over the distribution of rewards from transactions but instead have opportunities to distribute rewards to each other.  In game-theoretic language, she?s initiated the study of non-cooperative games within networks while previous research used cooperative games.  Molm has experimentally examined only two networks, and as yet no one has developed a general theory predicting the location of powerful positions in any network.
    Computer simulations, using Mathematica, suggest that the distribution of power among positions will be different in negotiated (cooperative) and non-negotiated (non-cooperative) networks.  In the simulation actors are programmed to reciprocate with a probability proportional to the value of the gifts they have received.  
    The simulations also suggest that whether or not the actors have complete information about the network and the pattern of giving should also affect the distribution of power.  The outcomes that result when actors have just local knowledge about what they have received and simply reciprocate do not form a Nash equilibrium.  Knowledgeable actors can learn that they are better off giving less frequently to actors who are dependent on them for rewards and more frequently to actors who are less dependent.