  Measuring individual productivity (or equivalently distributing the overall
productivity) in a network structure of workers displaying peer effects has
been a subject of ongoing interest in many areas ranging from academia to
industry. In this paper, we propose a novel approach based on cooperative game
theory that takes into account the peer effects of worker productivity
represented by a complete bipartite network of interactions. More specifically,
we construct a series of cooperative games where the characteristic function of
each coalition of workers is equal to the sum of each worker intrinsic
productivity as well as the productivity of other workers within a distance
discounted by an attenuation factor. We show that these (truncated) games are
balanced and converge to a balanced game when the distance of influence grows
large. We then provide an explicit formula for the Shapley value and propose an
alternative coalitionally stable distribution of productivity which is
computationally much more tractable than the Shapley value. Lastly, we
characterize this alternative distribution based on three sensible properties
of a logistic network. This analysis enhances our understanding of
game-theoretic analysis within logistics networks, offering valuable insights
into the peer effects' impact when assessing the overall productivity and its
distribution among workers.
