  Exchange of services and resources in, or over, networks is attracting
nowadays renewed interest. However, despite the broad applicability and the
extensive study of such models, e.g., in the context of P2P networks, many
fundamental questions regarding their properties and efficiency remain
unanswered. We consider such a service exchange model and analyze the users'
interactions under three different approaches. First, we study a centrally
designed service allocation policy that yields the fair total service each user
should receive based on the service it others to the others. Accordingly, we
consider a competitive market where each user determines selfishly its
allocation policy so as to maximize the service it receives in return, and a
coalitional game model where users are allowed to coordinate their policies. We
prove that there is a unique equilibrium exchange allocation for both game
theoretic formulations, which also coincides with the central fair service
allocation. Furthermore, we characterize its properties in terms of the
coalitions that emerge and the equilibrium allocations, and analyze its
dependency on the underlying network graph. That servicing policy is the
natural reference point to the various mechanisms that are currently proposed
to incentivize user participation and improve the efficiency of such networked
service (or, resource) exchange markets.
