A Resource Sharing Game with Relative Priorities

Motivated by cloud-based computing resources operating with relative
  priorities, we investigate the strategic interaction between a fixed
  number of users sharing the capacity of a processor. Each user
  chooses a payment, which corresponds to his priority level, and
  submits jobs of variable sizes according to a stochastic process.
  These jobs have to be completed before some user-specific
  deadline. They are executed on the processor and receive a share of
  the capacity that is proportional to the priority level. The users'
  goal is to choose priority levels so as to minimize their own
  payment, while guaranteeing that their jobs meet their deadlines.
  We fully characterize the solution of the game for two classes of
  users and exponential service times. For an arbitrary number of
  classes and general service times, we develop an approximation based
  on heavy-traffic and we characterize the solution of the game under
  the heavy-traffic assumption. Our experiments show that the
  approximate solution captures accurately the structure of the
  equilibrium in the original game.