An Equilibrium Analysis of Scrip Systems
  A game-theoretic model of scrip (artificial currency) systems is analyzed. It is shown that relative entropy can be used to characterize the distribution of agent wealth when all agents use threshold strategies---that is, they volunteer to do work iff they have below a threshold amount of money. Monotonicity of agents' best-reply functions is used to show that scrip systems have pure strategy equilibria where all agents use threshold strategies. An algorithm is given that can compute such an equilibrium and the resulting distribution of wealth. 
Ian A. Kash, Eric J. Friedman, Joseph Y. Halpern
cs.GT