Optimizing Scrip Systems: Crashes, Altruists, Hoarders, Sybils and   Collusion
  Scrip, or artificial currency, is a useful tool for designing systems that are robust to selfish behavior by users. However, it also introduces problems for a system designer, such as how the amount of money in the system should be set. In this paper, the effect of varying the total amount of money in a scrip system on efficiency (i.e., social welfare---the total utility of all the agents in the system) is analyzed, and it is shown that by maintaining the appropriate ratio between the total amount of money and the number of agents, efficiency is maximized. This ratio can be found by increasing the money supply to just below the point that the system would experience a "monetary crash," where money is sufficiently devalued that no agent is willing to perform a service. The implications of the presence of altruists, hoarders, sybils, and collusion on the performance of the system are examined. Approaches are discussed to identify the strategies and types of agents. 
Ian A. Kash, Eric J. Friedman, Joseph Y. Halpern
cs.GT cs.DC