Robustness And Optimization Of Scrip Systems

Abstract

A game theoretic model of scrip systems in analyzed. It is shown that scrip systems have pure strategy equilibria in a natural class of strategies. An algorithm is given that can compute such an equilibrium and the resulting distribution of money (scrip). The effect of varying the total amount of money in the 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 up to the point that the system experiences 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. In practice, agents in a scrip system will not have the necessary information to compute this equilibrium. However, a simple learning algorithm is investigated and simulation results are presented that show it enables agents to converge to equilibrium.