Analyzing Scrip Systems

Abstract

Scrip systems provide a non-monetary trade economy for exchange of resources. We model a scrip system as a stochastic game and study system design issues on selection rules to match potential trade partners over time. We show the optimality of one particular rule in terms of maximizing social welfare for a given scrip system that guarantees players' incentives to participate. We also investigate the optimal number of scrips to issue under this rule. In particular, if the time discount factor is close enough to 1, or trade benefits one partner much more than it costs the other, the maximum social welfare is always achieved no matter how many scrips are in the system. When the benefit of trade and time discount are not sufficiently large, on the other hand, injecting more scrips in the system hurts most participants; as a result, there is an upper bound on the number of scrips allowed in the system, above which some players may default. We show that this upper bound increases with the discount factor as well as the ratio between the benefit and cost of service. Finally, we demonstrate similar properties for a different service provider selection rule that has been analyzed in previous literature.

Kidney Exchange: An Operations Perspective

“…79 In this connection, there is often information about both when currently available donors will no longer be available and when donors who are not currently available will become available. 80 See, for example, Möbius (2001), Hauser and Hopenhayn (2008), Johnson et al (2014), andKash et al (2015) for literature on scrip systems and trading favors in dynamic games. 81 The main idea relies on the power of two choices in computer science (Mitzenmacher 2001), which allows creating the desired drift in the credits of each hospital.…”

Incentive-Compatible Mechanisms for Norm Monitoring in Open Multi-Agent Systems

“…Other work has shown that changing the random volunteer procedure can improve welfare [Johnson et al, 2014] and that this approach still works if more than one agent must be hired to perform work [Humbert et al, 2011]. Work from the systems community has looked at practical details such as the efficient implementation of a token bank [Vishnumurthy et al, 2003].…”

An Equilibrium Analysis of Scrip Systems

“…They associate a price (in bandwidth) with each file and find a market equilibrium in the resulting economy. Later work by Aperjis et al does use a currency, but the focus remains on establishing market prices [2008] Subsequent to our work, Dandekar et al [2011] examined networks where each agent can issue his own scrip, Rahman et al [2010] proposed a protocol to automatically adjust credit policies to maintain stability, Humbert et al [2011] modeled scrip systems where multiple agents combine to provide service, van der Schaar et al [2013] studied how to set parameters in a way that is robust to noise, and Johnson et al [2014] showed that welfare can be improved if the system prefers volunteers with low amounts of scrip.…”

“…If there is at least one volunteer, someone is chosen from among the volunteers (at random) to satisfy the request. Our model allows some agents to be more likely to be chosen (perhaps they have more bandwidth) but does not capture rules that take the amount of scrip volunteers have into account (such rules are considered by Johnson et al [2014]) or allow an agent to specify which agent is chosen. Allowing agents this type of control would break the symmetries we use to characterize the long-run behavior of the system, and would create new opportunities for strategic behavior.…”