An Equilibrium Analysis of Scrip Systems

Abstract

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' bestreply 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.

Analyzing Scrip Systems

“…They proposed a static game where users decide uploading/downloading rates, and they study the market clearing prices in equilibrium. The papers that are most closely related to ours are Friedman et al (2006), Kash et al (2007), Kash et al (2009a) and Kash et al (2009b). In fact, this stream of papers motivated our study.…”

“…Follow-on work in Kash et al (2009b) shows that social welfare increases as the number of scrips in the system increases up to this threshold of total scrips, after which the social welfare drops to zero due to the market crash. Kash et al (2009a), where the model is further generalized to include multiple player types, characterizes each player's threshold that achieves the optimal social welfare. In Kash et al (2009b), the authors further analyze the impact of altruists and hoarders in the scrip system.…”

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.…”

Kidney Exchange: An Operations Perspective

“…Understanding the bridge(s) between theory and practice. Kidney exchange has profited mightily from a literature ranging from stylized mathematical models published in analytical journals, to clinically oriented studies of designs adopted in practice 81 See for example Kash et al (2015); Johnson et al (2014); Hauser and Hopenhayn (2008); Möbius (2001) for literature on scrip systems and trading favors in dynamic games. 82 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.…”