1. Optimizing Scrip Systems: Efficiency, Crashes, Hoarders, and Altruists
Ian A.Kash, Eric J. Friedman,
Joseph Y. Halpern
Cornell University
June 15, 2007
EC Talk

2. What is Scrip? Non-governmental currency
Users pay other users for service with scrip
Free riding is prevented through the need to earn scrip
June 15, 2007
EC Talk

3. Related Work: Uses of Scrip Systems
Bookkeeping
Babysitting Coop [Sweeney and Sweeney ’77]
Yootles [Reeves et al]
Resource Allocation
Mirage [Chun et al ’05]
Mariposa [Stonebraker et al ’94]
Agoric Systems [Miller and Drexler ’88]
Preventing Free Riding
Karma [Vishnumurthy et al ’03]
June 15, 2007
EC Talk

4. Capitol Hill Baby Sitting Co-op
June 15, 2007
EC Talk

5. Related Work: Analysis of Scrip Systems
Auction Design
Mirage
Hens et al
Analysis of Baby Sitting Co-op type systems
Service is costless
Cannot provide and receive service at the same time
June 15, 2007
EC Talk

6. Outline of the Rest of the Talk
Model of a Scrip System
Theoretical Results
Practical Insights
June 15, 2007
EC Talk

7. Modeling a Scrip System
n agents
In round r, an agent is chosen to make a request (uniformly at random)
With probability b, each other agent can satisfy the request.
Each agent that can satisfy the request decides whether to volunteer
One volunteer is chosen uniformly at random to satisfy the request
For round r, requester gets a payoff of g (if someone volunteered) and pays $1, volunteer pays a small utility cost of –a and earns $1, and everyone else gets 0.
Total utility for an agent is the discounted sum of round payoffs:
June 15, 2007
EC Talk

8. Types of Agents Agents are characterized by a tuple of parameters
An agent’s type t = (at,bt,gt,dt,rt)
at: cost of satisfying a request
bt: probability of being able to satisfy a request
gt: value of having a request satisfied
dt: discount rate
rt: relative request rate
June 15, 2007
EC Talk

9. Threshold Strategies
In some round, I have k dollars and have to decide whether to volunteer. What should I do?
Sk: Volunteer if I have less than k dollars
k is your “comfort level,” how much you want to have saved up for future requests
S0 corresponds to never volunteering and
S¥ corresponds to always volunteering
June 15, 2007
EC Talk

10. Main Results
If all agents play threshold strategies, we can use maximum entropy to explicitly compute the steady-state distribution of money
There is an e-Nash Equilibrium where all agents play threshold strategies
There is an efficient algorithm to find this equilibrium.
June 15, 2007
EC Talk

11. Best Responses
Lemma: For all e, there exists a d such that if all types have dt > d and every agent but i plays a threshold strategy, then agent i has an e-best response that is a threshold strategy. Furthermore, agent i’s best response function is monotone in the strategies of the other agents.
June 15, 2007
EC Talk

12. Consequences of Monotonicity
There exist greatest and least Nash equilibria [Tarski ’55, Topkis ’79]
If some point k has BR(k) > k then the greatest equilibrium is nontrivial.
We can find the greatest equilibrium by iterating best responses.
June 15, 2007
EC Talk

13. Studying Agent Types with Maximum Entropy
The fraction of agents who
who are playing Sk and
have i dollars
June 15, 2007
EC Talk

14. Setting the Money Supply
June 15, 2007
EC Talk

15. Altruists
June 15, 2007
EC Talk

16. Dealing with Altruists
June 15, 2007
EC Talk

17. Other Results in the Paper
More on studying agent types from the empirical wealth distribution
How the system evolves under best-reply dynamics
Proof of the inevitability of a crash
Relationship between the crash and inflation in non-fixed price systems
Hoarders hurt social welfare, but can be handled by increasing the money supply
June 15, 2007
EC Talk

18. Recap
Maximum entropy and mononicity of the best reply function are keys to determining existence and properties of equilibria
Maximum entropy provides tools for studying the types of a population from the distribution of wealth
Manage the average amount of money to maximize agent welfare
Altruists (and other nonstandard agents like hoarders) can also be handled by managing the average amount of money
June 15, 2007
EC Talk

19. Thank You
June 15, 2007
EC Talk