Optimizing Scrip Systems: Efficiency, Crashes, Hoarders, and Altruists

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Optimizing Scrip Systems Efficiency, Crashes,
Hoarders, and Altruists

• Ian A.Kash, Eric J. Friedman,
• Joseph Y. Halpern
• Cornell University

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What is Scrip?

• Non-governmental currency
• Users pay other users for service with scrip
• Free riding is prevented through the need to earn
  scrip

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Related WorkUses 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

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Capitol Hill Baby Sitting Co-op
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Related WorkAnalysis 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

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Outline of the Rest of the Talk

• Model of a Scrip System
• Theoretical Results
• Practical Insights

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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

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Types of Agents

• Agents are characterized by a tuple of parameters
• An agents 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

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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

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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.

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Best Responses

• Lemma For all e, there exists a d such that if
  all types have dt gt 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 is best response function is
  monotone in the strategies of the other agents.

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Consequences of Monotonicity

• There exist greatest and least Nash equilibria
  Tarski 55, Topkis 79
• If some point k has BR(k) gt k then the greatest
  equilibrium is nontrivial.
• We can find the greatest equilibrium by iterating
  best responses.

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Studying Agent Types with Maximum Entropy
The fraction of agents who who are playing Sk
and have i dollars
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Setting the Money Supply
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Altruists
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Dealing with Altruists
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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

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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

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Thank You