Coordination Problems and Social Choice

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Coordination Problems and Social Choice

• A Cybernetic Analysis of Multi-Person Games

Brian Babcock
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Coordination Problems

• Many people choose among a set of options
• The value of each persons choice is increased if
  others make the same choice
• Example Wireless networks
• Two incompatible types of networks
• One is faster than the other
• Which network adapter should you buy?

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Coordination Problems

• Many other examples
• Operating systems
• Word processors
• Secure e-mail
• Wherever there are network externalities
• More and more common in the Information Age

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An Example Coordination Problem
Others Choice
A
B
A
5
0
Agents Choice
B
1
4
5
Which is the better choice?
A
B

• p probability that the other agent will choose
  A
• Value of choice A 5p
• Value of choice B p 4(1-p) 4-3p
• A is better when 5p gt 4-3p gt p gt 1/2
• B is better when 5p lt 4-3p gt p lt 1/2

0
5
A
4
1
B
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A Cybernetic Model
AgentsAction
Others Actions
Agents Model
Environment
Agents Observations
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Simulating the Process

• Two choices, A and B
• 100 Agents, each with a model How many agents
  prefer A?
• Initialize agents with random models
• Repeat
• Choose a random pair of agents
• Each agent chooses A or B based on their models
• They refine their models based on the interaction
• Terminate when all agents agree on whether A or B
  is the better choice

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How Social Choice Occurs

• Initially there is confusion
• Collectively, agents converge on a single choice
• That choice thus becomes the best choice
• The truth about the best choice is constructed by
  the agents interactions.

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Conversation
M1
M2
M1
M2
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Second-Order Agents

• First-order agents
• learn from other agents behavior
• convergence took 16 rounds on average
• Second-order agents
• learn from other agents behavior
• share models with other agents
• convergence took 6 rounds on average

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Achieving the optimal choice

• The agents could converge on A or B
• Each result occurs half the time
• (A,A) has value 5, (B,B) has value 4
• Would like to increase the probability of
  converging on A

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Advocates for Choice A

• Suppose 5 of the agents always choose A
• These advocates believe strongly in A
• Use marketing, free samples, pay-offs,
  propaganda, etc.
• Results
• First-order agents converge to A 75 of the time
• Second-order agents always converge to A
• Convergence time is unchanged (16 vs. 6 rounds)

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Making the problem harder
A
B
p is the probability that the other chooses A As
value is 5p Bs value is 3p4(1-p) 4-p A is
better if 5p gt 4-p gt p gt 2/3 B is better if
5p lt 4-p gt p lt 2/3
0
5
A
4
3
B

• A is still a better equilibrium than B
• A is worse unless at least 2/3 prefer A
• Less likely to converge to A

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Simulation Results (Harder Problem)

• No advocates
• First-order agents
• Always converge to B
• Avg. of 10 rounds
• Second-order agents
• Always converge to B
• Avg. of 3.6 rounds

• 15 advocates for A
• First-order agents
• Always converge to B
• Avg. of 14 rounds
• Second-order agents
• Always converge to A
• Avg. of 8 rounds

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Summary

• Many political and economic situations can be
  modeled as coordination problems
• Cybernetic modeling describes coordination
  problems well
• When agents share models as well as observing
  behavior, good things happen
• faster convergence
• easier to tilt the balance