1. Coordination Problems and Social Choice A Cybernetic Analysis of Multi-Person Games Brian Babcock

2. Coordination Problems Many people choose among a set of options The value of each person’s 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?

3. 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

4. Agent’s Choice Other’s Choice A B AB 5 1 0 4 An Example Coordination Problem

5. Which is the better choice? 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 > 4-3p ==> p > 1/2 B is better when 5p p < 1/2 0 41 5 A B B A

6. Agent’s Model Agent’s Action Others’ Actions Environment Agent’s Observations A Cybernetic Model

7. 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

9. 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.

10. Conversation M1’M1’M2’M2’ M1M1 M2M2 M1M1 M2M2

11. 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

12. 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

13. 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)

14. Making the problem harder 0 43 5 A B B A A is still a better equilibrium than B A is worse unless at least 2/3 prefer A Less likely to converge to A p is the probability that the other chooses A A’s value is 5p B’s value is 3p+4(1-p) = 4-p A is better if 5p > 4-p ==> p > 2/3 B is better if 5p p < 2/3

15. 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

16. 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”