Markets with Millions of Prices

1. Markets with Millions of Prices R. Hanson, J. Ledyard, T. Ishikida IFREE Mini-Conference in Experimental Economics, May 3, 2003

2. We Want: • Every nation*quarter: • Political stability • Military activity • Economic growth • US $ aid • US military activity

3. Combinatorial Info Markets • Most markets aggregate info as side effect • Info markets beat competing institutions • I.E.M. beat president polls 451/596 (Berg etal 2001) • But, markets fail when #prices >> #traders • Solutions: combo markets, market makers • Experiments to test, DARPA funded • Caltech students, 12-15 minute periods • Train, give info, let trade, see price accuracy

4. Experiment Environment (Really: W V X S U Z Y T ) Case A B C D E F G H 1 0 1 0 1 - - - - 2 1 0 0 1 - - - - 3 0 0 1 1 - - - - 4 1 0 1 1 - - - - 5 0 1 1 1 - - - - 6 1 0 0 1 - - - - 7 0 1 1 1 - - - - 8 1 0 0 1 - - - - 9 1 0 0 1 - - - - 10 1 0 0 1 - - - - Sum 6 3 4 10 - - - - Same A B C D E F G H A -- 1 2 6 -- -- -- -- B -- -- 7 3 -- -- -- -- C -- -- -- 4 -- -- -- -- D -- -- -- -- -- -- -- -- … • 8 binary vars: STUVWXYZ • 28 = 256 combinations • 20% = P(S=0) = P(S=T) = P(T=U) = P(U=V) = … = P(X=Y) = P(Y=Z) • 6 people, each see 10 cases: ABCD, EFGH, ABEF, CDGH, ACEG, BDFH • random map STUVWXYZ to ABCDEFGH

5. Theory Benchmarks

6. Simple Double Auction

7. Combinatorial Call

8. Individual Scoring Rule

9. Market Scoring Rule

10. Log Opinion Pool

11. Conclusions • Experiments on complex info problem • 256 prices from 6 subjects in 15 min. • Bayesian estimates way too high a bar • Simple DA ~ combo call ~ score rule < combo market maker ~< opinion pool • But pools have weight choice problem when expertise is varied, specialized

12. We Want: • Every nation*quarter: • Political stability • Military activity • Economic growth • US $ aid • US military activity

13. Environments: Goals, Training (Actually: X Z Y ) Case A B C 1 1 - 1 2 1 - 0 3 1 - 0 4 1 - 0 5 1 - 0 6 1 - 1 7 1 - 1 8 1 - 0 9 1 - 0 10 0 - 0 Sum: 9 - 3 Same A B C A -- -- 4 B -- -- -- C -- -- -- • Want in Environment: • explainable, fast, neutral • many variables, few directly related • few people, each not see all data cases • compute rational share-info estimates • Training Environment: • 3 binary variables X,Y,Z, 23 = 8 combos • P(X=0) = .3, P(X=Y) = .2, P(Z=1)= .5 • 3 people, see 10 cases of: AB, BC, AC • random map XYZ to ABC

14. 3 Variable Training Data

15. Experiment Structure • Subjects were Caltech students • 6 periods per session, 12-15 minutes each • Each subject trained in 3 variable session • Metric: Kulback-Leibler i qilog(pi /qi)

16. Troop Move Decision Advice $1 if War & Move Troops P(M) $1 if Move Troops P(W | M) $1 Compare! P(W | not M) $1 if Not Move Troops $1 if War & Not Move Troops P(not M)

17. Accuracy Simple Info Markets Market Scoring Rules Scoring Rules opinion pool problem thin market problem 100 .001 .01 .1 1 10 Estimates per trader Old Tech Meet New

18. D A C G F B E H A Scaleable Implementation • Overlapping variable patches • A simple MSR for each patch • Arbitrage neighbor patches • Limits profits to users who find inconsistencies • Only allow trade if all vars in same patch • User assets per patch, move via overlap • Regroup patches from request activity?