1. Learning under different market protocols (full vs
Learning under different market protocols (full vs. limited information)
Mikhail Anufriev, U of Amsterdam, Jasmina Arifovic, Simon Fraser U,
Valentyn Panchenko, U of New South Wales

2. Aims Compare 2 market designs in terms of efficiency
Call auction (batch)
Continuous double auction (CDA)
Study effect of information (open vs closed book) on efficiency (price and allocation)
Assume neither full rationality, nor irrationality,
instead use Individual Evolutionary Learning

3. Arifovic and Ledyard (2007, JEDC) “Call market book information and efficiency”
IEL – learning technique that aims to replicate behavior of economic agents
Ideas based on genetic algorithms, but adapted to economic decision problem
Call auction – bids from buyers and asks from sellers are collected in demand/supply curves, market clears at their intersection
Information: open/closed book

4. Related literature Gode and Sunder (1993, JPE)
- CDA, ZI agents, budget constraints,
- “resampling” - book is cleared after each transaction
Conclusion: CDA market mechanism leads to efficient allocation and price
Critique:
Gjerstad and Shachat (2007)
- Individual Rationality (budget constraints) is not a part of market mechanism
- Other measures of convergence may lead to different conclusions
LiCalzi and Pellizarri (2008)
- “Resampling” is important assumption, no convergence without resampling
- In environment without resampling sophisticated learning
(Gjerstad and Dickhaut, 1998) leads to efficient allocation and price

5. Set-up Buyers – consume 1 unit of commodity and has given value V
Sellers – endowed with 1 unit of commodity with given costs C
Each buyer/seller is allowed to transact only 1 unit
Buyers submit bid price, sellers submit ask prices according to IEL
Repeated trade over certain number of periods
Fixed environment – costs, value do not change
Mechanisms: Call Auction/CDA
Information: Open/Closed book

6. Walrasian Clearing
Surplus

7. Individual Evolutionary Learning
Each agent has an own finite pool of strategies (ask/bid prices)
Initially strategies are randomly drawn (within bounds of costs/valuations)
A strategy is used with some probability (initial probabilities are equal)
Probabilities are based on forgone payoffs
Pool is updated:
Experimentation (mutation) – with certain (small) probability a strategy in the pool is replaced with a new strategy (drawn around the old strategy)
Replication – form a new pool: compare strategies A and B in the old pool,
if U(B)>U(A), enter B instead of A is the new pool, otherwise enter A

8. Individual Evolutionary Learning
An agent selects a strategy with certain probability which depends on “foregone” payoff U
Buyer:
Seller:

9. Benchmark P* Call – closed: P* - clearing price of the last round
Call – open: P* - clearing price of a hypothetical call auction when only own bid/ask is modified
CDA – closed: P* - average price over the last round
CDA – open: P* - transaction price of a given agent in a hypothetical CDA auction when only own bid/ask is modified

10. Efficiency measure Surplus = total gains from trade
Benchmark G - Surplus is maximized in the call market when buyers bid their valuations and sellers ask their costs
Efficiency = G/Benchmark G

11. Simulations As in Arifovic and Ledyard (2007) 5 buyers and 5 sellers
Valuations [1, 0.93, 0.92, 0.81, 0.5]
Costs [0.66, 0.55, 0.39, 0.39, 0.3]
T=100 rounds
Prob. of mutation = 0.03
4 treatments

12. Demand/supply

13. Call Auction
Open Book
Closed Book

14. Call Auction: Individual Strategies
Open Book
Closed Book

15. CDA
Open Book
Closed Book

16. CDA: Individual Strategies
Open Book
Closed Book

17. Conclusions
Study effect of market mechanism and open/close design on efficiency and price
Use IEL to model behavior of agents
Findings
open book design leads to smaller spread and more stable price over time in both CA and CDA
closed book design is more efficient in terms of surplus under CDA
agents “coordinate” their bids/asks under open CDA
agents “learn” their costs/valuations under closed CDA