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
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
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
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
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
Walrasian Clearing
Surplus
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
Individual Evolutionary Learning
• An agent selects a strategy with certain probability which
depends on “foregone” payoff U
• Buyer:
s  U s /
*


V  P 
Us  
 if
0 




S
Ui
i 1
*

b

P
 s


*
b

P


 s

• Seller:
*

P
 C
Us  
0




 if


*

a

P
 s


*
a

P


 s

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
Efficiency measure
• Surplus = total gains from trade
G 
 (V
i
 P i )   (P j  C j )
• Benchmark G - Surplus is maximized in the call
market when buyers bid their valuations and
sellers ask their costs
• Efficiency = G/Benchmark G
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
Demand/supply
Call Auction
Open Book
Closed Book
Call Auction: Individual Strategies
Open Book
Closed Book
CDA
Open Book
Closed Book
CDA: Individual Strategies
Open Book
Closed Book
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