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

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: Seller:

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 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