Learning to trade in an unbalanced market

Transcription

1 Florian Hauser, Dept. Banking and Finance, Universität Innsbruck, Marco LiCalzi, Dept. Management, Università Ca Foscari Venezia,

2 Outline 1 Motivation 2 Market Model 3 Results 4 Summary

3 Motivation Fano S, LiCalzi M, Pellizzari P (2011), Convergence of outcomes and evolution of strategic behavior in double auctions. Journal of Evolutionary Economics, forthcoming: The competitive outcome obtains under different market architectures if the size of the market is sufficiently large. The choice of the order-clearing rule affects trading behavior.

4 Motivation Agent-based literature has paid scant attention to the study of unbalanced markets: Anufriev M, Arifovic J, Ledyard J., Panchenko V (2011), Efficiency of continuous double auctions under individual evolutionary learning with full or limited information. Journal of Evolutionary Economics Gode DK, Sunder S (1997), What makes markets allocationally efficient? Quarterly Journal of Economics 112:

5 Motivation Market Model Results Summary Motivation An important issue, as traders on the long side of a market wind up holding the short end of the stick Taylor CR (1995), The long side of the market and the short end of the stick: Bargaining power and price formation in buyers, sellers, and balanced markets. Quarterly Journal of Economics Our research questions: How does (a) learning, and (b) the market protocol affect prices, allocative efficiency, and split-up of the surplus between buyers and sellers in unbalanced markets.

6 Market Model n = b + s profit-maximizing traders, where b are buyers and s are sellers. Each agent trades at most one unit of one generic good. Each buyer i has a private valuation v i and each seller j has a private cost c j, with v i, c j U(0; 1). Profits are v p for buyers and p c for sellers.

7 Market Model We test two different market protocols: Simultaneous order-clearing (call market), referred to as S. Asynchronous order-clearing (continuous double auction), referred to as A. We simulate two different kinds of trading behavior: When starting the simulation, agents truthfully report their valuations/costs, referred to as TT. Learning takes place by means of genetic programming, denoted as GP. Resulting settings: S-TT, S-GP, A-TT, A-GP

8 Convergence of prices to the competitive outcome S- A- TT... GP TT... GP Figure: Average price (black) and standard deviation (grey) for the case s = 50 and b = 5s.

9 Convergence of prices to the competitive outcome Table: Each cell exhibits the average transaction price for S-TT (top-left), S-GP (top-right), A-TT (bottom-left), A-GP (bottom right). s = 1 s = 5 s = 50 b = s b = 5s Confirming the result in Fano et al. (2011): in a balanced market, the evolution of trading strategies stabilizes prices around the competitive price p, particularly when the market grows large.

10 Convergence of prices to the competitive outcome Table: Each cell exhibits the average transaction price for S-TT (top-left), S-GP (top-right), A-TT (bottom-left), A-GP (bottom right). s = 1 s = 5 s = 50 b = s b = 5s There is a mismatch between the prices under the baseline case of S-TT (top-left) and the prices under S-GP, A-TT, or A-GP in small unbalanced markets.

11 Convergence of prices to the competitive outcome Table: Each cell exhibits the average transaction price for S-TT (top-left), S-GP (top-right), A-TT (bottom-left), A-GP (bottom right). s = 1 s = 5 s = 50 b = s b = 5s Note that P(S-GP) > P(A-GP). Thus, under learning asynchronous order-clearing works to the advantage of the long side.

12 Convergence of prices to the competitive outcome Table: Each cell exhibits the average transaction price for S-TT (top-left), S-GP (top-right), A-TT (bottom-left), A-GP (bottom right). s = 1 s = 5 s = 50 b = s b = 5s In large, unbalanced markets, there is a mismatch between S-TT and A-TT, but learning does lead to competitive prices under both regimes.

13 Trading functions under simultaneous order clearing s = 1 s = 5 s = 50 b = s b = 5s

14 Trading functions under asynchronous order clearing s = 1 s = 5 s = 50 b = s b = 5s

15 Allocative efficiency S- A- TT... GP TT... GP Figure: Efficiency (black) and buyers /sellers surplus ratio (grey) under simultaneous (left) and asynchronous (right) order clearing for the case s = 50 and b = 5s.

16 Allocative efficiency Table: Average ratios for S-GP vs. S-TT (left) and for A-GP vs. S-TT (right). s = 1 s = 5 s = 50 b = s b = 5s Allocative efficiency is higher under S than under A and grows to 1 as the size of the market increases.

17 Allocative efficiency and learning Table: Average ratios for A-TT vs. S-TT (left) and for A-GP vs. A-TT (right). s = 1 s = 5 s = 50 b = s b = 5s Loss in allocative efficiency when traders using truth-telling switch from simultaneous to asynchronous order-clearing. The pursuit of individual profits (learning) is socially beneficial under asynchronous order-clearing.

18 Efficiency - long side vs. short side Table: Average ratios for buyers to sellers surplus under S-TT (left), S-GP (center), and A-GP (right). s = 1 s = 5 s = 50 b = 3s b = 5s Increasing the market size makes the long side worse off. Optimizing trading strategies under simultaneous order-clearing further deteriorates the long side s position. Asynchronous order-clearing under optimized strategies improves the long side s performance.

19 Summary In unbalanced markets, traders on the long side of a market indeed wind up holding the short end of the stick. With truth-telling, the long side of the market will prefer simultaneous over asynchronous order clearing. Under simultaneous order clearing, learning is disadvantageous for the long side and decreases allocative efficiency. Under asynchronous order clearing, learning is advantageous for the long side and increases allocative efficiency.