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2012 | OriginalPaper | Buchkapitel

6. Evolution, Noise Traders, and Market Efficiency in a One-Sided Auction Market

verfasst von : Guo Ying Luo

Erschienen in: Evolutionary Foundations of Equilibria in Irrational Markets

Verlag: Springer New York

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Abstract

This chapter builds an evolutionary model of one-sided buyer auction market toexamine if the informational efficiency would still occur as a long run outcome. Here, each trader’s behavior is preprogramed with its own inherent and fixed probabilities of overpredicting, predicting correctly, and underpredicting the fundamental value of the asset. This chapter shows that, if each buyer’s initial wealth is sufficiently small relative to the market supply and if the variation in the asset’s random shock is sufficiently small, then as time gets sufficiently large, the proportion of time, that the asset price is arbitrarily close to the fundamental value, converges to one with probability one.

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Vorheriges Kapitel Natural Selection, Random Shocks, and Market Efficiency in a Futures Market

Nächstes Kapitel The Evolution of Money as a Medium of Exchange in a Primitive Economy

Sometimes, secondary markets do exist for commercial paper and private placements. But usually the transaction costs of setting up these markets have proven to be prohibitive.

Other examples of auctions, where there is a fixed supply of an asset and no short sales, can be found in both the theoretical and experimental economics literature (e.g., Wilson (1979) and Forsythe et al. (1982)).

Allen and Yannelis (2001) present a comprehensive discussions on various rational equilibrium outcomes in various differential information economies.

Their results are partly due to the difference in the utility functions of both types of traders, the absence of wealth accumulation and the absence of wealth flows between the two types of traders.

This one-sided buyer market with one unit of an asset being supplied each time period is also used in Blume and Easley (1992).

This specification of beliefs or predictions is consistent with Grossman (1976, 1978), Figlewski (1978), and Hellwig (1980).

For negative predictions not to occur, the lower bound for predictions is constrained to zero. That is b _s ^t = maxz _s + u _s ^t, 0.

Alternatively, one can assume different initial endowments of wealth for all traders. However, the same results with respect to convergence of the asset price will hold, provided that the initial endowment of wealth for all entering traders is bounded from above.

For simplicity it is assumed that each trader potentially invests all of his or her wealth in each period. The results of this chapter would still hold if each trader spends only a fraction of his or her total wealth on trading activity. A smaller fraction could reflect more risk aversion on the part of the trader.

It is apparent that, given the demand function, any trader’s wealth can never be negative. This is due to the fact that each trader begins with a positive level of initial wealth and short sales are not allowed.

A related paper which examines the relationship between accuracy of agents’ predictions, wealth accumulation and the convergence of prices to the true value, is Sandroni (2000).

That is, for trader t where b _s ^t = p _s, \({q}_{s}^{t} = \frac{{V }_{s-1}^{t}} {{\sum }_{{t}^{{\prime}}\in {M}_{s}}{V }_{s-1}^{{t}^{{\prime}}}}\left [1 -{\sum }_{{t}^{{\prime}}\in {A}_{s}}{q}_{s}^{{t}^{{\prime}} }\right ]\) where \({A}_{s} =\{ {t}^{{\prime}}\mid {b}_{s}^{{t}^{{\prime}} } > {p}_{s}\}\) and \({M}_{s} =\{ {t}^{{\prime}}\mid {b}_{s}^{{t}^{{\prime}} } = {p}_{s}\}\). It would not alter the results if any alternative method of allocating shares of the asset is used in this situation.

In fact, there can be a positive probability of traders with other types of predictive behavior. For example, such trader types could enter with prediction behavior that imitates past successful traders (e.g., Lettau (1997)). Nevertheless, as long as the θ − Assumption holds, the presence of these types of traders would not disrupt convergence.

The variation in random shock here refers to E(exp(ω_t) − 1)ω_t > 0.

For the simulations, as T grows, the computer (c.p.u.) time to complete the simulations grows in proportion to T ². To conduct 100 simulations in a reasonable length of c.p.u. time, T was constrained to be 3000. However, for five simulations the time was extended to 5000. By time period 5000, on average across five simulations, \(\frac{\#\left \{s\leq 5000:\left \vert {p}_{s}-{z}_{s}\right \vert <0.10\right \}} {5000} \ = 0.64.\) This shows further convergence.

Allen, B., and N.C. Yannelis. 2001. Differential information economies: An introduction. Economic Theory 18:263–273.CrossRef

Barrow, J.H. 1992. The Adapted Mind. New York: Oxford Press.

Biais, B., and R. Shadur. 2000. “On the Survival of Irrational Traders: A Darwinian Approach”, European Economic Review 44:469–490.CrossRef

Billingsley, P. 1995. Probability and Measure. New York: John Wiley & Sons.

Blume, L., and D. Easley. 1992. “Evolution and Market Behavior”, Journal of Economic Theory 58:9–40.CrossRef

Bosch, A and S. Sunder. 2000. “Tracking the Invisible Hand: Convergence of Double Auctions to Competitive Equilibrium”, Computational Economics 16(3):257–284.CrossRef

Castro, L.I. de, Marialaura, P., and Yannelis, N. 2011. “A new perspective to rational expectations:maximin rational expectations equilibrium”. Working paper, Department of Economics, University of Illinois at Urbana Champaign.

De Long, J.B., A. Shleifer, L. H. Summers and R. J. Waldmann. 1990. “Noise Trader Risk in Financial Markets”. Journal of Political Economy 98:703–738.CrossRef

Durrett, R. 1991. Probability: Theory and Examples Belmont, CA: Wadsworth & Brooks/Cole.

Figlewski, S. 1978. “Market ‘Efficiency’ in a Market with Heterogeneous Information”. Journal of Political Economy 86(4):581–597.CrossRef

Forsythe, R., Palfrey, T.R., and C. R. Plott. 1982. “Asset Valuation in an Experimental Market”. Econometrica 50:537–567.CrossRef

Friedman, M. 1953. Essays in Positive Economics. Chicago: University of Chicago Press.

Gnedenko, B.V. 1962. The Theory of Probability. New York, NY: Chelsea Publishing Company.

Gode, D.K., and S. Sunder. 1993. “Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality”. Journal of Political Economy 101(1):119 –137.CrossRef

Grossman, S. J. 1976. “On the Efficiency of Competitive Stock Markets where Traders Have Diverse Information”. Journal of Finance 31:573–585.CrossRef

Grossman, S.J. 1978. “Further Results on the Informational Efficiency of Competitive Stock Markets”. Journal of Economic Theory 18:81–101.CrossRef

Hellwig, M.F. 1980. “On the Aggregation of Information in Competitive Markets”. Journal of Economic Theory 22:477–498.CrossRef

Kahneman, D., Slovic, P., and A. Tversky (eds.). 1982. Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press.

Lettau, M. 1997. “Explaining the Facts with Adaptive Agents: The Case of Mutual Fund Flows”. Journal of Economic Dynamics and Control 21:1117–1147.CrossRef

Luo, G. 1995. “Evolution and Market Competition”. Journal of Economic Theory 67:223–250.CrossRef

Luo, G. 1998. “Market Efficiency and Natural Selection in a Commodity Futures Market”. Review of Financial Studies 11(3):647–674.CrossRef

Luo, G. 2001. “Natural Selection and Market Efficiency in a Futures Market with Random Shocks. Journal of Futures Markets 21(6):489–516.CrossRef

Olsen, R.A. 1998. “Behavioral finance and its Implications for Stock-price Volatility”. Financial Analysts Journal 54(2):10–18.CrossRef

Plott, C.R., and S. Sunder. 1982. “Efficiency of Experimental Security Markets with Insider Information: An Application of Rational-Expectations Models”. Journal of Political Economy 90(4):663–698.CrossRef

Radner, R. 1979. “Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices”. Econometrica 47:655–678.CrossRef

Sandroni, A. 2000. “Do Markets Favor Agents Able to Make Accurate Predictions?” Econometrica 68:1303–1341.CrossRef

Schneider, S.L., and L.L. Lopes. 1986. “Reflection in Preferences under Risk: Who and When may Sugget Why?” Journal of Experimental Psychology: Human Perception and Performance 12:535–548.CrossRef

Sitkin, S.B., and A.L. Pablo. 1992. “Reconceptualizing the Determinants of Risk Behavior”. Academy of Management Review 17(1):9–38.

Tversky, A., and D. Khaneman. 1974. “Judgment under Uncertainty: Heuristics and Biases”. Science 185:1124–1131.CrossRef

Wilson, R. 1979. “Auctions of Shares”. Quarterly Journal of Economics 93(4):675–690.CrossRef

Titel: Evolution, Noise Traders, and Market Efficiency in a One-Sided Auction Market
verfasst von: Guo Ying Luo
Verlag: Springer New York
Buch: Evolutionary Foundations of Equilibria in Irrational Markets
Print ISBN: 978-1-4614-0711-9

Electronic ISBN: 978-1-4614-0712-6

Copyright-Jahr: 2012
DOI: https://doi.org/10.1007/978-1-4614-0712-6_6