تحول، بازده و معامله گران پرسر و صدا در بازار مزایده یک طرفه

Natural selection is used to examine a one-sided buyer auction market. With each trader's behavior preprogrammed with its own inherent and fixed probabilities of overpredicting, predicting correctly and underpredicting the fundamental value of the asset, informational efficiency occurs. 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. This is established under a weak restriction regarding traders’ behavior.

Traditionally, in the literature, the derivation of an informationally efficient market has tended to rely on the presence of traders’ rational expectations, strategic usage of market information or adaptive learning behavior where noise traders gradually become informed traders. However, due to individuals’ limited ability to process and manage complex information, the assumption of rationality is challenged. This further calls into question the achievement of market efficiency. On the other hand, there is Friedman's (1953) well-known conjecture that, because noise traders will sooner or later lose money to the informed traders, the informed traders will come to dominate the market and drive the asset price toward the fundamental value. An intuitively appealing aspect of Friedman's conjecture is the idea of natural selection among traders. The idea of abandoning rationality on the part of traders is consistent with a growing literature in behavioral economics and finance. The behavioral approach focuses on the behavior patterns drawn from psychological theory (e.g., Kahneman et al., 1982). Often judgmental decisions are based on cognitive rules of thumb used to simplify the decision-making process. Using such rules to assess uncertain events and make predictions, often leads to systematic errors or biases. In the context of a one-sided auction, such systematic errors take the form of consistent patterns of predicting biases, which are captured by the probabilities of overpredicting and underpredicting the asset value; these predicting probabilities become the key to modeling traders’ behavior. In this paper it is assumed that traders are rather unsophisticated and each trader consistently overpredicts or underpredicts with some fixed probabilities. In an evolutionary sense, each trader is genetically preprogrammed with its own inherent and fixed probabilities of overpredicting, underpredicting and predicting correctly the asset value. Since a trader has a positive probability of overpredicting or underpredicting the asset value, the trader has a positive probability of acting upon noise as if it were information. Therefore, in this sense, traders are called noise traders in this paper. Within the context of a double-sided auction, Luo 1998 and Luo 2001 shows that with no requirement of traders’ rationality such as rational expectations and adaptive learning, natural selection among traders through redistribution of wealth is sufficient to cause the convergence to an informationally efficient market. It is noteworthy, however, that in the context of a double-sided auction, the allowance for short sales implies that the supply of the asset is virtually elastic. While the majority of financial markets adopts a double-sided auction market, there is a significant number of markets which are essentially one-sided auction markets with a perfectly inelastic supply. A key distinction between a one-sided and a double-sided auction market is that traders in a double-sided auction market are allowed to short sell. In a one-sided auction market, short sales are not possible because of the lack of a secondary market. The absence of secondary markets often occurs in the sale of short-term commercial paper, municipal notes, non-negotiable certificates of deposit and private placements and sometimes occurs in markets for bonds (e.g., Japanese corporate bonds).1 Other examples of one-sided auctions include the leasing of mineral rights, the leasing of oil drilling permits and the leasing of timber rights.2 The recent emergence of internet online purchasing provides some other interesting examples. There are three purposes of this paper. The first purpose is to show that the market mechanism of a one-sided auction, itself, can promote an efficient outcome through natural selection. To this end, this paper adopts the idea of natural selection and formulates an evolutionary model of a one-sided buyer's auction market. It shows that even without a rationality assumption like rational expectations or adaptive learning and even when each trader merely acts upon its own inherent and fixed probabilities of overpredicting, predicting correctly and underpredicting the asset value, an informationally efficient market can occur. This stands in contrast with the conventional literature which states that an efficient outcome is promoted through rational expectations or adaptive behavior on the part of market participants (e.g., Grossman 1976 and Grossman 1978; Radner, 1979; Hellwig, 1980). A second purpose of this paper is to identify, in the context of this evolutionary approach, an alternative less restrictive condition for achievement of an efficient outcome in the one-sided auction market other than the one used in the double-sided auction market. For convergence to occur in the context of a double auction, Luo 1998 and Luo 2001 requires that in each time period there is a positive probability that the entering trader has an arbitrarily high probability of predicting the fundamental value correctly. Furthermore, within the context of a double auction the allowance for short sales implies that the supply of contracts is elastic. In contrast, in this paper, the supply of the asset is perfectly inelastic and the market is a one-sided buyer auction. For convergence to occur, a less restrictive condition is that there is a positive probability in each time period that the entering trader has an arbitrarily low probability of overpredicting the fundamental value and has a probability, of predicting arbitrarily close to the fundamental value, being bounded away from zero by a positive number. This result is very intuitive. If traders who overpredict with a low probability (implying a small number of upward biases) are characterized as being relatively risk averse (in a behavioral finance sense (e.g., Sitkin and Pablo, 1992), for convergence to occur, it is sufficient that there are enough traders with a sufficiently degree of risk aversion. The importance of the presence of these risk averse traders in the natural selection process leading to market efficiency, is consistent with Barrow (1992) and Olsen (1998) who see decision attributes that exhibit aversion to negative impacts (here caused by overpredicting) as having evolutionary value in selecting the long run outcome. Nevertheless, to obtain convergence to efficiency, competition among traders is needed. That is, in a one-sided auction market where the market supply is perfectly inelastic, competition means that each trader's initial wealth must be sufficiently small relative to the fixed market supply. However, it is remarkable that even when there is a perfectly inelastic supply of the asset and even when the number of traders increases over time, with each entering trader coming in with a finite amount of wealth, the price can be eventually assured to remain in a small interval containing the fundamental value. A third purpose of this paper is to quantify the extent to which a variation in movement of the underlying asset's liquidation value around the fundamental value influences the extent of convergence of the asset price to the fundamental value. This paper, like Luo (2001), accounts for a random shock around the fundamental value. This paper shows that, the bigger is the variation in the random shock about the fundamental value, the bigger is the variation of the asset price about the fundamental value. The evolutionary approach in this paper stands in contrast with recent literature which has analytically studied the impact of noise traders on the market price within the context of rational models. For example, De Long et al. (1990) study an overlapping generation model, where an informed trader and a noise trader both maximize their expected utilities. They find that the noise trader can cause the market price to deviate systematically away from its fundamental value.3 For the convergence of the asset price to the fundamental value, rationality models (where utility or profit maximization occurs) sometimes rely on learning and imitation to make uninformed traders become more informed. For example, Grossman (1978) allows investors to acquire information about past distributions of prices which in turn produces more informed investors. This has also been explored in the experimental laboratory market. Plott and Sunder (1982) show that constant replication allows a learning by traders which resembles a rational expectations equilibrium. Related literature in applying an evolutionary approach to examining market behavior are Blume and Easley (1992), Biais and Shadur (1993) and Luo (1995). Blume and Easley (1992) study a dynamic model of an asset market with a finite number of traders with different investment rules. They find that the market can select for an irrational rule and the market may not be efficient. Biais and Shadur (1993) apply Darwinian dynamics to the selection of the number of informed traders and noise traders based on their payoffs. They find that noise traders can persist in the long run. The results in the above two papers have illustrated that the natural selection in the market alone is not sufficient to generate an efficient market outcome. Luo (1995) further shows that natural selection, in conjunction with competition in the market, is sufficient to lead the market to select the most efficient firms (those producing at or near the minimum efficient scale) and as a result the market price converges to the perfectly competitive price. This paper shows analytically that the market can reach an efficient market outcome with the presence of irrational noise traders. The coexistence of market efficiency and participants’ irrationality has also been illustrated in some recent experimental literature as well. For example, Gode and Sunder (1993) design a series of experiments to examine a double auction market where traders submit bids and offers randomly. They find that allocation efficiency in the double auction can be generated from individual participants’ irrationality. Bosch and Sunder (1994) design a similar series of experiments to examine multimarket double auctions. They reach the same conclusion. This paper is organized into four sections. Section 2 outlines the model. The results can be found in the Section 3. Section 4 summarizes and concludes the paper.

This paper uses an evolutionary idea of natural selection to examine the convergence of the asset price to its fundamental value in a one-sided auction market where traders are modeled as unsophisticated. Traders cannot learn or strategically use any information from the market or other participants and they merely act upon their preprogrammed behavior rules, which reflect their inherent noisiness. Specifically, in this dynamic asset market, the market supplies one unit of a one period risky asset each time period. Traders enter the market sequentially over time. The liquidation value of the asset is the product of the fundamental value of the asset and the exponential of a random shock. The fundamental value of the asset is determined in the beginning of each time period, but unknown to any market participants. The random shock is realized at the end of each time period. Each trader's behavior is exogenously preprogrammed instead of endogenously derived from some optimization problem. In other words, each trader's behavior is characterized by his or her predetermined probabilities of overpredicting, predicting correctly and underpredicting the fundamental liquidation value. Each trader's prediction in each time period is generated from a probability distribution described by his or her predetermined probabilities of overprediction, exact prediction and underprediction with respect to the fundamental liquidation value. The asset market is a one-sided auction market. The market serves as a selection process which evaluates all the traders with different prediction error distributions, rewarding the traders who place good bids and taking money away from the traders who place bad bids. Over time this process gradually places more weight on the accurate information into the asset price and places less weight on noise into the asset price. Eventually the asset price only reflects the accurate information and eliminates noise. Informational efficiency occurs in the long run. More precisely, as long as at any point in time there is a positive probability that the entering trader has an arbitrarily low probability of overpredicting the fundamental value and has a probability, of predicting arbitrarily close to the fundamental value, being bounded away from zero by a positive number, the following is true. With probability 1, if each trader's initial wealth is sufficiently small relative to the market supply and if the variation of the 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 1. In the limit, each individual's demand for the risky asset is infinitesimally small relative to the market supply. Consequently, no individual can influence the asset price. In this one-sided auction market, losses are possibly incurred when overbidding occurs. From a behavioral finance perspective, one can interpret traders with low probability of overpredicting the fundamental value (implying a small number of upward biases) as relatively risk averse. For this reason, one may also interpret the θ-Assumption as an allowance for the entry of a sufficient number of buyers with a sufficient degree of risk aversion and with a positive probability (however small) of bidding arbitrarily close to the fundamental value. The presence of this group of buyers provides the driving force for the long run convergence. Finally, the variation in the random shock about the fundamental value influences the extent to which efficiency occurs. The bigger is the variation in the random shock about the fundamental value, the bigger are the deviations of the asset price from the fundamental value.