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					A Middleman in the Ambiguous Situation -An Experimental EvidenceKazuhito Ogawa∗ Yuhsuke Koyama†and Sobei H. Oda‡ , July 16, 2003

Abstract This paper describes how undergraduates act as intermediaries, who buys a commodity from a supplier and sells it to a consumer at a higher price to gain a profit margin. A series of experiments was conducted to see how subjects play the monopolistic intermediary against given but unknown supply and demand curves. The results show that most subjects make a two-stage search: they first search for a pair consisting of the bid price and the ask price that equalise the quantity they can (must) buy with the quantity they can sell; then, while keeping the trading quantity, they adjust the prices to obtain a locally maximum profit. This suggests that monopolistic firms can act as intermediaries even if they are not as informed as they are supposed to be in the market microstructure theory. In addition, we investigate how people cope with ambiguity, by applying general knowledge to those problems whose details are unknown.

JEL: C91 Laboratory, Individual Behavior, L12 Monopoly Key Words: market microstructure, middleman, experimental economics, two-stage search, ambiguity model

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Introduction

It is a widely held premise that a market is said to be in equilibrium if demand equals supply. Certainly, if every unit of a commodity is traded at the equilibrium price, the number of units that buyers are willing to purchase at that price equals the number of units the sellers are ready to sell. Yet a question arises: How, why and by whom is the equilibrium price found and enforced on all traders? The general equilibrium theory tacitly assumes an auctioneer, who repeats auctions until he or she finds the equilibrium price set and then lets all market participants trade at that price set. This theory, however, does not explain why most markets actually function without such an altruistic, tireless, and exceedingly capable auctioneer. Market microstructure theory (O’hara 1995; Spulber 1996, 1999, 2002) posits that some market participants, say monopolistic firms, voluntarily act as auctioneers to earn profits. The theory explains price formulation in terms of a profit-seeking in-market agents’ conscious strategy. By posting prices at which they will buy and sell at their own risk, the acting auctioneers decrease the uncertainty under which other traders buy and sell, which activity brings them profit, or the margin between the two prices. In other words, market microstructure theory lies between the traditional equilibrium theory that does not deduce, but assumes, equilibrium, and the extreme

School of Economics, Kyoto University, JSPS Research Fellow Yoshida, Sakyo-ku, Kyoto 606-8501, Japan e-mail: O-kazu@m3.people.or.jp † Tokyo Institute of Technology Nagatsuta Campus : 4259 Nagatsuta-cho, Midori-ku Yokohama, 226-8502 Japan e-mail: koyama@dis.titech.ac.jp ‡ Faculty of Economics, Kyoto Sangyo University Motoyama, Kamikamo, Kita, Kyoto 603-8555, Japan e-mail: oda@cc.kyoto-su.ac.jp

∗ Graduate

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self-organization theory that insists that some order can emerge through interactions among homogeneous agents. Market microstructure theory explains price formulation as a consequence of price setters’ purposeful behavior. We have designed a single-person game to examine whether monopolistic firms can act as intermediaries if they are not as fully informed as they are supposed to be in the basic model of market microstructure theory. We have recruited undergraduates to play the game, in which they are asked to determine the bid and ask prices repeatedly against given but unknown supply and demand curves as monopolistic intermediaries. Most of them showed good performance, which suggests that monopolistic firms could act as intermediaries even if they are not fully informed. The experimental results also describe how people cope with ambiguity. Most subjects made a two-stage search: they first searched for a pair including the bid price and the ask price that would equalise the quantity they could buy with the quantity they could sell; then, while keeping the trading quantity, they adjusted the prices to obtain a locally maximum profit. By using general knowledge and the power of inference, they set a sub-goal to solve a problem whose details were unknown. This paper is organised in the following way. In Section 2, we shall present the basic market microstructure model as well as its experimental design. In Section 3, we shall examine how subjects behaved in the experiments in details, and in Section 4, we shall refer to the ambiguity model to explain our subjects’ behaviour. In Section 5, we shall discuss our experiment in a broader context to conclude our analysis.

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The Model
p,w

S=w 3/4
Profit

Walrasian Equilibrium D=1-p
q

1/4 0 1/4 1/2

Figure 1: The basic intermediation model Let us recall the simplest demand and supply analysis: The market equilibrium is determined at the intersection of the supply and demand curves. Yet how can it be realised? Walras assumes an auctioneer who is expected to repeat auctions until he discovers the equilibrium price (Blaug 1996, p. 555 and p. 673). One difficulty with this explanation is that the auctioneer is assumed to be a sincere altruist who earns nothing for himself in order to maximise the sum of the sellers’ and buyers’ surplus. Since it presumes an outsider’s free effort to discover the equilibrium price set, Walras’ example cannot be an endogenous explanation of the market equilibrium. Spulber (1999, pp. 30–32) assumes monopolistic intermediaries who organise markets to earn profits. See Figure 1, where the market supply and demand curves are shown for a commodity. Suppose that there is a monopolistic intermediary in the market. If she knows the supply and demand functions, the intermediary can readily calculate the bid price w (the price at which 2

she buys the commodity from its sellers) and the ask price p (the price at which she sells the commodity to its buyers) that maximise her profit margin; if she posts 0.25 to the sellers as w and 0.75 to the buyers as p, she buys and sells 0.25 units to gain the maximum profit 0.125 (= 0.25 × (0.75 − 0.25)). The Walrasian equilibrium is realised if she chooses 0.5 as w and p, but there is no reason for her to do so, as then she earns nothing. That is an endogenous explanation of the emergence of the market order.1 We have designed a single-person game to determine whether subjects can act as the monopolistic intermediary if they lack the prior knowledge of the curves. This is because it appears too strong to be satisfied in the real economy to assume that monopolistic intermediaries know the supply and demand curves for their inputs and outputs. In the game the player is asked to determine, as the monopolistic intermediary of a commodity, the bid price w and the ask price p to earn the profit margin: π = py − wx where x represents the number of units of the commodity he or she buys from its producers, while y stands for the number of units of the commodity he or she sells to its consumers. We have designed two market treatments to determine x and y: the stock market treatment and the fish market treatment. Under the former treatment, subjects are allowed to refuse to buy or sell some units at the prices they have chosen, while under the latter treatment, they must accept all sell orders at the bid price they have determined. That is to say, the intermediary’s trading volume and profit are determined by x = y = min (S (w), D (p)) π = (p − w) min (S (w), D (p)) under the stock market treatment, while they are x = S (w) ≥ y = min (S (w), D (p)) π = py − wx = (p − w) min (S (w), D (p)) + w min (0, (D (p) − S (w)) (2) (1)

under the fish market treatment. Here, S (w) and D (p) represent the market supply function and the market demand function, respectively. The only difference between the two treatments is that the dead inventory, or the number of units which are bought but not sold, min (0, (S (w) − D (p)), is always zero under the stock market treatment, whereas it can be positive under the fish market treatment. We recruited 51 undergraduates from Kyoto Sangyo University through an advertisement on the WWW that promised a monetary reward contingent on performance in the game, and performed the experiment at the Kyoto Sangyo University Experimental Economics Laboratory on the 25th May and the 5th June, 2002. Each subject played the monopolistic intermediary for three sessions each for twenty rounds under the same market treatment (25 subjects under the stock market treatment and 26 subjects under the fish market treatment). The supply and demand functions were replaced as the session changed; Figure 2 shows the three sets of functions, that were used commonly for both market treatments. In each session, subjects were asked to choose two integers between 1 and 100 as w and p. Since the system is programmed to reject such an input as w > p and to request another input, there were 4,900 pairs of prices from which one could choose. Details of the experiment mentioned above were written in the instruction manual and read by the instructor prior to the subjects playing a ten-round training session. Apart from the exact forms of the supply and demand curves, we should also mention that S (w) is non-decreasing while D (p) is non-increasing. In addition, to make each subject’s decision-making easier, the history of his or her choices and results (w, p, x, y and π) were shown on their monitors for each session. In fact, although it was not mentioned to the subjects explicitly, their decision making was made more difficult by our setting of the supply and demand functions.
1 A few remarks may be called for here. First, we ignore such unrealistic cases where the intermediary’s profit cannot be maximized by a finite value of the bid price or the ask price; this is the case in Figure 1 if the demand curve D = 1 − p is replaced with D = x−1 . Secondly, the explanation is not perfectly endogenous, meaning that a trader is privileged to be the monopolistic intermediary. The emergence of an intermediary is another topic, which we do not discuss in this paper.

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Figures 4 to 7 show the values of S (w) (in the lower margin), D (p) (in the right margin) and π (w, p) (in the interior) for 30 ≤ w ≤ 53 (in the upper margin) and 70 ≤ p ≤ 100 (in the upper margin). Since the demand and supply curves are stepped, the domain of (w, p) is divided ¯ ¯ into those rectangles where S (w) = S and D (p) = D. For example, the yellow rectangle stands for those price pairs that realise S (w) = 4 and D (p) = 2 in Figure 4, while a green rectangle represents those price pairs that realise S (w) = D (p) = z in Figures 4 to 7. In each rectangle, ¯ π (w, p) increases as w decreases and/or p increases so that it reaches the largest at the upper-left corner, where w = min w and p = max p (in the above-mentioned yellow rectangle, profit is maximised at (w, p) = (42, 94) = ( min w, max p). This makes the surface of π (w, p) rough. The graph has a unique peak for all (p, w) if the demand and supply functions are such linear function as in Figure 1, but it has a number of local peaks for our problems. To illustrate it, we can check how π (w, p) varies along w + p = 124 for Problem One. As Figure 3 shows, the graph has local peaks at (w, p) = (24, 100), (30, 94), (36, 88), . . . for Problem One. In Figure 4, we can see that the line, a part of which is shown in red, runs through the green rectangles (in other words, S (w) = D (p) for w + p = 124) and the local peaks are at the upper-left corners of those green rectangles. As is common to all three problems, profit is maximised locally in every direction at the upper-left corners of green rectangles and is maximised globally at one of them (at (42, 82) in the present example). The globally maximum profit is circled in red in Figures 4 to 7). The monetary reward (yen) was calculated in the following way: 0.3 × (total profit) for the experiments under the stock market treatment, and 600 + 0.25 × (total profit) under the fish market treatment. In the stock market treatment the maximum, the average and the minimum reward were 2,710, 2,422 and 1,710 yen respectively, while in the fish market treatment they were 2,800, 2,260 and 1,330 yen respectively. The subjects’ actual working hours totalled about two hours, while the average hourly rate for part-time jobs available for undergraduates is about 800 yen.
S (w)=4 ¯ D (p)=D ¯ S (w)=S ¯ D (p)=D

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3.1

The Analysis
Overview

In our experiments, subjects’ profit was larger under the stock market treatment than it was under the fish market treatment (the difference is significant at the 5 per cent level for all cases; see Table 1). This is quite understandable, because for any pair of w and p, profit is larger under the stock market treatment (if S (w) < D (p)) or the same in either treatment (if S (w) ≥ D (p)). The profit difference is mostly due to the burden of dead inventory; under the fish market treatment subjects suffer dead inventory, whose average amount was three units, twice a session. As Tables 2 and 3 show, neither the trading volume min (S (w), D (p)) nor the profit margin p − w differs significantly between the treatments except for one case. Thus we shall discuss the behaviour of subjects in the remainder of this paper without mentioning the market treatment unless it is deemed necessary. Although they differed widely from subject to subject for the first round of each session, the chosen price pairs were concentrated into a smaller zone for the last (twentieth) round. This can be checked statistically in Tables 4 and 5,2 where the coefficient of the determinant is higher for the last round except for one. We can examine it more closely in Figures 10 and 11. The red points and blue points stand for the first choices and the last choices respectively, while green rectangles are those in Figures 4 to 7. The last choices are concentrated near or in the green rectangles. In addition, more than one third of the last choices are on the upper-left corners of the green rectangles. In other words, at the last round, one out of three subjects chose such a price pair that realised a locally maximum
2 The reason that the coefficient of determinant is lower in the last turn than in the first turn is that a subject decides a price set far from other subjects in the last turn.

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Price 100 90 80 70 60

100

94

88 82 76 70 64
60 72 66 78

84

90

Supply

50 48 40 30 30 20 10 24 36 42

54

58 52 46 40 34 Demand

Quantity 1 2 3 4 5 6 7 8 9 10 11 12

(a) Problem 1

Price 100 90 80 70 60 50 40 30

100 96 91 85 78 70 62
60 48 42 36 30 24 54 66 72 84 78 90

Price 100

100 93 86
84 90

Supply

90 80 70 60

80 74 68 62
60 48 42 54 66 72

Supply

78

51 40 28 15 Demand 1
Quantity

50 40 30 30 20 10 24 36

57 52 47 43

39

20 10

Demand
Quantity 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

(b) Problem 2

(c) Problem 3

Figure 2: Demand and supply functions

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profit (we refer to the global optimal price pair, which are shown in red in Figures 10 and 11, as a local optimal price set). Needless to say, subjects did not discover locally optimal price pairs suddenly at the last round, but controlled the prices thoughtfully toward locally optimal price pairs. We can check this price control by examining how the subjects behaviour and performance were different between the first and and second ten rounds. Behaviour: Subjects changed w and p more violently in the first ten rounds. Tables 8 to 11 show the average variance of the trading volume for the first and the second ten rounds. The Wilcoxon test confirms that the average variance is significantly higher in the first half for most cases. Performance: Subjects realised S (w) = D (p) more frequently in the second ten rounds. Figures 12 and 13 shows with which percentage S (w) < D (p), S (w) = D (p) and S (w) > D (p) were realized in the first and second ten rounds of each session. The percentage for S (w) = D (p) is significantly larger in the second half of every session. The first observation suggests that subjects gradually narrowed the area from which they chose a price pair, while the second observation attests that subjects chose more rational price pairs in the last ten rounds. Here, “rational” means that there remains room for increasing profit if S (w) = D (p); if S (w0 ) < D (p0 ), an increase in p from p0 to such a value p1 that satisfies D (p1 ) = S (w0 ) always increase profit from (p0 − w0 )S (w0 ) to (p1 − w0 )S (w0 ); similarly if S (w0 ) > D (p0 ), an adequate decrease in w increases profit.

3.2

search strategy

The equality between S (w) and D (p) was realised not by fluke, but as a sub-goal they had set at the beginning of the experiment. It was confirmed after the experiment by a questionnaire. Among the questions, there was, “How did you choose the ask and bid prices?” To this about sixty percent of the subjects essentially gave the same answer: “First I aimed to realize S (w) = D (p). Then I varied w and p to increase profit without altering the value of S (w) or that of D (p).” The subjects’ self-description of the two-stage searching strategy is consistent with their behaviour in the experiment. Figure 14 shows the trajectory of (w, p) for four sessions. In each session it mostly lies inside the central rectangle, where S (w) = D (p) holds and at the upper-left corner, where profit is maximised locally (eventually globally in (a) and (c)). The trajectory points upward to the left in the rectangle, and after protruding from its upper and/or left edge once or twice, returns into the rectangle to terminate at its upper-left corner. This property, which is not limited to the above-mentioned examples but applies to more than half the sessions in the experiment, corroborates the subjects’ above-mentioned answer. The rationale behind the two-stage searching is that the searching period allowed to our subjects was short in absolute terms and long in relative terms; a ten-round searching could check only 0.2 percent of the 4,900 alternatives while it accounts for fifty percent of a twenty-round session. Under the circumstances, they gave priority to the rapid discovery of a price pair that equalise S (w) to D (p) to secure a minimum profit. Once they found a price pair that satisfied S (w) = D (p) = z , ¯ they had only to decrease w to minS (w)=¯ w and increase p to maxD (p)=¯ p) to obtain a locally z z maximum profit. The two-phased searching is a secure and systematic strategy. Let us conclude this section with examining how subjects ceased to search. We have classified all sessions into the following eight cases: S1 Keep on searching. S2 Choose the globally or locally optimal price pair; leave it to keep on searching. S3 Choose a non-locally-optimal price pair; keep it without additional searching. S4 Choose a non-locally-optimal price pair; make an additional search to return and keep the price pair. S5 Choose a non-locally-optimal price pair; make more than one additional search to return and keep the price pair. 6

S6 Choose the globally or locally optimal point; keep it without additional searching. S7 Choose the globally or locally optimal point; make an additional search to return and keep the price pair. S8 Choose the globally or locally optimal point; make more than one additional search to return and keep the price pair. Here, a session q = {q1 , q2 , . . ., q20 }, where qi stands for the price pair chosen in the ith round of the session, is classified according to the following rules: 1. A session q belongs to A if q19 = q20 ; it belongs to B otherwise. 2. A session q ∈ A belongs to A1 if q20 is the globally optimal price set; it belongs to A2 otherwise. 3. A session q ∈ B belongs to S2 if a qi is the globally or locally optimal price set; it belongs to S1 otherwise. 4. A session q ∈ A1 belongs to S6 if qi = q20 = qj is not satisfied for any pair of i and j (i < j); it belongs to S7 if qi = q20 = qj is satisfied for certain i and j (i < j) and i is uniquely determined; it belongs to S8 otherwise. 5. A session q ∈ A2 belongs to S3 if qi = q20 = qj is not satisfied for any pair of i and j (i < j); it belongs to S4 if qi = q20 = qj is satisfied for certain i and j (i < j) and i is uniquely determined; it belongs to S5 otherwise. The results of our experiments are classified in Table 12, where the numbers in the parentheses represent the cases where the last choice was the globally optimal price set. Most of those subjects who chose the same price set for the last two rounds had checked another price at least once before fixing their choice. This is what is expected if subjects employed the two-stage searching.

4

Interpretations

Our subjects were asked to make decisions repeatedly under ambiguous situations, or without even probabilistic knowledge about the outcome of each choice. Let us compare our experiment with the Ellsberg Paradox, where subjects are asked a single choice under ambiguity, and with Hay’s search problem, where subjects are asked to make decisions repeatedly under uncertain but nonambiguous circumstances. There, single-person games examining human attitudes to ambiguity or uncertainty can be examined purely without being disturbed by game theoretic interactions among players. The Ellsberg Paradox is summarised in the following way: most people prefer a lottery whose winning probability is fifty percent to a lottery whose winning probability is unknown, but since they know nothing but that the winning probability of the latter lottery lies between 0 and 1, people cannot help but estimate it at 0.5, which is the same as the winning probability of the former lottery. Enhorn and Hogarth (1986) have developed the ambiguity model to explain the paradox. Their idea is expressed by σ = q + k. Here, σ represents the probability that is used for decision making, while q and k stand for the anchor and the adjustment probability, respectively. The anchor represents the initial probability, which is calculated with available information, while the adjustment probability is determined by the subject’s personal experience and attitude to ambiguity, or state of ignorance. The paradox disappears if most people are ambiguity-averse, thus q = 0.5 and k = 0 for the first lottery while q = 0.5 and k < 0 for the second one. Although in our game what is ambiguous is not the winning probabilities of lotteries but the amount of money to be win, we can describe why and how our subjects followed the two-stage strategy in terms of the ambiguity model.

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step 0: The subject allots a pair of two values (qi , ki ) to each of 4,900 price pairs ri = (w (ri ), p (ri )) (1 ≤ i ≤ 4, 900 and 1 ≤ w (ri ) < p (ri ) ≤ 100). For each price pair the value of qi is a rough estimation of profit calculated from roughly estimated demand and supply curves, while the value of ki is considerably more negative because of ambiguity. step 1: Choose the price pair ri∗ = (w (ri∗ ), p (ri∗ )) whose qi∗ + ki∗ is the largest. step 2: Ambiguity vanishes at the chosen point and decreases from place to place according to the distance from the point: qi∗ = π (w (ri∗ ), p (ri∗ )), ki∗ = 0 and all kj (j = i∗) decreases; the nearer rj is to ri∗ , the more kj decreases in absolute value. step 3: All qj (j = i∗) are revised according to qi∗ and the general knowledge of the supply and demand curves: step 3.1: If S (wi∗ ) < D (pi∗ ), it is taken into account that (unless pi∗ is so close to 100 that there seems little room for increasing the ask price) π (wi∗ , pi∗ ) < π (wi∗ , pk ) = S (wi∗ ) (pk − wi∗ ) for a certain pk (pi∗ < pk ) and that (unless wi∗ is excessively low) possibly π (wi∗ , pi∗ ) < π (wk , pi∗ ) = D (wi∗ ) (pi∗ − wk ) for a certain wk (wi∗ < wk ), etc. step 3.2: If D (pi∗ ) < S (wi∗ ), it is taken into account that (unless wi∗ is so close to 1 that there seems little room for decreasing the bid price) π (wi∗ , pi∗ ) < π (wi , pk∗ ) = D (pi∗ ) (pk∗ − wi ) for a certain wk (wk < wi∗ ) and that (unless pi∗ is excessively high) possibly π (wi∗ , pi∗ ) < π (wk∗ , pi ) = S (wi∗ ) (pi∗ − wk ) for a certain pk (pk < pi∗ ), etc. step 3.3: If S (wi∗ ) = D (pi∗ ), it is taken into account that there usually exists a certain price pair rn = (wn , pn ) in a upper-left neighbourhood of ri∗ : π (wi∗ , pi∗ ) < π (wl , pl ) < π (wm , pm ) < π (wn , pn ) for all wi∗ > wl > wm > wn and pi∗ < pl < pm < pn . step 4: Return to 1 with the revised table of qi + ki . Subjects first activate Steps 3.1 and 3.2 unless their first choice satisfies S (wi ) = D (pi ) by fluke. They drive the chosen ri toward an area where S (wi ) = D (pi ). Although some subjects may not find it until they repeat the process of choosing a price pair a few times, they adopt Steps 3.1 and 3.2 not by pure trial and error or reinforcement learning. Subjects can drive ri , without checking outcomes in their neighbourhood because they know that the supply curve is upward sloping while the demand curve is downward sloping. On the other hand, Step 3.3 is activated only after ri arrives at a point in an area where S (wi ) = D (pi ). It puts ri to the upward left corner of the area, where profit is maximised locally. Though such local movement of ri to a local optimal point may be realised by reinforcement learning or its variation, in the experiments many subjects moved ri in the upward-left direction without checking a point in the lower–right area. This suggests that the subjects’ knowledge and reasoning also play important roles in Step 3.3. It should be also mentioned that once Step 3.3 is activated, only proximal points are chosen from then. This decreases ambiguity in the area where S (wi ) = D (pi ) so that if a point is chosen in the (upper and/or left) outside of the area, ri returns to the upward left corner of the area; the decrease in ambiguity in the neighbourhood is so large that Steps 3.1 and 3.2 cannot drive ri to another area where S (wi ) = D (pi ). In short, the dynamics of choice are explained by the sum of ambiguity k, which significantly decreases in the neighbourhood of the chosen and realised price pairs, and q, which is revised by logical inference and the general knowledge of the supply and demand curves. Note also that 3.1 and 3.2 drives the next choice to a distant price pair while 3.3 leads to the newest upper-left locally optimal price pair. Now let us see the search experiments by Hey (1982, 1987). In Hey’s experiments, subjects were not informed of the stochastic distribution of the value among alternatives3, but were allowed
3 In Hey (1987) half of the subjects knew the price distribution. Moreover, subjects in Hey (1982) were not paid while subjects in Hey (1987) were paid.

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to check a range of alternatives to see the value when desired if they pay a certain cost for every additional search. Under those circumstances, search theory asserts that if he or she finds such an alternative whose value exceeds a reservation value, one should stop searching and take it. Hey (1982) also reported that only about twenty percent of the subjects followed search theory. About sixty percent of the subjects made one or more bounces in their search: they stopped searching to choose a previous one, not the last one. A possible interpretation, which Hey himself does not mention, is given by the ambiguity model. Subjects might have started searching with a minimum requirement q with a desirable addition k, possibly because they lacked general knowledge of search theory or computational power. As they checked more alternatives, they may have adjusted q and k. When they discovered an alternative whose value exceeded the current value of q, the value of k may have been still positive; in fact it might have been revised upwards by the discovery of the minimum acceptable alternative. This could have caused them to make additional searches. If they were not able to find a more profitable alternative by the additional searches, subjects may have stopped searching with the previously found alternative. A difference between Hey’s experiments and ours is that the search based on the ambiguity model is more rational in the latter, firstly because there exists a more rational search in the former, and secondly because q and k can be adjusted more rationally as is mentioned above. By following the two-stage search, subjects can find a price pair that brings S (w) = D (p) to set k and decrease k monotonically to obtain a locally optimal price pair. The ambiguity model only defines a general frame for searching under ambiguity. How efficiently it can be used may depend on subjects’ general ability and knowledge. In this relation, though we should not minimise the human ability to invent an adequate multi-stage strategy on the spot, we should mention here that all subjects did not take full advantage of it. Our experiment provides a clear example. Figure 14 (d) shows that the trajectory first runs up vertically through the rectangle then horizontally to the upper left corner. This implies that the subject first increased the ask price (while keeping the same bid price) to discover the maximum ask price that keeps S (p) = 4, then (while maintaining the ask price) altered the bid price to find out the minimum bid price that maintains S (w) = 4. This is further evidence that subjects may simplify (divide) the search problem to set a sub-goal. Yet this was not efficient. The subject, who was informed prior to commencing the experiment that the supply and demand functions are, not x = S (w, p) and y = D (w, p), but x = S (w) and y = D (p), could have changed w and p simultaneously to check both functions independently. Had he done so, he could have reached the upper left corner of the central rectangle more quickly.

(42,82)

160 140 120 100 profit 80 60 40 20 0
(48,76)

(36,88) (30,94)

Profit

p+w=124

Figure 3: Profit for S (w) = D (p); Problem One under the stock market treatment

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p/w 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 S(w)

128
126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80

30 70 69 68 67 66 65

31 69 68 67 66 65 64 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78

32 33 68 67 67 66 66 65 65 64 64 63 63 62 124 122 122 120 120 118 118 116 116 114 114 112 112 110 110 108 108 106 106 104 104 102 102 100 100 98 98 96 96 94 94 92 92 90 90 88 88 86 86 84 84 82 82 80 80 78 78 76 76 74 2

34 66 65 64 63 62 61 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72

35 65 64 63 62 61 60 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70

156
153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102

36 64 63 62 61 60 59 116 114 112 110 108 106

37 63 62 61 60 59 58 114 112 110 108 106 104 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99

38 39 62 61 61 60 60 59 59 58 58 57 57 56 112 110 110 108 108 106 106 104 104 102 102 100 100 147 147 144 144 141 141 138 138 135 135 132 132 129 129 126 126 123 123 120 120 117 117 114 114 111 111 108 108 105 105 102 102 99 99 96 96 93 3

40 60 59 58 57 56 55 108 106 104 102 100 98 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90

41 59 58 57 56 55 54 106 104 102 100 98 96 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90 87

160
156 152 148 144 140 136 132 128 124 120 116 112

42 58 57 56 55 54 53 104 102 100 98 96 94 138 135 132 129 126 123

43 57 56 55 54 53 52 102 100 98 96 94 92 135 132 129 126 123 120 156 152 148 144 140 136 132 128 124 120 116 112 108

44 45 56 55 55 54 54 53 53 52 52 51 51 50 100 98 98 96 96 94 94 92 92 90 90 88 132 129 129 126 126 123 123 120 120 117 117 114 152 148 148 144 144 140 140 136 136 132 132 128 128 124 124 120 120 116 116 112 112 108 108 104 104 100 4

46 54 53 52 51 50 49 96 94 92 90 88 86 126 123 120 117 114 111 144 140 136 132 128 124 120 116 112 108 104 100 96

47 53 52 51 50 49 48 94 92 90 88 86 84 123 120 117 114 111 108 140 136 132 128 124 120 116 112 108 104 100 96 92

140
135 130 125 120 115 110

48 52 51 50 49 48 47 92 90 88 86 84 82 120 117 114 111 108 105 136 132 128 124 120 116

49 51 50 49 48 47 46 90 88 86 84 82 80 117 114 111 108 105 102 132 128 124 120 116 112 135 130 125 120 115 110 105

50 51 50 49 49 48 48 47 47 46 46 45 45 44 88 86 86 84 84 82 82 80 80 78 78 76 114 111 111 108 108 105 105 102 102 99 99 96 128 124 124 120 120 116 116 112 112 108 108 104 130 125 125 120 120 115 115 110 110 105 105 100 100 95 5

52 48 47 46 45 44 43 84 82 80 78 76 74 108 105 102 99 96 93 120 116 112 108 104 100 120 115 110 105 100 95 90

53 47 46 45 44 43 42 82 80 78 76 74 72 105 102 99 96 93 90 116 112 108 104 100 96 115 110 105 100 95 90 85

D(p)

1

2

3

4

5

6

Figure 4: S (w), D (p) and π (w, p); Problem One under the stock market treatment

p/w 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 S(w)

30 70 69 68 67 132 130 128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80

31 69 68 67 66 130 128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78

32 33 68 67 67 66 66 65 65 64 128 126 126 124 124 122 122 120 120 118 118 116 116 114 114 112 112 110 110 108 108 106 106 104 104 102 102 100 100 98 98 96 96 94 94 92 92 90 90 88 88 86 86 84 84 82 82 80 80 78 78 76 76 74 2

34 66 65 64 63 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72

35 65 64 63 62 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70

36 64 63 62 61 120 118 116 114 112 165 162 159 156 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102

37 63 62 61 60 118 116 114 112 110 162 159 156 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99

38 39 62 61 61 60 60 59 59 58 116 114 114 112 112 110 110 108 108 106 159 156 156 153 153 150 150 147 147 144 144 141 141 138 138 135 135 132 132 129 129 126 126 123 123 120 120 117 117 114 114 111 111 108 108 105 105 102 102 99 99 96 96 93 3

40 60 59 58 57 112 110 108 106 104 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90

41 59 58 57 56 110 108 106 104 102 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90 87

42 58 57 56 55 108 106 104 102 100 147 144 141 138 135 132

172
168 164 160 156 152 148 144 140 136 132 128 124 120 116 112

43 57 56 55 54 106 104 102 100 98 144 141 138 135 132 129 168 164 160 156 152 148 144 140 136 132 128 124 120 116 112 108

44 45 56 55 55 54 54 53 53 52 104 102 102 100 100 98 98 96 96 94 141 138 138 135 135 132 132 129 129 126 126 123 164 160 160 156 156 152 152 148 148 144 144 140 140 136 136 132 132 128 128 124 124 120 120 116 116 112 112 108 108 104 104 100 4

46 54 53 52 51 100 98 96 94 92 135 132 129 126 123 120 156 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96

47 53 52 51 50 98 96 94 92 90 132 129 126 123 120 117 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96 92

48 52 51 50 49 96 94 92 90 88 129 126 123 120 117 114 148 144 140 136 132 128 124 150 145 140 135 130 125 120 115 110

49 51 50 49 48 94 92 90 88 86 126 123 120 117 114 111 144 140 136 132 128 124 120 145 140 135 130 125 120 115 110 105

50 51 50 49 49 48 48 47 47 46 92 90 90 88 88 86 86 84 84 82 123 120 120 117 117 114 114 111 111 108 108 105 140 136 136 132 132 128 128 124 124 120 120 116 116 112 140 135 135 130 130 125 125 120 120 115 115 110 110 105 105 100 100 95 5

52 48 47 46 45 88 86 84 82 80 117 114 111 108 105 102 132 128 124 120 116 112 108 130 125 120 115 110 105 100 95 90

53 D(p) 47 46 1 45 44 86 84 2 82 80 78 114 111 108 3 105 102 99 128 124 120 4 116 112 108 104 125 120 115 110 5 105 100 95 90 85 6

Figure 5: S (w), D (p) and π (w, p); Problem Two under the stock market treatment

10

p/w 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 S(w)

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 D(p) 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 1 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 126 124122120118116 114 112110108106104 102 100 98 96 94 92 90 88 86 84 82 80 124 122120118116114 112 110108106104102 100 98 96 94 92 90 88 86 84 82 80 78 122 120118116114112 110 108106104102100 98 96 94 92 90 88 86 84 82 80 78 76 2 120 118116114112110 108 106104102100 98 96 94 92 90 88 86 84 82 80 78 76 74 118 116114112110108 106 104102100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 116 114112110108106 104 102100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 114 112110108106104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 112 110108106104102 150 147144141138135 132 129126123120117 114 111108105102 99 110 108106104102100 147 144141138135132 129 126123120117114 111 108105102 99 96 108 106104102100 98 144 141138135132129 126 123120117114111 108 105102 99 96 93 3 106 104102100 98 96 141 138135132129126 123 120117114111108 105 102 99 96 93 90 104 102100 98 96 94 138 135132129126123 120 117114111108105 102 99 96 93 90 87 102 100 98 96 94 92 135 132129126123120 117 114111108105102 99 96 93 90 87 84 100 98 96 94 92 90 132 129126123120117 152 148144140136132 128 124120116112108 98 96 94 92 90 88 129 126123120117114 148 144140136132128 124 120116112108104 96 94 92 90 88 86 126 123120117114111 144 140136132128124 120 116112108104100 4 94 92 90 88 86 84 123 120117114111108 140 136132128124120 116 112108104100 96 92 90 88 86 84 82 120 117114111108105 136 132128124120116 112 108104100 96 92 90 88 86 84 82 80 117 114111108105102 132 128124120116112 108 104100 96 92 88 88 86 84 82 80 78 114 111108105102 99 128 124120116112108 130 125120115110105 86 84 82 80 78 76 111 108105102 99 96 124 120116112108104 125 120115110105100 5 84 82 80 78 76 74 108 105102 99 96 93 120 116112108104100 120 115110105100 95 82 80 78 76 74 72 105 102 99 96 93 90 116 112108104100 96 115 110105100 95 90 80 78 76 74 72 70 102 99 96 93 90 87 112 108104100 96 92 110 105100 95 90 85 2 3 4 5

30 70 69 68 67 66 65 64

Figure 6: S (w), D (p) and π (w, p); Problem Three under the stock market treatment

p/w 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 S(w)

30 40 39 38 37 36 35 128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80

31 38 37 36 35 34 33 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78

32 36 35 34 33 32 31 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 2

33 34 33 32 31 30 29 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74

34 32 31 30 29 28 27 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72

35 30 29 28 27 26 25 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70

36 -8 -9 -10 -11 -12 -13 80 78 76 74 72 70 156 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102

37 -11 -12 -13 -14 -15 -16 77 75 73 71 69 67 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99

38 -14 -15 -16 -17 -18 -19 74 72 70 68 66 64 100 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 3

39 -17 -18 -19 -20 -21 -22 71 69 67 65 63 61 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93

40 -20 -21 -22 -23 -24 -25 68 66 64 62 60 58 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90

41 -23 -24 -25 -26 -27 -28 65 63 61 59 57 55 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90 87

160
156 152 148 144 140 136 132 128 124 120 116 112

42 -68 -69 -70 -71 -72 -73 20 18 16 14 12 10 96 93 90 87 84 81

43 -72 -73 -74 -75 -76 -77 16 14 12 10 8 6 92 89 86 83 80 77 156 152 148 144 140 136 132 128 124 120 116 112 108

44 -76 -77 -78 -79 -80 -81 12 10 8 6 4 2 88 85 82 79 76 73 152 148 144 140 136 132 128 124 120 116 112 108 104 4

45 -80 -81 -82 -83 -84 -85 8 6 4 2 0 -2 84 81 78 75 72 69 148 144 140 136 132 128 124 120 116 112 108 104 100

46 -84 -85 -86 -87 -88 -89 4 2 0 -2 -4 -6 80 77 74 71 68 65 144 140 136 132 128 124 120 116 112 108 104 100 96

47 -88 -89 -90 -91 -92 -93 0 -2 -4 -6 -8 -10 76 73 70 67 64 61 140 136 132 128 124 120 116 112 108 104 100 96 92

48 -140 -141 -142 -143 -144 -145 -52 -54 -56 -58 -60 -62 24 21 18 15 12 9 88 84 80 76 72 68 140 135 130 125 120 115 110

49 -145 -146 -147 -148 -149 -150 -57 -59 -61 -63 -65 -67 19 16 13 10 7 4 83 79 75 71 67 63 135 130 125 120 115 110 105

50 51 -150 -155 -151 -156 -152 -157 -153 -158 -154 -159 -155 -160 -62 -67 -64 -69 -66 -71 -68 -73 -70 -75 -72 -77 14 9 11 6 8 3 5 0 2 -3 -1 -6 78 73 74 69 70 65 66 61 62 57 58 53 130 125 125 120 120 115 115 110 110 105 105 100 100 95 5

52 -160 -161 -162 -163 -164 -165 -72 -74 -76 -78 -80 -82 4 1 -2 -5 -8 -11 68 64 60 56 52 48 120 115 110 105 100 95 90

53 D(p) -165 -166 -167 1 -168 -169 -170 -77 -79 -81 2 -83 -85 -87 -1 -4 -7 3 -10 -13 -16 63 59 55 4 51 47 43 115 110 105 5 100 95 90 85 6

Figure 7: S (w), D (p) and π (w, p); Problem One under the fish market treatment

11

p/w 30 31 100 40 38 99 39 37 98 38 36 97 37 35 96 132 130 95 130 128 94 128 126 93 126 124 92 124 122 91 122 120 90 120 118 89 118 116 88 116 114 87 114 112 86 112 110 85 110 108 84 108 106 83 106 104 82 104 102 81 102 100 80 100 98 79 98 96 78 96 94 77 94 92 76 92 90 75 90 88 74 88 86 73 86 84 72 84 82 71 82 80 70 80 78 S(w)

32 36 35 34 33 128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 2

33 34 33 32 31 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74

34 32 31 30 29 124 122 120 118 116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72

35 36 37 30 -8 -11 29 -9 -12 28 -10 -13 27 -11 -14 122 84 81 120 82 79 118 80 77 116 78 75 114 76 73 112 165 162 110 162 159 108 159 156 106 156 153 104 153 150 102 150 147 100 147 144 98 144 141 96 141 138 94 138 135 92 135 132 90 132 129 88 129 126 86 126 123 84 123 120 82 120 117 80 117 114 78 114 111 76 111 108 74 108 105 72 105 102 70 102 99

38 -14 -15 -16 -17 78 76 74 72 70 159 156 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 3

39 -17 -18 -19 -20 75 73 71 69 67 156 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93

40 -20 -21 -22 -23 72 70 68 66 64 153 150 147 144 141 138 135 132 129 126 123 120 117 114 111 108 105 102 99 96 93 90

41 42 43 -23 -68 -72 -24 -69 -73 -25 -70 -74 -26 -71 -75 69 24 20 67 22 18 65 20 16 63 18 14 61 16 12 150 105 101 147 102 98 144 99 95 141 96 92 138 93 89 135 90 86 132 172 168 129 168 164 126 164 160 123 160 156 120 156 152 117 152 148 114 148 144 111 144 140 108 140 136 105 136 132 102 132 128 99 128 124 96 124 120 93 120 116 90 116 112 87 112 108

44 -76 -77 -78 -79 16 14 12 10 8 97 94 91 88 85 82 164 160 156 152 148 144 140 136 132 128 124 120 116 112 108 104 4

45 -80 -81 -82 -83 12 10 8 6 4 93 90 87 84 81 78 160 156 152 148 144 140 136 132 128 124 120 116 112 108 104 100

46 -84 -85 -86 -87 8 6 4 2 0 89 86 83 80 77 74 156 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96

47 -88 -89 -90 -91 4 2 0 -2 -4 85 82 79 76 73 70 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96 92

48 -140 -141 -142 -143 -48 -50 -52 -54 -56 33 30 27 24 21 18 100 96 92 88 84 80 76

150
145 140 135 130 125 120 115 110

49 -145 -146 -147 -148 -53 -55 -57 -59 -61 28 25 22 19 16 13 95 91 87 83 79 75 71 145 140 135 130 125 120 115 110 105

50 51 -150 -155 -151 -156 -152 -157 -153 -158 -58 -63 -60 -65 -62 -67 -64 -69 -66 -71 23 18 20 15 17 12 14 9 11 6 8 3 90 85 86 81 82 77 78 73 74 69 70 65 66 61 140 135 135 130 130 125 125 120 120 115 115 110 110 105 105 100 100 95 5

52 -160 -161 -162 -163 -68 -70 -72 -74 -76 13 10 7 4 1 -2 80 76 72 68 64 60 56 130 125 120 115 110 105 100 95 90

53 D(p) -165 -166 1 -167 -168 -73 -75 2 -77 -79 -81 8 5 2 3 -1 -4 -7 75 71 67 4 63 59 55 51 125 120 115 110 5 105 100 95 90 85 6

Figure 8: S (w), D (p) and π (w, p); Problem Two under the fish market treatment
p/w 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 100 40 38 36 34 32 30 -8 -11 -14 -17 -20 -23 -68 -72 -76 -80 -84 -88 -140 -145 -150 -155 99 39 37 35 33 31 29 -9 -12 -15 -18 -21 -24 -69 -73 -77 -81 -85 -89 -141 -146 -151 -156 98 38 36 34 32 30 28 -10 -13 -16 -19 -22 -25 -70 -74 -78 -82 -86 -90 -142 -147 -152 -157 97 37 35 33 31 29 27 -11 -14 -17 -20 -23 -26 -71 -75 -79 -83 -87 -91 -143 -148 -153 -158 96 36 34 32 30 28 26 -12 -15 -18 -21 -24 -27 -72 -76 -80 -84 -88 -92 -144 -149 -154 -159 95 35 33 31 29 27 25 -13 -16 -19 -22 -25 -28 -73 -77 -81 -85 -89 -93 -145 -150 -155 -160 94 34 32 30 28 26 118 -14 -17 -20 -23 -26 -29 -74 -78 -82 -86 -90 -94 -146 -151 -156 -161 93 6 2 -2 -54 -59 -64 -69 126 124 122 120 118 116 78 75 72 69 66 63 18 14 10 92 124 122 120 118 116 114 76 73 70 67 64 61 16 12 8 4 0 -4 -56 -61 -66 -71 91 122 120 118 116 114 112 74 71 68 65 62 59 14 10 6 2 -2 -6 -58 -63 -68 -73 90 120 118 116 114 112 110 72 69 66 63 60 57 12 8 4 0 -4 -8 -60 -65 -70 -75 89 118 116 114 112 110 108 70 67 64 61 58 55 10 6 2 -2 -6 -10 -62 -67 -72 -77 88 116 114 112 110 108 106 68 65 62 59 56 53 8 4 0 -4 -8 -12 -64 -69 -74 -79 87 114 112 110 108 106 104 66 63 60 57 54 51 6 2 -2 -6 -10 -14 -66 -71 -76 -81 86 82 78 74 70 18 13 8 3 86 112 110 108 106 104 102 150 147 144 141 138 135 90 85 110 108 106 104 102 100 147 144 141 138 135 132 87 83 79 75 71 67 15 10 5 0 84 108 106 104 102 100 98 144 141 138 135 132 129 84 80 76 72 68 64 12 7 2 -3 83 106 104 102 100 98 96 141 138 135 132 129 126 81 77 73 69 65 61 9 4 -1 -6 82 104 102 100 98 96 94 138 135 132 129 126 123 78 74 70 66 62 58 6 1 -4 -9 81 102 100 98 96 94 92 135 132 129 126 123 120 75 71 67 63 59 55 3 -2 -7 -12 75 70 65 80 100 98 96 94 92 90 132 129 126 123 120 117 152 148 144 140 136 132 80 79 98 96 94 92 90 88 129 126 123 120 117 114 148 144 140 136 132 128 76 71 66 61 78 96 94 92 90 88 86 126 123 120 117 114 111 144 140 136 132 128 124 72 67 62 57 77 94 92 90 88 86 84 123 120 117 114 111 108 140 136 132 128 124 120 68 63 58 53 76 92 90 88 86 84 82 120 117 114 111 108 105 136 132 128 124 120 116 64 59 54 49 75 90 88 86 84 82 80 117 114 111 108 105 102 132 128 124 120 116 112 60 55 50 45 74 88 86 84 82 80 78 114 111 108 105 102 99 128 124 120 116 112 108 130 125 120 115 73 86 84 82 80 78 76 111 108 105 102 99 96 124 120 116 112 108 104 125 120 115 110 72 84 82 80 78 76 74 108 105 102 99 96 93 120 116 112 108 104 100 120 115 110 105 71 82 80 78 76 74 72 105 102 99 96 93 90 116 112 108 104 100 96 115 110 105 100 70 80 78 76 74 72 70 102 99 96 93 90 87 112 108 104 100 96 92 110 105 100 95 2 3 4 5 S(w) 52 -160 -161 -162 -163 -164 -165 -166 -74 -76 -78 -80 -82 -84 -86 -2 -5 -8 -11 -14 -17 60 56 52 48 44 40 110 105 100 95 90 53 D(p) -165 -166 -167 -168 1 -169 -170 -171 -79 -81 -83 2 -85 -87 -89 -91 -7 -10 -13 3 -16 -19 -22 55 51 47 4 43 39 35 105 100 5 95 90 85

Figure 9: S (w), D (p) and π (w, p); Problem Three under the fish market treatment market average total profit statistical difference z-value stock fish 8058.88 (83.3%) 6623.77 (68.4%) 850 (8.8%) 1.65∗

Table 1: The difference in profit ( *: significant at the 5 % level)

12

5

Concluding Remarks

Since we examined the subjects’ behaviour in details in the previous two sections, let us conclude this paper with a few remarks on our experiments from the viewpoint of market microstructure theory. First, we could mention that our approach is faithful to the tradition of market experiments. Smith (1962) designed the double auction to examine how sellers and buyers behave if an auction is repeated till equilibrium is discovered. We designed the model mentioned in Section 2 to see how subjects act as a monopolistic intermediary if they know neither the market supply curve nor the market demand curve. Although the basic theories are different (partial equilibrium theory and market microstructure theory), both experiments check whether the theories work if its assumption is not fully satisfied. A difference between Smith’s experiments and ours is the part the subjects play. In most market experiments the experimenter designs the trading rules and organises trade, leaving only the roles of sellers and buyers to subjects. To the contrary, we automatise sellers and buyers as agents and let subjects act as intermediaries who organise the market. Certainly, the former approach is useful for analysing and improving trade in well-organised markets. The intermediary or firm should, however, be a player in the game so that the adjustment of prices would be endogenous if we are interested in most actual markets, where commodities are traded without such exogenous help from the Warlasian auctioneer. We hope economic experiments, combined with market microstructure theory, contribute to understanding how markets function in the real economy.

Acknowledgement
This research was supported by the Open Research Centre “Experimental Economics: A new method of teaching economics and the research on its impact on society, ” the Graduate School of Economics, Kyoto Sangyo University and the Japan Society for the Promotion of Science, Grantin-Aid for Scientific Research (B), 13480115. We thank Atsushi Iwasaki, Kouhei Iyori, Nariaki Nishino and Syuichi Imura for helpful comments and illuminating discussion. stock market 37.53 38.33∗ 35.79 fish market 33.94 32.78∗ 33.43

problem-1 problem-2 problem-3

Table 2: The average bid-ask spread (∗ : significant at the 5%) level

problem-1 problem-2 problem-3

stock market 3.75 3.88 3.72

fish market 3.88 4.06 3.75

Table 3: The average trading volume

References
[1] Tversky A. and Kahneman D. Advances in prospect theory : Cumulative representation of uncertainty. Journal of Risk and Uncertainty, pp.297–323, 1992.

13

(36,88) 3 subjects

(48,76) 3 subjects (42,82) 13 subjects

(a) Problem-1, the stock market

(36,91) 1 subject

(42,85) 7 subjects

(48,78) 3 subjects

(b) Problem-2, the stock market

(36,86) 4 subjects (42,80) 9 subjects

(48,74) 5 subjects

(c) Problem-3, the stock market

14 Figure 10: First Choice and Last Choice in the Stock Market: (x, y) is a local or the global optimal price set and the green squares indicate the area that satifies S(w) = D(p).

problem-1
100

(30,94) 1 subject
90

(36,88) 2 subjects
80

ask price 70

20th turn 1st turn

(42,82) 6 subjects
60

50

(48,76) 2 subjects

40 10 15 20 25 30 35 40 45 50 55 60

bid price

(a) Problem-1, the fish market

(30,96) 1 subject

(36,91) 1 subject

(42,85) 3 subjects

(48,78) 4 subjects

(b) Problem-2, the fish market

(30,93) 1 subject

(36,86) 4 subjects (42,80) 9 subjects (48,74) 3 subjects

(c) Problem-3, the fish market

15 Figure 11: First Choice and Last Choice in the Fish Market: (x, y) is a local or the global optimal price set and the green squares indicate the area that satifies S(w) = D(p).

first turn last turn

problem-1 0.67 0.83

problem-2 0.02 0.65

problem-3 0.01 0.74

Table 4: The Coefficient of Determinant in the Stock Market problem-1 0.00 0.10 problem-2 0.06 0.26 problem-3 0.11 0.09

first turn last turn

Table 5: The Coefficient of Determinant: the Fish Market local optimal 6 (24 %) 4 (16 %) 9 (36 %) global optimal 13 (52 %) 7 (28 %) 9 (36 %)

problem-1 problem-2 problem-3

Table 6: The number of subjects in the stock market who reach a locally optimal or globally optimal price set. local optimal 5 (19 %) 6 (24 %) 8 (31 %) global optimal 6 (23 %) 3 (12 %) 9 (35 %)

problem-1 problem-2 problem-3

Table 7: The number of subjects in the fish market who reach a locally optimal or globally optimal price set. problem-1 1.098 0.579 −2.892∗ problem-2 0.812 0.227 −2.058∗∗ problem-3 0.750 0.188 −3.081∗

the first half the latter half z-value

Table 8: Average variance of the number of demand units in the Stock Market ∗ shows the 1 % significance, ∗∗ shows the 5% significance and ∗ ∗ ∗ shows the 10 % significance. problem-1 0.648 0.662 −1.951∗∗∗ problem-2 0.684 0.224 −2.058∗∗ problem-3 0.604 0.165 −3.054∗

the first half the latter half z-value

Table 9: Average variance of the number of supply units in the Stock Market problem-1 0.839 0.303 −3.721∗ problem-2 0.487 0.376 −2.070∗∗ problem-3 1.045 0.403 −2.375∗∗

the first half the latter half z-value

Table 10: Average variance of the number of demand units in the Fish Market

16

stock pattern 1

84%

58%
Demand = Supply (the first half) Demand < Supply (the first half) Demand > Supply (the first half) Demand = Supply (the latter half) Demand < Supply (the latter half) Demand > Supply (the latter half)

18% 10% 24%

6%

(a) Problem-1, the stock market

stock pattern 2

80%

58%

Demand = Supply (the first half) Demand < Supply (the first half) Demand > Supply (the first half) Demand = Supply (the latter half) Demand < Supply (the latter half) Demand > Supply (the latter half)

16%

14%

6%

26%

(b) Problem-2, the stock market

stock pattern 3

54%
Demand = Supply (the first half) Demand < Supply (the first half) Demand > Supply (the first half) Demand = Supply (the latter half) Demand < Supply (the latter half) Demand > Supply (the latter half)

82%

28%

12%

6%

18%

(c) Problem-3, the stock market

Figure 12: Quantity Adjustment in the Stock Market

17

fish pattern 1
68% 50%
Demand = Supply (the first half) Demand < Supply (the first half) Demand > Supply (the first half)

14%

Demand = Supply (the latter half) Demand < Supply (the latter half) Demand > Supply (the latter half)

12% 36% 20%

(a) Problem-1, the fish market

fish pattern 2

70% 54%
Demand = Supply (the first half) Demand < Supply (the first half) Demand > Supply (the first half) Demand = Supply (the latter half) Demand < Supply (the latter half) Demand > Supply (the latter half)

10%

14% 16%

36%

(b) Problem-2, the fish market

fish pattern 3

74% 48%
Demand = Supply (the first half) Demand < Supply (the first half) Demand > Supply (the first half) Demand = Supply (the latter half) Demand < Supply (the latter half) Demand > Supply (the latter half)

20%

10% 16%

32%

(c) Problem-3, the fish market

Figure 13: Quantity Adjustment in the Fish Market

18

the first half the latter half z-value

problem-1 0.465 0.416 −1.943∗∗∗

problem-2 0.527 0.521 −1.816∗∗∗

problem-3 0.820 0.450 -1.435

Table 11: Average variance of the number of supply units in the Fish Market treatment

ask price
86

the stock market problem 1 subject No.4
ask price
78

the stock market problem 1 subject No.2 4 units77
76 75

3 units
84 82

He reaches here at the 11th round.
price set

4 units

80

price set

74

5 units73
78
72

76

71 70

5 units
74 39 40 41 42 43 44 45 46 47

bid price

6 units 69
46 47 48 49 50 51 52 53

bid price

3 units

4 units

4 units

5 units

(a) the globally optimal price set in stock market

(b) a locally optimal price set in the stock market

the fish market problem 1 subject No.7
ask price
84

the fish market problem 1 subject no 9
ask price
78

3 units 83
82

4 units 77
76 75 74

81

80

price set

4 units 79
78

5 units 73
72 71

price set

77

70

76 40

3 units

42

44

46

48

50

52

bid price

6 units 69
46 47 48 49 50 51 52 53 54

bid price

4 units

5 units

4 units

5units

(c) the globally optimal price set in the fish market

(d) a locally optimal price set in the fish market

Figure 14: Price adjustment

Search rules Stock market Fish market

1 5 16

2 16 (5) 13 (4)

3 5 5

4 3 5

5 5 6

6 4 4 (0)

7 12 (5) 13 (6)

8 25 (18) 16 (10)

Table 12: Search–ending rules

19

[2] Mark Blaug. Economic theory in retrospect. Cambrige University Press, fifth edition, 1996. [3] Kahneman. D and Tversky. A. Prospect theory: An analysis of decision under risk. Econometrica, Vol. 47, pp.263–292, 1979. [4] D. Davis and C.A. Holt. Experimental Economics. Princeton University Press, 1993. [5] D. Kahneman and A. Tversky (eds). Choices,values, and frames. Cambrige University Press, 2000. [6] Hillel J. Enhorn and Robin M. Hogarth. Decision making under ambiguity. Journal of Business, S225–S250, 1986. [7] John D. Hey Search for rules for search. Journal of Economic Behavior and Organization, Vol. 3, pp.65–81, 1982. [8] John D. Hey. Still searching. Journal of Economic Behavior and Organization, Vol. 8, pp.137– 144, 1987. [9] Charles A. Holt. Classroom games trading in a pit market. Journal of Economic Perspectives, Vol. 10, pp.196–203, November 1996. [10] Knetsch.Jack L., Kahneman. D, and Thaler. R.H. Anomalies The endowment effects ,loss aversion and state quo bias. Journal of Economic Perspectives, Vol. 2, pp.193–206, 1991. [11] Jan Pieter Krahnen and Martin Weber. Marketmaking in the laboratory: Does competition matter ? Experimental Economics, Vol. 4 issue 1, pp.55–85, 2001. [12] O’Hara Maureen. Market Microstructure Theory. Blackwell Publishers, 1995. [13] Vernon L. Simth. An experimental study of competitive market behavior. The Journal of Political Economy, 1962. [14] Daniel F. Spulber. Market Microstructure -Intermediaries and the theory of the firm-. Cambrige University Press, 1999. [15] Daniel F. Spulber. Market microstructure and incentives to invest. Journal of Political Economy, Vol. 110, pp.352–381, 2002.

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