The Role of Information in a Continuous Double Auction: an Experiment and Learning Model

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The Role of Information in a Continuous Double Auction: an

Experiment and Learning Model

Mikhail Anufriev, Jasmina Arifovic, John Ledyard,

Valentyn Panchenko

PII:

S0165-1889(22)00091-4

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https://doi.org/10.1016/j.jedc.2022.104387

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DYNCON 104387

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Journal of Economic Dynamics & Control

Please cite this article as: Mikhail Anufriev, Jasmina Arifovic, John Ledyard, Valentyn Panchenko, The

Role of Information in a Continuous Double Auction: an Experiment and Learning Model,

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The Role of Information in a Continuous Double

Auction: an Experiment and Learning Model

∗

Mikhail Anufriev

Jasmina Arifovic

†

John Ledyard

Valentyn Panchenko

20 May 2021

University of Technology Sydney, Business School, Economics Discipline Group

PO Box 123, Broadway, NSW 2007, Australia

Department of Economics, Simon Fraser University,

Burnaby, B.C., Canada V5A 1S6

Division of the Humanities and Social Sciences, California Institute of Technology,

MC 228-77, Pasadena, CA 91125, USA

School of Economics, UNSW Business School, University of New South Wales,

Sydney, NSW 2052, Australia

†

Sadly, Jasmina Arifovic passed away on January 24, 2022

Abstract

We analyze trading in a modified continuous double auction market. We

study how more or less information about trading in a prior round affects

allocative and informational efficiency. We find that more information re-

duces allocative efficiency in early rounds relative to less information but

that the difference disappears in later rounds. Informational efficiency is

not affected by the information differences. We complement the experiment

with simulations of the Individual Evolutionary Learning model which, af-

ter modifications to account for the CDA, seems to fit the data reasonably

well.

JEL codes: D83, C63, D44.

Keywords:

Continuous Double Auction, Experiments, Individual Evolutionary Learn-

ing.

∗

We thank the organizers and participants of the 2021 Conference on Markets and Economies

with Information Frictions, and especially the discussant, Te Bao, for many suggestions that

helped to improve the paper. We also thank participants of the ESA meeting in Tucson, and the

seminar at Simon Fraser University for their comments on the earliest results of this research.

We are grateful to Michiel van de Leur for providing research assistance during earlier stages

of this research. Mikhail Anufriev acknowledges financial support from the Australian Research

Council through Discovery Project DP200101438.

1 Introduction

Is more detailed past information important for the performance of financial markets?

In particular, does access to past trading information affect the allocative efficiency of

the market? Will more information lead to higher or lower market volatility? These

questions are receiving growing attention in the literature, especially as access to infor-

mation gets easier and algorithmic trading spreads. In the experimental literature, one

of the earliest contributions on the importance of information in trading is by

. In the

context of the double action, he compares the environment with incomplete informa-

tion, when each trader knows only its marginal value or cost, and complete information,

when all traders know values and costs of all traders. He finds that convergence to the

competitive equilibrium price occurs slower under complete information.

study the

effect of the availability of past information for allocative efficiency in double auctions

organized as a call market. In this paper, we address these questions for the markets

that have an order book, such as the continuous double auction (CDA). For this purpose

and to disentangle several confounding effects that the use of the order book brings to

the behavior of traders, we propose a new trading mechanism and run an experiment

that matches this mechanism with treatments corresponding to different access to past

information. Further, we complement the experimental results with an evolutionary

learning model and show that the model is able to capture the experimental outcomes,

particularly during the initial, learning stage of the market.

The double auction, a centralized market with many buyers and sellers, comes in

many flavors; see, e.g.,

and

. Two of the most well known implementations are

the call market (CM) and the continuous double auction (CDA). The key difference

between these two mechanisms is that in the call market, orders are submitted and

cleared simultaneously, while in the CDA market orders are submitted asynchronously

and are cleared at different times during the trading session. In the call market, after all

orders are submitted, the market is cleared at a single equilibrium price. Buyers with

bids at or above that price and sellers with offers below or at that price trade. In the

CDA, the order book keeps all unsatisfied orders (bids and offers). When a new order

arrives, if possible it is matched with the closest order at the opposite side of the book,

or, otherwise, it is stored in the book. There are specific prices for every transaction.

In this paper, we are interested in a hybrid double auction, called the “Continuous

1

As a bid arrives, it is matched with the lowest offer from the book among those that are

below or equal to the bid. If there are several offers in the book satisfying this criteria, the bid

is matched with the offer that arrived the earliest (i.e., according to the time/price priority).

As an offer arrives, it is matched with the highest bid in the book among those that are above

or equal to the offer. Again, time/price priority is applied. In both cases, the transaction price

is the price of the order that was in the book, i.e., arrived earlier. During the trading session,

brokers see the dynamically changing book but agents do not. As explained later, in this paper,

agents cannot condition their behavior on the book’s current state, but may condition it on the

historical data from the book.

Double Auction with Synchronous Decisions” (CDA-SD). In the CDA-SD, the orders are

formulated simultaneously, as in the call market, but they are cleared asynchronously,

as in the CDA.

We focus on this market mechanism for two reasons. First, due to legal

aspects as well as considerations of efficiency, many participants in financial markets

delegate trading to brokers. This leads to a separation between investors’ decisions

(to formulate the order, i.e., the highest price to buy or the lowest price to sell) and

the activity of brokers (who have access to the market and execute trades). We focus

on investors who naturally make their decisions at some specified time, such as in the

beginning of a day, and from whose perspective the trading mechanism (which is CDA,

as in most of the markets) is not as important. Thus, we think of the CDA-SD – that

combines synchronous decisions with realistic trading protocol – as the mechanism useful

to study the behavior of investors.

Second, we address the question of the impact of past information availability for

market efficiency by building on the earlier contribution of

, AL henceforth.

The

CDA-SD mechanism allows us to disentangle the effect of access to information about

the trading history from the effect of an influence of the contemporaneous state of the

order book on the trading strategies. We focus on the former effect, keeping our analysis

closer to the AL.

AL found that more information is harmful for call markets: in their experiment,

allocative efficiency is smaller in the treatment where participants could see all offers

submitted in the previous session, in comparison with the treatment where such detailed

information is not available. AL complement their experiments with simulations of the

computational model where artificial agents use the Individual Evolutionary Learning

(IEL) algorithm.

Our previous work,

, AALP henceforth, theoretically addresses

2

In this way, we abstract from optimal timing considerations in order placement. Optimal

order timing in the CDA is investigated by

who find find that the optimal arrival has a skewed

hump-shaped distribution which depends on the environment and the market size.

3

The quest for the sources of market efficiency attracts a lot of attention in the economic

literature. The results of experiments with human subjects starting with

show quick conver-

gence towards competitive equilibrium, resulting in high allocative efficiency of the continuous

double auction (CDA). Market efficiency is determined by both market rules and traders behav-

iors, and disentangling one from another is challenging (

show that the “Zero-Intelligent”

(ZI) agents submitting orders randomly are able to achieve high level of efficiency. However, the

results strongly depend on the behavioral assumption that the ZI are trading within the budget

constraints, see

and

4

Even when traders are observing the order book closely, their orders arrive to the market with

delays, resulting in some randomness in the outcome of trading. Furthermore, many financial

exchanges deliberately introduce “speed-bumps”, i.e., (random) delays in the execution of orders

to avoid market instabilities, see Table 2 in

, who model uncertainty in order execution timing.

Thus, whereas the sort of decisions that our subjects made in our CDA-SD experiments differ

from the decisions in the standard CDA experiments, our construction is, in this respect, closer

to the real markets.

5

This learning model is an appropriate modelling tool for repeated complex environments, see

. For recent examples of IEL applications, see

and

. The agents in IEL are boundedly

rational, as they learn without taking into account that other agents are learning as well. IEL can

be thought of as a simplified version of genetic algorithm learning, introduced in the economic

the efficiency of CDA under two different information feedbacks. Assuming that the

artificial agents use the same IEL as in AL, AALP focus on the bidding strategies that the

algorithm selects in the stationary state.

AALP find that the past available information

affects the set of these selected strategies, though this difference does not translate into

different allocative efficiency. Some other market characteristics are affected, however.

For instance, price volatility decreases when the amount of past information increases.

The experiment designed in this paper not only tests these conjectures, but also

allows us to go beyond the analysis based on the stationary state. Indeed, the initial,

learning phase is as important as the stationary dynamics, because in the real markets

the environment (sets of valuations/cost of traders) may often change from period to

period, and even experienced traders may find themselves in a situation that is similar

to the initial few periods of our experiment. We find that in the experiments there is

a significant effect of information on allocative efficiency in the first periods with

information leading to lower efficiency

. This is the same effect as AL found for call

markets. However, learning in our experiment is quicker, when there is more past infor-

mation available, so that eventually allocative efficiency in both information treatments

becomes comparable, as in the stationary state studied in AALP. By looking at several

other measures, including the price volatility, we also find that the exact configuration

of the demand/supply schedules affects the outcome at least as much as the information

structure. Finally, we ask whether the IEL model, as introduced in AALP, can capture

both short and long-term features of the dynamics. The availability of experimental

data allows us to find a simple but intuitive improvement in the IEL algorithm that

captures the data relatively well in both experimental treatments. This is an example of

how experiments are crucial in complementing theoretical analysis, especially when that

analysis is based on a computational model with bounded rationality assumptions.

The rest of the paper is organized as follows. Section 2 introduces the information

differences that we study, discusses related literature, and formulates the experimental

hypotheses on the basis of the previous theoretical study of the AALP,

. Section 3

explains the experimental design and provides the details of the experiment that we run

in two locations. Section 4 presents the experimental results. In Section 5 we revisit the

Individual Evolutionary Learning model with the experimental data and demonstrate

that a slight variation in the model can fit the data well. Section 6 concludes. The

Appendix contains the experiment instructions and some estimation results.

literature in

and used recently in

. The word “individual” in IEL stresses that the agents

are not involved in social learning, as in the models based on imitation behavior like in

; see

for an example stressing the difference between the two types of learning.

6

The AALP prove, for selected demand/supply schedules, that certain bidding strategy pro-

files are evolutionary stable under the IEL. They run simulations for other, more complicated,

demand/supply schedules, but study these simulations after 100 transitory periods, where initial

learning takes place.

7

Computational agent-based models have gained popularity in Economics and Finance, for

recent advances see

and

2 Role of information and IEL

In this section we introduce two different information settings used in the literature.

We also introduce the Individual Evolutionary Learning (IEL) model that

(AALP)

studied theoretically.

2.1 Two information feedback scenarios

Financial markets have witnessed an increasing access of the traders to past detailed

information, see, for instance,

and

pose the question: will the allocative efficiency

of markets increase if agents use richer past information? AL do this in the context

of a call market, focus on learning under repeated trading, and disentangle the two

information scenarios. In the

“closed” book

scenario, agents have no access to the

individual level data from the past market session; they only know the past market

clearing price. In contrast, in the

“open” book

scenario, the information about past

individual orders is available to traders. The latter scenario provides traders with strictly

more information than the former. It turns out, perhaps surprisingly, that access to more

information results in a lower market efficiency. AL find this by conducting experiments

with human subjects and via simulations of the Individual Evolutionary Learning (IEL)

model with artificial traders.

The difference between the two information scenarios above, when extended to the

CDA markets, is in the access to the orders from the previous session. To separate

any strategic effects that information from the current order book may produce when

decisions are made

during

the trading session, we introduce the CDA with Synchronous

Decisions (CDA-SD) mechanism. This is the market with an order book matching the

orders that

arrive

asynchronously, but where the traders

formulate

their orders simul-

taneously. Thus, in the CDA-SD, the orders are decided before the trading session, and

arrive at random times during the session. The session is organized as the standard CDA

with the order book. This construction allows us to keep the distinction between the

same two information scenarios that AL studied, which we call

Aggregate-level

(market)

feedback

(

) and

Individual-level

(orders)

feedback

(

). In the

Aggregate Feedback

case, all traders have access only to the average transaction price of the past session. In

the

Individual Feedback

case, all traders have a detailed access to the order book of

the previous session. The

corresponds to the closed book scenario in AL and the

corresponds to the open book scenario in AL.

Several related studies vary information availability and compare market perfor-

mance. Apart from allocative efficiency, this literature focuses on the market character-

8

We do not use the open/closed book terminology that AL and AALP used to avoid a

confusion with the cases when agents may access the

current

session order book.

istics related to “information efficiency”. Information efficiency refers to the market’s

ability to aggregate individual information (for example, individual valuations and cost)

into the price. When markets are informationally efficient, there are no systematic

deviations of the price from its equilibrium values. Low price volatility (for repeated

trade in a fixed environment) is another measure reflecting information efficiency. An

empirical study of

found behavioral and market changes that followed the New York

Stock Exchange decision to open past order books to traders to increase transparency.

In particular, this decision resulted in lowering the price volatility and increasing market

liquidity, that is in higher information efficiency. The theoretical study of

, where the

call market mechanism is assumed, compares the case of “open book” information envi-

ronment that occurred as the result of an NYSE decision (our

case) with the “closed

book” information environment that existed before (our

case). The study finds that

larger transparency favors traders that demand liquidity (e.g., those who submit market

orders) at the expense of the traders who provide liquidity (e.g., specialists and limit

order traders).

Theoretical studies of the CDA typically rely on simulations and abstract from many

factors that are in place in real markets (order size, market orders, possibility of cancel-

lations, and so on), and focus on the impact of information only.

investigate trading

strategies in a market organized as a CDA with order book and find that the amount

of information about the book (beyond the best quotes) has little effect on the perfor-

mance.

compare call markets with CDAs. The strategies of traders evolve over time

following a genetic algorithm that favours strategies of better performing agents. It

turns out that, in the call market, traders become price-takers, offering their valuation

or cost, and in the CDA, they become price-makers, bidding the equilibrium market

price.

use IEL and compare the

and

information environment under the CDA

market. They find that traders behave more like price-takers in the

environment and

tend to be more like price-makers in the

environment, as more information becomes

available.

All of the studies discussed above are focused on outcomes after some learning stage,

that is on some “equilibrium” outcome. In this paper, instead, we are interested in the

experimental evidence of immediate learning of human subjects under the two feedback

environments. We will use the equilibrium predictions of the IEL algorithm from AALP

to formulate hypothesis and organize the results. However, we will extend their IEL

algorithm in Section 5 to better match our short-run experimental data.

2.2 The IEL model

The Individual Evolutionary Learning (IEL) model (

) is an appropriate computa-

tional test-bed to study the market design questions discussed above. Indeed, in a

complex environment with a large strategy space, it is fairly impossible to get analytic

solutions to equilibrium models, and it is also unlikely that traders will behave fully

rationally from the outset. The IEL model defines a computational algorithm that sim-

ulates the process of learning.

show that this algorithm performs better than other

learning rules, and the outcomes of the IEL model are very similar to experimental

outcomes in many situations where subjects have continuous or large strategy spaces.

Given the three building blocks – (i) a specific environment, consisting of traders’

endowments and valuations and costs, (ii) a trading protocol, defining the outcome of

the trading session given the strategies of traders, and (iii) information feedback, i.e.,

what information is available to traders between consecutive trading sessions – the IEL

algorithm defines a multi-dimensional stochastic process. The state variables of this

process are the individual bidding strategies that agents use and the aggregate market

variables, such as prices. IEL can be used to produce theoretical predictions. For

example, the two information feedback cases,

and

, as defined above, create a

contrasting set of IEL-simulations and corresponding statistics for allocative efficiency,

average price, price volatility, and so on.

IEL, in its simplest form, has only two parameters, the size of the strategy space,

that reflects the cognitive capacity of traders, and the probability of experimentation,

that models the rate at which new strategies are experimented with at each stage. IEL

also depends on the specification of “hypothetical” utility; that is, the utility that traders

would have received from playing a strategy in the past. Traders are boundedly rational

and compute hypothetical utility without taking into account the learning processes

of others. Hypothetical utilities depend, generally, on the environment, the trading

protocol and the information feedback.

2.3 IEL for the CDA-SD markets

The IEL model that AALP study can be used on the CDA-SD markets to confront the

and

settings. We present their results in order to formulate our experimental

hypotheses.

The trading sessions are in discrete time, with periods indexed by

. Several buyers

and sellers, whose valuations and cost are exogenously given and fixed over all periods,

trade repeatedly. Each trader can buy or sell at most one unit of a good every period.

Traders know their own valuations and costs, but not the valuations and costs of others,

neither do they know the distributions. Utilities are linear; that is, they are valuation

minus transaction price for buyers and transaction price minus cost for sellers. Agents

who do not trade, get utility 0. Let

and

denote the valuation of buyer

and cost

of seller

, respectively. The set of valuations and costs define an environment.

Trade on the CDA-SD market is organized as follows. In the beginning of each

period, each trader submits one order (bid for a buyer, offer for a seller). These orders

arrive at the market organized as the CDA in random order. The CDA defines a (possibly

empty) set of trades and corresponding transaction prices, according to the standard

rules (as described in the Introduction).

After the period ends, all traders receive the same between-period feedback. Two

feedback scenarios are considered. The richer

scenario provides each trader with a

detailed information about the order book from the previous period. Specifically, each

trader can see all individual bids and offers, as well as how the order book evolved. The

scenario provides each trader with the average transaction price only.

Under the IEL algorithm, every artificial agent is endowed with an individual pool

of strategies, evolving in time. The pools are denoted as

b,t

and

s,t

for buyer

and for

seller

, respectively, and are composed of

real numbers belonging to the

admissible

intervals, which are [0

] for buyer

and [

100] for seller

When simulations start,

at period

= 1, the initial pools are formed by

uniform draws from the corresponding

admissible interval, independently for all agents. In this period, each agent takes one

of the strategies from the pool with equal probability and submits it. The trading

mechanism matches orders and defines prices. After the period, each trader receives an

information according to the feedback. Before the next period starts, the IEL model

plays a role in (i) updating each agent’s pool and (ii) selecting a new order from that

pool. The same process then is repeated and so on.

In the beginning of every period, the pools of all traders are updated independently,

in two consecutive stages. At the

experimentation

stage, every element of the pool is

either removed with probability

, or remains with probability 1

−

. If an element is

removed, it is replaced by an element drawn from some distribution truncated to the

admissible interval of the trader.

After this procedure is repeated independently for

each of the

positions in the previous period pool, an intermediate pool is formed.

At the

replication stage

, the final pool is obtained, element-by-element, repeating the

following process

times. Two randomly chosen strategies from the intermediate pool

are compared with each other (with replications), with the best of them occupying

a place in a new pool. The comparison between strategies is made according to a

performance measure, called hypothetical utility, denoted as

since this utility

depends on the information feedback. After the new pools are formed, the strategy is

selected for each trader randomly from their pool, with probabilities proportional to the

hypothetical utilities. For instance, the probability that buyer

selects bid

in period

9

The size of the pool is kept constant, but note that it is possible (and in fact common) that

the pool has repeated strategies. In all our environments, the valuations and costs are between

0 and 100. We impose individual rationality constraints, not permitting traders to submit offers

that could result in a negative profit.

10

Simulations in AALP use the uniform distribution. However, we found that our experimental

data are matched better when the experimentation occurs from the truncated normal distribu-

tion, with the mean given by the element that is replaced. In other words, local experimentation

describes the data better.

under

is given by

b,t

(

) =

b,t

(

)

∑

b,t

(

)

where

b,t

(

) is the hypothetical utility of buyer

at time

from bidding

AALP specified the hypothetical utilities as follows. For the

setting (“closed”

book in AL), where only the average price of all transactions from the previous period,

−

, is reported back to each trader, the hypothetical utilities are

b,t

(

) =







−

≥

−

otherwise

(1)

for buyer

. Analogously, the hypothetical utility of seller

s,t

(

) =







−

≤

−

otherwise

(2)

For the

setting (“open” book in AL), where traders can see the whole book of the

previous session, the agents substitute their orders to the last session book and find their

corresponding utility. The hypothetical utility of buyer

from bid

b,t

(

) =







−

∗

b,t

−

(

) if bid

would lead to a trade at

∗

b,t

−

(

)

otherwise

Analogously, seller

computes the hypothetical utility of offer

s,t

(

) =







∗

s,t

−

(

)

−

if offer

would lead to a trade at

∗

s,t

−

(

)

otherwise

In other words, the hypothetical utility is what a trader would get last period with the

order, if all other traders submitted the same orders they did and the sequence of the

orders in the book would be the same.

2.4 AALP results and experimental hypotheses

AALP study the stationary state of the IEL algorithm after a long transitory period.

They found that, in the long-run, the strategies employed by the artificial traders depend

on the information feedback.

In the

case, traders learn to become “price-makers”,

11

The assumption of the same sequence is a reasonable behavioral assumption. Alternatively

traders could “simulate” all possible sequences of orders’ arrival and evaluate expected hypo-

thetical utility. However, the number of computations for this is very large.

12

More precisely, the major differences are in the strategies of the infra-marginal traders, i.e.,

traders who should trade in the demand/supply imposed equilibrium model. The other, extra-

as they tend to submit similar orders belonging to the range of the equilibrium prices.

This leads to relatively stable prices, with low volatility and high information efficiency.

The occasional experimentation of IEL, leads however to the possible loss of allocative

efficiency due to missing transactions. The strategies and dynamics are different under

the

case, where traders submit the orders outside of the equilibrium price range,

close to their valuations and cost (to make sure that they transact), and behave thus

similarly to the “price-takers”. As they do so, the price gets volatile, sometimes leaving

the equilibrium price range, and lowering informational efficiency. The loss of allocative

efficiency occurs due to possible trading of the extra-marginal traders (who should not

trade in the equilibrium). In both cases, the allocative efficiency is in the range of

88%

−

95% for most of the IEL parameters.

One important caveat to these results is that the AALP describe only some but

not necessarily all stationary states. Moreover, the results hold precisely only for the

specific schedules taken from

. Simulations for more sophisticated environments, similar

to those that we use in the experiment reported in this paper, suggest that the result

about low information efficiency in the

setting can be extended, but the impact of

the feedback on allocative efficiency is somewhat uncertain due to a strong interaction

with the environment.

This discussion leads to the following two hypotheses that our experiment will test.

Hypothesis 1.

Full allocative efficiency of

100%

is not achieved under the CDA-SD both

in the

(‘closed’ book) and in the

(‘open’ book) information feedback scenario. The

ranking of the allocative efficiency for the two information feedback scenarios depends

on the schedule.

Hypothesis 2.

Price volatility is significantly higher in the

(‘closed’ book) than in

the

(‘open’ book) information feedback scenario. The average transaction price stays

in the equilibrium price range in the

, but may leave it in the

Both parts of Hypothesis 2 suggest that the

will have lower information efficiency

than the

3 Experiment

The identical experiment sessions were run in two locations. 8 sessions were conducted

in October 2010 at the Business Experimental Research Laboratory (BizLab) at the

marginal traders submit random admissible strategies but trade very rarely. We define the infra-

and extra-marginal traders in Section 3.

13

For most of the IEL parameters in the AALP, the allocative efficiency is slightly higher in

the

case, for our

schedule in Section 3. Instead, it is substantially higher in the

case,

for the schedule that is very similar to our

schedule in Section 3.

UNSW, Sydney; and 10 sessions were conducted in October 2012 and February 2013 at

Caltech’s Laboratory for Experimental Economics and Political Science (EEPS). The

experiments were computerized using the zTree software (

). In both locations, the sub-

jects were mostly undergraduate and some postgraduate students majoring in different

areas. The participants were recruited from the large pools through the ORSEE system

(

There were 10 participants in each session. The session incorporated two blocks,

with 20 trading rounds each. Blocks corresponded to two different environments, i.e.,

sets of valuations and cost. The valuation and cost of every participant were kept the

same during all trading rounds of each block. In each round, 5 buyers and 5 sellers

traded according to the CDA-SD protocol. Each buyer demanded one unit of a com-

modity whose valuation was privately known, and each seller could sell one unit of that

commodity whose cost was privately known. Every participant was able to submit an

order with up to two decimal digits. These individual (limit) orders, bids and offers, were

collected before the trading period, and then the order book was simulated with random

arrival of these orders. The calculation of the payoff per trading round is standard for

trading experiments: the buyer’s payoff is given by valuation minus transaction price, if

the buyer traded, and 0, otherwise. The seller’s payoff is given by the transaction price

minus cost, if the seller traded, and 0, otherwise.

The procedure and incentives were

explained to the participants before the experiment.

We ran two treatments of the experiment that differed in the feedback that par-

ticipants received between trading rounds. Those corresponded to the

Aggregate-level

(market)

feedback

(

) and

Individual-level

(orders)

feedback

(

) scenarios explained

in Section 2.1. Before every trading round, the participants could see information from

the previous round and analyze it for 20 seconds. Then the information window was

supplemented on the screen with a decision window and subjects had additional 60 sec-

onds to submit the offer. In the treatments with the

scenario, participants only

knew the previous average price of all transactions, their previous period earning (from

which they could infer whether they traded, and if yes, then their transaction price) and

their cumulative earnings. In the treatments with the

scenario, in addition to this

information, participants were faced with the whole order book of the previous period,

i.e., with all 10 submitted bids and asks (without identities of traders) in the order of

their arrival. If no transaction was recorded during the previous round, participants in

both treatments were informed about this, and the participants in the

treatment

could see the evolution of the order book.

Figure 1 shows the screen from the

treatments with combined information and

14

To prevent negative payoffs, the bids could not to exceed the buyer’s valuations and the

offers could not exceed the seller’s cost.

15

There were only 3 periods with no transactions. This is less than 0

5% from the total number

of 720 trading periods (9

4 = 36 trading blocks with 20 periods each).

Figure 1:

Information and decision windows shown in the treatment with individual

level information feedback,

. The decision part contained the counter. When the offer

was overdue, the overdue message appeared (in red).

decision windows. The decision window (identical in both

and

treatments) is

in the lower part of the screen, below the table. It shows the role of the participant,

the valuation (or cost), contains the window to type the offer, and displays the time

counter. The information window for the

treatment contains, in the upper part,

the table with four columns showing (from left to right) the step when the order of

the participant arrived, whether it resulted in a transaction, the average price of all

transactions, and the last period and cumulative earnings. Then, in the middle part, it

shows how the order book evolved in the previous session. The information screen in

the

treatment had only the last two columns of the upper table and no middle part.

The examples of the screens from all treatments can be found in Appendix A.3.

In the experiment, we used two different market schedules, both with 5 buyers and

sellers, see Figure 2. Running an experiment with different schedules is necessary to

check robustness of the differences between the information scenarios. We picked two

schedules that differ in the equilibrium quantity and price ranges and have been used in

the previous studies.

Schedule

(the left panel) has 4 trades in equilibrium with the

range of equilibrium prices [55

66). In schedule

(the right panel), the equilibrium

16

For schedule

, the valuations/costs are

1

= 100,

2

= 93,

3

= 92,

4

= 81,

5

= 50,

1

= 30,

2

3

= 39,

4

= 55 and

5

= 66. This is schedule 1 in

and it was referred as

‘AL’ in simulations in

. For schedule

, the valuations/costs are

1

= 90,

2

= 70,

3

= 50,

4

= 30,

5

= 10,

1

= 5,

2

= 25,

3

= 45,

4

= 65 and

5

= 85. This schedule is very similar

to schedule 2 in

and the symmetric ‘S5’ market in

Figure 2:

Demand/Supply diagrams for the market configurations considered in the

paper.

Left:

-market.

Right:

-market.

quantity is 3 and equilibrium price range is [45

50]. Thus,

allows more trades and

has a larger range of equilibrium prices, leading to potentially higher efficiency than

The traders that would trade in equilibrium are called infra-marginal and those

who would not trade in equilibrium are called extra-marginal. The total surplus of trade

(regardless of the mechanism) is maximized when the infra-marginal buyers (IMB) trade

with infra-marginal sellers (IMS). There are 4 IMB and 4 IMS in

with the largest

surplus equal to 203. There are 3 IMB and 3 IMS in

with the largest surplus equal to

135. The

allocative efficiency

is defined as the fraction of this surplus extracted during

the trading session.

After reading the instructions (see Appendix A) and completing a test designed to

check the subjects’ understanding of the instructions, the first block of the experiment

started. In the beginning of this block each participant was randomly assigned to be a

buyer or a seller; every buyer saw their valuation and every seller saw their cost. After

20 trading rounds, a new block began. Every buyer changed their role to become a

seller, every seller changed their role to become a buyer, and the valuations and costs

were assigned according to a new schedule.

Then the next 20 trading rounds started.

When those were over, subjects filled in a questionnaire and collected earnings equal to

a show-up fee of 5 dollars and all their accumulated payoff over 40 trading rounds.

The experiment has a 2

2 design, as we varied information feedback and the

schedule.

In total we have 4 treatments (2 information feedback scenarios and 2

17

We verified it by running a simple simulation where agents from a schedule are matched

randomly and the total surplus is computed. For

we achieve an average efficiency of 46% in

comparison to an efficiency of 10% for

18

The subjects knew about the change of the role between blocks. To balance expected payoffs

for the participants, we re-assigned the buyers with higher valuations in the first block to become

the sellers with higher cost in the second block, and the same for the sellers from the first block

who became buyers. The subjects did not know this.

19

In each session we used both schedules, running them in different orders. We found no

significant impact of the order in which the schedule appeared. We also found no evidence

Treatments

UNSW

Caltech

Total

AF-1

aggregate feedback; schedule

AF-2

aggregate feedback; schedule

IF-1

individual feedback; schedule

IF-2

individual feedback; schedule

Table 1:

Treatments of the experiment and the number of observations.

different schedules), see Table 1. Taking into account sessions in both locations, we

have 9 observation for each treatment.

4 Experimental Results

We present the results in the same order as the two hypotheses formulated in Section 2.4.

We start with the allocative efficiency in Section 4.1 and then discuss the measures of

informational efficiency in Section 4.2. Our findings are supported with a regression

analysis, the details of which can be found in Appendix B.

Before presenting the results, we provide an overview of how we analyzed the data.

We illustrate the time evolution of average allocative efficiency in Fig. 3 for the two

information treatments (averaging the results from all sessions for both schedules). Al-

location efficiency initially goes up quickly but exhibits variability in time over the whole

course of the experiment. Variability is observed for other characteristics we are inter-

ested in, as well, and is present in almost any session of the experiment. Therefore, we

start by averaging the characteristic of interest (such as allocative efficiency) in each

session over a specified time period and focus on the corresponding mean.

We distin-

guish, in particular, the initial periods (periods 1-5) and the subsequent periods (periods

6-20). Distinguishing the initial five periods from the rest of the treatment allows us

to focus on the learning phase of the experiment. We can also separately look at the

later periods that may correspond to a stationary state. Recall that the hypotheses in

Section 2.4 are based on the theoretical IEL results from AALP. Those results, in turn,

reflected one of the

stationary states

of the model.

After the data of a specific characteristic, such as allocative efficiency, are averaged

over time for each session, the session-specific statistics are averaged over all sessions of a

given treatment. As the results are independent between different sessions, we compute

the mean values and the standard errors of such averaging. We use those means and

standard errors to perform the statistical tests. Specifically, for the same characteristic

that the experience of participants with one schedule would affect their behavior with another

schedule, which is not surprising given that participants changed their roles between blocks.

20

To limit the effect of possible outliers, we have done the same analysis based on the medians

(not on the means) of data over time. The results are similar and are available upon the request.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Allocative Efficiency

Figure 3:

Evolution of allocative efficiency in the experiment.

we make the pair-wise comparisons between treatments, compute the

-statistics for the

difference in mean test, and report in the text whether the difference is significant at the

5% level.

Table 2 reports the p-values and other data behind the figures and results.

To be more precise in our findings, we run regressions of the following type for

various characteristics, using the trading periods as the observation units:

Allocative Efficiency =

DInfo +

DInit +

(DInfo

DInit)

DLoc +

DSch +

DExp + error

(3)

In this regression the dummy variables are set as follows: DInfo is 1 for

and 0 for

; DInit is 1 for periods 1-5 and 0 for periods 6-20; DLoc is 1 for Caltech and 0 for

UNSW; DSch is 1 for schedule

and 0 for

; DExp is 1 for the first block and 0 for

the second block of the experiment. Appendix B collects the corresponding estimates

for different characteristics.

Running an experiment in two different locations (UNSW and Caltech) is useful to

make sure that the differences in treatments are not affected by the participant pool.

However, we often find a significant effect of location, with average efficiencies being

higher in the Caltech sessions than in the UNSW sessions, when compared for the same

treatments.

On the other hand, we found that the effect of information feedback (

21

The appropriate t-statistics is the difference of two means divided by the squared root of

the sum of the squares of the two standard errors. The p-values are reported for the one-sided

tests and are based on 18 independent observations (as we pool the data over locations and

schedules).

22

The other characteristics (defined later) are: the number of “missed” transactions, indicator

of whether the average price is outside of the equilibrium range, and price volatility.

23

We find the same effect using the coefficient estimate on the DLoc dummy in the regressions

reported in Appendix B. At the 5% level of significance, the location effect is significant for the

allocative efficiency (that is higher in the Caltech sessions), and the out-of-equilibrium index and

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

AF, periods 1-5

IF, periods 1-5

AF, periods 6-20

IF, periods 6-20

Allocative Efficiency

Figure 4:

Allocative efficiency in the experiment.

) is in the same direction for both locations.

Thus, we pool data along location

when we present them visually and make the pairwise tests for the mean.

4.1 Allocative Efficiency

We begin with an illustration in Figure 4 of one of the key results from the experiment.

This figure compares the allocative efficiency across two information treatments,

and

, for the first five and remaining 15 periods of the experiment.

We make three observations from Figure 4. First, in the initial periods, allocative

efficiency is larger for the

than for the

treatment. Thus, similar to the call mar-

kets analyzed in AL, an increase in an amount of information available to the traders

results in a lower allocative efficiency. Second, in the remaining periods of the experi-

ment, allocative efficiencies under the two information treatments are very close to each

other. Thus under the CDA, the negative effect of more information is only temporary.

The ‘Allocative efficiency’ part of Table 2 confirms that the difference between treat-

ments is significant in the initial periods but not in the remaining periods. Finally, we

notice that allocative efficiency reaches 80%. On the one hand, this is lower than that

achieved in the IEL simulations in the AALP, where average efficiency is above 88% in

both schedules, for most of the parameters. On the other hand, 80% is much larger than

the efficiencies we would get under the random allocation process (that adjusts for the

difficulty of the schedule) described in footnote 17.

volatility (both are lower in the Caltech sessions).

24

Our findings are similar to those in

who compare performances of different subject pools in

a number of elicitation tasks. They find that the Caltech students’ behavior is closer to rational

and that the direction of comparative statics between treatments is consistent across locations.

25

The allocative efficiency in periods 6-20 of the experiment, in both treatments and for both

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Schedule 1

Schedule 2

Allocative Efficiency

AF, periods 1-5

IF, periods 1-5

AF, periods 6-20

IF, periods 6-20

Figure 5:

Comparison of the allocative efficiency across information treatments for the

two schedules separately.

In Figure 4, the data are pooled across schedules. To justify that this is appropriate,

we show the allocative efficiency disaggregated across schedules in Figure 5. (The data

behind this figure are also in the ‘Allocative efficiency’ part of Table 2). We can see that

the effect of the information treatments is the same for both schedules for the first five

periods of the experiment and for the remaining periods.

To find the reason for low allocative efficiency, we investigate in Figure 6 the average

number of transactions. For schedule

, the equilibrium number of transactions is 4.

We can see that, with time, the number of transactions increased, but it is never close to

the equilibrium 4 transactions. For schedule

, the equilibrium number of transactions

is 3. Again, the actual average number increases in time but it is smaller than 3. The

‘Missed transactions’ part of Table 2 reports the statistics for the difference between the

equilibrium and experimental number of transactions. Testing across treatments, we

find that the difference is significant but only for the initial periods, consistently with

the allocative efficiency results. From Figure 6 and Table 2, we can see that the gap

between the equilibrium and experimental number of transactions is larger for the

Apparently, this contributes to a smaller allocative efficiency for schedule

schedules, is larger than the allocative efficiency for 97% of simulations for the random allocation.

This can be compared with similarly computed numbers of 93% and 97% in the

treatment,

and 85% and 82% in the

treatment, for schedules 1 and 2, correspondingly. This suggests

that, once learning is done after first five periods, in both treatments the efficiency is pretty

high. It was also high in the first 5 periods for the

treatment, which is significantly better

than for the

treatment.

26

For periods 1-5, the difference in the allocative efficiency between the

AF-S1

and

IF-S1

is significant with p-value 0

023; this difference between the

AF-S2

and

IF-S2

is marginally

significant with p-value 0

120. For periods 6

−

20 the differences are not significant in both cases

with p-values 0

622 and 0

414, respectively.