Cooperation without Coordination: Signaling, Types and Tacit Collusion in Laboratory Oligopolies

Douglas Davis

Virginia Commonwealth University Richmond VA 23284-4000

(804) 828-7140 dddavis@vcu.edu

Oleg Korenok

Virginia Commonwealth University Richmond VA 23284-4000

(804) 828-3185 okorenok@vcu.edu

Robert Reilly

Virginia Commonwealth University Richmond VA 23284-4000

(804) 828-3184 rjreilly@vcu.edu

8 March 2007

Abstract: This paper reports an experiment conducted to examine tacit collusion

in posted offer markets. In addition to a baseline treatment, we study a ‘forecasting’

treatment, which allows an improved identification of intended signals, and a ‘types’

treatment, which examines pricing outcomes among cohorts of homogeneously

‘cooperative’ or ‘competitive’ subjects. Results indicate that while signals tend to affect

subsequent pricing decisions, signaling does not affect long term transaction prices. On

the other hand ‘types’ are stable across sessions and powerfully affect results. Markets

comprised of ‘cooperative’ types tend to generate persistently higher transaction prices

than do markets comprised of ‘competitive’ types.

Keywords: Experiments, Tacit Collusion, Price Signaling, Types JEL codes C9, L11, L13 ______________________________________ * We thank without implicating Bart Wilson for helpful comments. Financial assistance from the National Science Foundation and the Virginia Commonwealth University Faculty Excellence Fund is gratefully acknowledged. Thanks also to Matthew Nuckols for programming assistance. Experiment instructions, an appendix and the experimental data are available at www.people.vcu.edu/~dddavis

1. Introduction

Laboratory markets organized under posted offer trading rules generate

competitive outcomes in a robust collection of circumstances. Nevertheless, in a few

rather specialized contexts, deviations from competitive (and static Nash equilibrium)

predictions arise with some frequency. Experimentalists broadly attribute such

deviations to tacit collusion. However, this ‘tacitly collusive’ behavior does not

correspond at all closely with the type of coordinated outcomes that are the focus of

attention by antitrust authorities. Rather than establishing a common price and coming to

some agreement as to how that price is to be maintained, (as is contemplated as a source

of concern, for example, in the 1992 U.S. DOJ/FTC Horizontal Merger Guidelines),

supra competitive prices more typically vacillate substantially, both within and across

markets.

An understanding of factors driving this sort of tacitly collusive behavior is

important both to improve our understanding of behavioral oligopoly and, potentially, for

antitrust policy. From a behavioral perspective, the tendency for participants to earn

more than static Nash equilibrium predictions when earnings in the Nash equilibrium are

very low is one of the standard stylized results of experimental analysis. Pertinent

examples outside market contexts include ‘prisoner dilemma’ games, ‘trust’ games and

VCM games. However, the price-setting game is distinct from these other games, since

‘cooperative’ and ‘competitive’ behavior are much more difficult to isolate, due both to

the relatively high cost of unilateral cooperation, as well as to the richer scope of strategic

actions.1 From a policy perspective, an understanding of ‘unorganized’ tacit collusion

may help enrich antitrust analysis. To the extent that sellers can collude without

1 For example, compare the oligopoly pricing game with a VCM game. In the repeated VCM game the limit to ‘cooperation’ is the unilateral a contribution of one’s entire endowment to the group exchange, or public good. This limiting act typically returns a positive return in the form of the return to the group account. In contrast the limiting cooperation action in a repeated pricing game consists of unilaterally posting a price above the maximum price posted by other sellers, a choice which typically returns a profit of zero to the signaling seller. To appreciate the richer strategy space in the repeated pricing game, observe that in a VCM game, reductions in contributions to the group account increase participant earnings at a constant rate, independent of others’ decisions. In contrast, in the repeated pricing game, a seller may earn very high profits by pricing just under his or her rivals. Thus, in the repeated pricing game, a signaler may have either cooperative or competitive intentions. For example, a seller posting a high price may alternatively seek to permanently raise price levels, or hope to lure rivals into raising prices so that they can be quickly undercut.

exhibiting any of the standard indicators of coordinated activity, antitrust authorities

might seek richer alternative patterns of potentially problematic actions.

This paper reports an experiment conducted to gain some insight into the factors

driving supra-competitive prices in posted offer markets. Specifically, we study two

possible links between sellers and prices. First, we study price signaling. In an oligopoly

environment where sellers have no opportunities for explicit collusion, communications

sent in the form of prices in the market place represent the most probable method of

coordinating behavior. Curiously, in the extensive experimental oligopoly literature,

price signaling, and the effects of these activities on prices has not been a prominent topic

of investigation (Durham et al. 2004 is an important exception).2 One important

impediment to a study of price signaling is the difficulty of distinguishing price signals

from other motives for pricing decisions. For example, in addition to signaling an

intention to cooperate in a period, a seller may increase prices in an effort to search the

price space, or to compete with the anticipated prices of rivals in a subsequent period.

Here, we isolate price signaling activity by having sellers forecast the maximum price to

be posted by rivals in a subsequent period. This forecasting game, in conjunction with a

design in which the highest pricing seller sells zero units, allows a clean identification of

an intended signal: Any price above a seller’s forecast of his or her rivals’ maximum

price will result in sales of zero, and would be irrational unless the seller is signaling an

intention to cooperate.

A second dimension of our investigation regards ‘types’ or individual propensities

to behave either cooperatively or competitively. ‘Type’ has been identified as an

determinant of behavior particularly in public goods contexts (e. g., Fiscbacher, Gächter

and Fehr, 2001, Burlando and Guala, 2005, Kurzban and Houser, 2005 and

Gunnthorsdottir, Houser, and McCabe 2007) and is an important component of the new

‘behavioral public finance’. However, in the context of oligopoly, individual propensities

to cooperate or compete have largely been overlooked. Here, we use decisions from an

initial series of sessions to classify participants in terms of a cooperativeness scale. In a

pair of subsequent sessions we use this scale to identify cooperative and competitive

cohorts, which we invited back for subsequent sessions to assess whether tendencies

2 In their pioneering oligopoly experiment Friedman and Hoggatt (1980) also discuss price signaling.

2

observed in the initial sessions were stable across treatments, and, the extent to which

collecting like ‘types’ affects outcomes.

By way of preview, we find that both signaling and type affect market

performance. Nearly all participants send signals, and those signals tend to elicit price

responses. Signaling activity alone, however, does little to affect overall price levels.

Mean transaction prices are low in some markets with high levels of signaling activity,

and, conversely, mean transaction prices are high in some markets where very few

signals were sent. On the other hand, individual propensities to behave either

cooperatively or competitively are relatively stable across sessions, and they very

prominently affect market outcomes. Markets comprised of ‘cooperative’ types tend to

generate high mean prices, while markets comprised of ‘competitive’ types tend to

generate low prices.

The remainder of this paper is organized as follows. Section 2 below overviews

the near continuous posted offer framework, and presents the experiment design and

conjectures. A short section 3 explains experiment procedures. Sections 4 and 5 report

experimental results. The paper concludes with a brief sixth section.

2. Experiment Design.

We use here a variant of a ‘swastika’ design initially studied by Smith and

Williams (1989) which we examine in a ‘near continuous’ variant of the standard posted-

offer institution developed by Davis and Korenok (2006). Our design choice is

advantageous in that it is both very easy for participants to understand, and it is an

environment where tacit collusion has been previously observed (e.g,. Cason and

Williams, 1990, Davis and Korenok, 2006). The ‘near continuous’ variant of the posted

offer institution usefully allows the collection of comparatively long series of both prices

and prices signals in a relatively short time frame. Extensive repetition is particularly

useful for an examination of signaling behavior, as any study of signaling requires that

participants become experienced both with the primary market pricing game as well as

the possible informational content of price deviations. Below we explain our

implementation of the posted offer trading institution in subsection 2.1. The subsequent

3

subsection 2.2 develops the market design, and subsection 2.3 explains our experimental

treatments and conjectures.

2.1. The ‘Near Continuous’ Posted Offer Trading Institution. The ‘posted offer’

trading institution is a standard tool in the experimental analysis of markets. Posted offer

rules both parallel many features of retail trade, and may be analyzed as a non-

cooperative game of Bertrand-Edgeworth competition. Under posted-offer rules, the

market consists of a series of trading periods. In each trading period sellers, endowed

with unit costs, simultaneously make price decisions. Once all seller decisions are

complete, prices are displayed publicly, and an automated buyer program makes all

purchases profitable to the buyer at the posted prices. Figure 1 illustrates a screen display

for a seller S1 in a computerized implementation of the posted offer market. As seen in

the upper left corner of the Figure, seven seconds remain in trading period 4. Moving

down the left side of the figure, observe that in this period seller S1 has four units, each

of which cost $2.00. To enter a decision, a seller just types an entry in the ‘price’ box

and clicks on his mouse.

o

A ‘near continuous’ variation of this institution, developed recently by Davis and

Korenok (2006), allows sellers a rich set of opportunities for a seller to both send and

respond to price signals. Davis and Korenok truncate sharply the maximum length of

decision periods, from 2 minutes to, say, 12 seconds, in this way increasing a tenfold

factor the number of periods that may be included in session. A series of recent

Seller ID S1 Standing PricesPeriod 4 S1 S2 S3Seconds to Close 7 4.20$ 4.30$ 4.10$

Price Offer Qty Sales Qty4 3

Forecast Maximum Price of Others$4.35 $4.30

1 $2.002 $2.003 $2.004 $2.00

Period Earnings $7.60Cumulative Earnings $26.50

Current Last PeriodHigh Forecast Prize Low Forecast Prize

Current and Past Period Prices

$3.00

$4.00

$5.00

$6.00

S1 S2 S3

Period Earnings

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00

S1

Figure 1. Screen Display for a ‘Near Continuous’ Posted Offer Institution

4

experiments indicate that the additional experience profile allowed by truncating the

maximum period length allows for the development of very substantially longer

experience profiles. In contexts where strategic opportunities are absent, Davis and

Korenok (2006) report than static Nash predictions organize outcomes far better in ‘near

continuous’ markets than in conventional posted offer markets with fewer trading

periods. In strategic contexts, Davis (2006) and Davis, Korenok and Reilly (2007) find

that sellers uniformly identify and extensively experiment with strategic opportunities,

such as unilateral market power.3 In the present context, the increased number of periods

allowed by ‘near continuous’ framework very considerably increases sellers’

opportunities to both send and respond to price signals.

Numerical and graphical summaries of the previous period’s prices and earnings

help participants to see market results quickly. The ‘Standing Prices’ displayed at center

top of Figure 1 indicate that in the previous period, period 3, S1 posted a price of $4.20

while S2 and S3 posted prices of $4.30 and $4.10, respectively. The bolded bars shown

at the bottom center of the figure make it clear that S1 posted the second highest price in

period 3. Further, comparison of the bolded bars to the light gray bars, which summarize

the previous period (period 2), shows that sellers S1, S2, S3 all reduced their prices in

period 3 relative to period 2. In period 3, S1 sold three of the four units he offered and

earned $6.60 (S1 also earned $1.00 from the forecasting game, explained below), as

shown on the ‘Period Earnings’ bar chart. The earnings chart also indicates that seller

S1’s earnings in period 3 fell relative to period 2.

2.2 Market Design. Figure 2 illustrates supply and demand arrays for the variant

of the ‘swastika’ design used here. Three sellers are each endowed with 4 units with a

constant cost of $2 per unit. Aggregate supply is thus 12 units at prices in excess of $2.

The (simulated) buyer purchases seven units at any price of $6 or less. Our

implementation of the ‘swastika’ design differs from previous implementations in that we

impose a minimum price of $3 per unit. Given the excess supply of four units, in the

3 However, Davis (2006) also observes tacit collusion even when sellers have not static market power. Davis, Korenok and Reilly (2007) find that unless sellers are re-matched into new groups each trading period, the tacit collusion allowed by extensive repetition tends to undermine the predicted comparative static effects of reducing the number of sellers from 3 to 2. The purpose of the present paper is to study in closer detail this tacit collusion.

5

competitive equilibrium all sellers post a price of $3 and earn strictly positive expected

earnings of $2.33 per trading period.

$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

0 3 6 9 12

D

Quantity

S1 S1 S1 S1 S2 S2 S2 S2 S3 S3 S3 S3

Excess Supply

SPrice

pc

Figure 2: Supply and Demand Arrays for a Three-Seller Swastika Design

Notice, that the competitive equilibrium is the unique Nash equilibrium for the

market evaluated as a stage game. To see that this outcome is an equilibrium, observe

that earnings will fall to zero for any seller who unilaterally raises price above a common

price of $3. For uniqueness, observe that at common price above $3 a seller could

increase earnings by posting a price 1¢ below the common price. For any vector of

heterogeneous prices above $3, the highest pricing seller will sell nothing.

This design is useful for studying price signaling, for three reasons. First,

previous research indicates that this design frequently stimulates tacit collusion (Cason

and Williams, 1990, Davis and Korenok, 2006). Second, the simple demand and cost

conditions help participants understand underlying market structure, thus reducing the

number of initial periods participants need to appreciate the pertinent incentives that the

design induces. Third, the design (in conjunction with the forecasting treatment

described below) helps isolate signaling activity. Given an excess supply of four units at

any price at or below $6.00, the high pricing seller in any period is certain to sell zero

units. Any seller posting a price in excess of the maximum price he or she expects rivals

to post in the subsequent period can reasonably be interpreted as sending a signal to the

other sellers.

6

2.3 Treatments and Conjectures. Our experiment consists of three treatments: a

baseline treatment, a ‘forecasting’ treatment, and a ‘types’ treatment. We describe these

in turn, below.

2.3.1. Baseline. In the baseline treatment, participants make price decisions in a

market consisting of 120 periods, using the supply and demand arrays shown in Figure 2.

Each period lasts a maximum of 12 seconds. Participants are told as common knowledge

the underlying aggregate supply and demand conditions. The final period is not

announced in advance. Decisions in the baseline treatment allow us to verify that tacit

collusion persists in this variant of the swastika design. In particular, we are concerned

that the guarantee of positive earnings, induced by our inclusion of a minimum

admissible price does not undermine the tacitly collusive behavior observed in other

markets. This is our first conjecture.

Conjecture 1: Tacit collusion, in the form of prices in excess of those consistent with the competitive equilibrium, is resilient to the inclusion of both a minimum admissible price that guarantees a positive profit, and to a forecasting treatment.

Results of the baseline treatment are further useful in that they allow an analysis

of the effects of other treatments, as discussed below.

2.3.2. Forecasting. The relatively short duration of most posted offer experiments

conducted to date has made impractical any effort to assess links between price signaling

activity and supra competitive pricing. The most important exception is an analysis by

Durham et al. (2004) of some 80 period markets. Although Durham et al. did not

explicitly design their experiment to examine price signaling behavior, the frequency of

supra competitive prices led these authors to conduct an ex post analysis of price

signaling. Durham et al. define a price signal as “any price submitted by any firm that is

greater than or equal to the lowest posted price that failed to attract buyers in the previous

period” (p. 155).

This definition, while fairly natural, suffers the potential deficiencies that it may

both include some price postings that were not intended to be signals, and may exclude

other postings that were. When prices are trending upward, the signaling definition used

by Durham et al. may errantly include as signals those prices posted by sellers who turn

out to be overly optimistic about rivals’ price raising intentions On the other hand, the

7

Durham et al. definition would miss any signals sent by a seller attempting to interrupt a

downward price trend by submitting a price postings that either maintains a current price

level, or decreases the price level by less than rivals. In an effort to more definitively

isolate price signaling behavior, we introduce here a ‘forecasting’ treatment. In this

treatment, sellers predict the maximum price their rivals will post in the subsequent

period. If a seller’s forecast is within 5¢ of the subsequently observed maximum price

posted by rivals, the seller earns a ‘high’ forecast prize of $1.00, if the seller’s forecast is

within 25¢ of the rival’s maximum the seller earns a ‘low’ forecast prize of 50¢.

Otherwise the forecast prize is zero. Chesapeake

A review of the screen display in Figure 1 illustrates the presentation of the

forecasting game to sellers. After posting a price, the cursor moves to the ‘forecast’ box.

The seller then enters a price forecast and presses ‘enter’. Forecast earnings are

illustrated graphically as supplements to the period earnings bar. For example, in Figure

1 S1’s forecast for period 3 was within 5¢ of the rival’s maximum $4.30 so seller S1’s

earnings for period 3 are supplemented by $1.00, as indicated by the supplemental shaded

box in the seller’s earnings chart.4

The forecasting game, in conjunction with a design where the highest pricing

seller sells zero units, allows a clean identification of an intended signal: Any price

above a seller’s forecast maximum price will result in sales of zero, and would be

irrational unless the seller intends to send a signal.5 To the extent that the forecasts allow

a more precise identification of price signaling activity, we can examine the effects of our

refined definition of signaling.

4 Our introduction of a forecasting game emulates the expectations elicitation techniques used in some early asset market experiments (e.g., Williams, 1987, Smith, et al. 1988 and Dwyer et al. 1993). Concerns about biasing pricing behavior with the forecasting game are somewhat diminished relative to this earlier literature because sellers here are unable to use their market decisions to affect their chances of winning the forecasting game. 5 It is possible that a risk-seeking seller could post a price in excess of his or her signal. For example, suppose a seller believed that the maximum price others would post in the subsequent period was $4.00 with probability 2/3 and $4.15 with probability 1/3. This seller’s, point forecast of the next period’s maximum price is $4.05. Posting $4.05 would maximize expected earnings from the forecasting game. In the pricing game, a risk neutral seller would maximize earnings in by posting a price of $3.99 (yielding an expected profit from pricing of $3.96). However, if the seller was risk seeking, she might post a price of $4.14 to take advantage of the increased earnings available by shading under $4.15 (a possible $4.56). Although we cannot dismiss this possibility, we doubt that it importantly affected outcomes. Behavioral evidence suggests that few participants are risk seeking.

8

Conjecture 2: Price signals measured in terms of deviations from a seller’s forecast of rivals’ prices differ significantly from price signals based on previous period price postings.

We also explore the relationship between signaling and prices.

Conjecture 3: Price signaling activity elicits higher prices.

Two separate dimensions of conjecture 3 merit discussion. First is the question of

whether or not rivals recognize signals and respond to them with higher prices. If rivals

fail to understand a signaler’s intended communications, an enhanced capacity to identify

when signals are sent may translate into relatively little in the way of price responses.

The second dimension regards the link between signaling activity and overall

price levels. Even if rivals tend to respond immediately to signals, it is not obvious that

signals will affect overall price levels. Sellers, for example, might respond to signals but

then quickly reduce prices again, resulting in a price history that does not differ

noticeably from a noisy market where signals are uncommon. We will assess both

dimensions of conjecture 3.

2.3.3. A ‘types’ treatment. Overall price levels may be a function of inherent

propensities of participants to cooperate or compete. Markets composed of ‘cooperative’

participants, for example, may generate high price levels even in the absence of signals.

Conversely, markets composed mostly of ‘competitive’ participants may generate low

price levels even if sellers signal very frequently. Here, we attempt to identify types by

ranking participants in terms of their competitiveness or cooperativeness in an initial

session. Then we invite participants who scored low on the cooperativeness scale to

participate in a second session with other low-scoring subjects. Similarly, we invite

participants who scored high on the cooperativeness scale back for a second session with

other high-scoring subjects. Our fourth conjecture regards the relationship between type

and price levels.

Conjecture 4: Types affect market outcomes. Markets composed of ‘competitive’ types generate persistently lower prices than do markets composed of ‘cooperative’ types.

9

Of course, an evaluation of ‘types’ and the effect of types on market performance

is possible only if ‘types’ are identifiable, and if type identities remain stable across the

games. This is our fifth, and final conjecture

Conjecture 5. Types are both identifiable and stable across markets.

3. Experimental Procedures.

To evaluate conjectures 1 to 5 we conduct the following experiment. In a first

series of sessions, nine (and in one instance twelve) player cohorts are invited into the

laboratory to participate in three (four) triopolies. At the outset of each session a monitor

randomly seats participants at visually isolated computers. The monitor then reads aloud

instructions, as the participants follow along on printed copies of their own. Each session

consists of two 120 period sequences, a baseline sequence and a forecasting sequence.

Prior to the first sequence, instructions explain price-posting procedures, as well as the

minimum admissible price of $3.00. Participants are also given as common knowledge

full information regarding aggregate supply and demand conditions shown in Figure 2.

To ensure that participants understand these underlying conditions the monitor elicits

responses to a series of possible price postings.6 After giving participants an opportunity

to ask questions, the first sequence begins, and consists of 120 periods each with a

maximum length of 12 seconds. After period 120, the baseline sequence is terminated

without prior announcement, and participants record their earnings.

With the exception of a few MBA and graduate economics students, participants

were volunteers recruited from upper level undergraduate business and economics classes

at Virginia Commonwealth University in the spring semester of 2006. All participants in

the initial set of sessions were ‘experienced’ in the sense that they had previously

participated in a ‘near continuous’ posted offer session, but for a different study, with

different supply and demand conditions. Earnings for the initial sessions, which lasted

between 80 and 100 minutes, ranged from $21 to $46 and averaged about $31. In the two

experienced sessions, earnings ranged from $21 to $57 and averaged $37.

6 Specifically, the monitor elicits sales and earnings calculations for the vectors ($5.50, $5.00, $4.00), ($7.00, $6.50, $6.01, and ($4.00, $4.00, $4.00). The first illustrates earnings calculations, and emphasizes that the high pricing seller is left out of the market. The second price vector emphasizes that prices must be $6.00 or less for positive earnings. The final vector explains the tie-breaking procedure.

10

Following the first sequence, a monitor remixes participants into entirely new

groups, and reads instructions for a second sequence.7 Conditions for the second

sequence match those in the first, except that the maximum period length is increased to

18 seconds and the forecasting game is added. After giving participants time to ask

questions, the second sequence began. After 120 periods, this sequence ended, again,

without prior announcement. Following the forecasting sequence, participants complete

a short questionnaire regarding the forecasting game. Upon completion of the

questionnaire, participants are paid privately the sum of their earnings for the two

sequences, converted at U.S. currency at a rate of $100 lab = $1 U.S. plus a $6

appearance fee, and are dismissed one at a time. We conducted five initial sessions, with

a total of 48 different participants. No one participated in more than a single session.

4. Experimental Results- Initial Sessions. 4.1 Overview. The mean transaction price paths for the 16 baseline and the 16 forecasting

markets, shown in Figures 3 and 4 provide an overview of results for the baseline and

forecasting sessions, respectively. Inspection of these figures provides information

pertinent to conjecture 1. Figure 3 indicates that our variants of previously investigated

swastika designs (including 3 rather than 4 sellers, full information about underlying

market conditions, as well as a minimum price that ensures positive earnings at the

competitive outcomes) do not undermine a propensity for sellers to engage in ‘tacit

collusion’. With the exception of market b3-iv (e.g, the 4th baseline market conducted in

session 3), mean transaction prices persistently varied above the $3.00 minimum. Also

noteworthy in Figure 3 is the variability of outcomes across markets. Although sellers

never engaged in stable pricing patterns, in some instances, such as markets b3-i and b5-

iii, price swings are relatively small across periods. Other markets, such as b2-i and b5-ii

are characterized by relatively slow ‘Edgeworth cycles’. In still other markets, such as

b1-i and b4-i, prices oscillate widely across periods.

Mean transaction price paths for the forecasting sequences, shown in Figure 4

parallel results in Figure 3 in that prices generally exceed the $3.00 competitive

7 In the nine person cohorts, for example, markets in the initial sequences are ordered (1,2,3), (4,5,6) and (7,8,9). In the second sequence markets shift to (1,4,7), (2,5,8) and (3,6,9). Thus, for the second sequence, each participant is in a market with participants he or she has not been paired with previously.

11

prediction, and that outcomes vary substantially across markets. A comparison of the

transaction price series across panels suggests that the addition of the forecasting

treatment does little to affect pricing decisions.8 In any case, the forecasting treatment

clearly does nothing to dampen prices in this design. This is our first finding.

b1-i

$3.00

$6.00

0 60 120

b1-ii

$3.00

$6.00

0 60 120

b1-iii

$3.00

$6.00

0 60 120

b2-i

$3.00

$6.00

0 60 120

b2-ii

$3.00

$6.00

0 60 120

b2-iii

$3.00

$6.00

0 60 120

b3-i

$3.00

$6.00

0 60 120

b3-ii

$3.00

$6.00

0 60 120

b3-iii

$3.00

$6.00

0 60 120

b3-iv

$3.00

$6.00

0 60 120

b4-i

$3.00

$6.00

0 60 120

b4-ii

$3.00

$6.00

0 60 120

b4-iii

$3.00

$6.00

0 60 120

b5-i

$3.00

$6.00

0 60 120

b5-ii

$3.00

$6.00

0 60 120

b5-iii

$3.00

$6.00

0 60 120

Figure 3. Mean Transaction Price Paths: Baseline Markets

Finding 1: Tacitly collusive outcomes persist in our version of in the swastika design where (a) sellers earn strictly positive earnings in the competitive equilibrium and (b) sellers forecast rivals maximum prices.

8 On average, mean prices in the first third of the forecasting treatment tended to be slightly higher than in the first third of the baseline treatment. These differences (which could reasonably be attributable to experience), were significant at a 5% level in only 10 of the first forty periods. Except for this initial difference mean prices in the two treatments are very similar.

12

Consider next the relationship between our refined signaling measure and the

measure used previously by Durham et al. (2004). For this comparison, we consider only

outcomes in the forecasting sequences. A first question regarding signaling behavior is

whether the refined identification of signaling (incorporating forecasts) appreciably

strengthens our analysis. Specifically, we define a ‘market-based signal’ (‘sm it‘) as a

price posted by participant i in period t that exceeds the maximum price posted in the

previous period, which in our context is the lowest posted price that failed to attract

buyers. Consistent with our analysis we define also a ‘forecast signal’ (‘sf it’) as a price

in excess of a seller’s forecast of rivals’ maximum posted price for a period. The

histogram in Figure 5 plots the incidence of each type of signal in the 16 forecasting

sequences. As is evident from the histogram, using either definition, nearly all sellers

send at least some signals. Under sf, 2 of 48 sellers sent no signals. Under sm, 3 of 48

subjects failed to signal at least once.

f1-i

$3.00

$6.00

0 60 120

f1-ii

$3.00

$6.00

0 60 120

f1-iii

$3.00

$6.00

0 60 120

f2-i

$3.00

$6.00

0 60 120

f2-ii

$3.00

$6.00

0 60 120

f2-iii

$3.00

$6.00

0 60 120

f3-i

$3.00

$6.00

0 60 120

f3-ii

$3.00

$6.00

0 60 120

f3-iii

$3.00

$6.00

0 60 120

f3-iv

$3.00

$6.00

0 60 120

f4-i

$3.00

$6.00

0 60 120

f4-ii

$3.00

$6.00

0 60 120

f4-iii

$3.00

$6.00

0 60 120

f5-i

$3.00

$6.00

0 60 120

f5-ii

$3.00

$6.00

0 60 120

f5-iii

$3.00

$6.00

0 60 120

Figure 4. Mean Transaction Price Paths: Forecasting Markets

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Notice also in Figure 5 that signaling activity under the two measures differs

substantially. For example, while sellers sent nearly 9 signals per sequence under sm,

they averaged more than 20 per sequence under sf . Further, signaling activity under sf is

far more disperse across participants. Under sf, 15 of 48 participants sent signals in at

least 30 periods (e.g., ¼ of the sequence), while under sm only 2 of the 48 participants

sent signals in at least 30 periods.

02468

1012141618

0 5 10 15 20 25 30 35 40 45 50 >50Number of Signals

sf sm sm

sfN

umbe

r of P

artic

ipan

ts

Figure 5. A Comparison of Two Signaling Measures.

We interpret the higher incidence of signals under definition sf as suggesting that

sellers tend to be considerably more interested in price coordination than the use of the sm

would suggest. Signaling to encourage other sellers to raise price from a low level will

be captured by both sf and sm. However, as mentioned above, only sf would capture

signals intended to retard the erosion of market prices from a high level. As the contract

price paths in Figures 3 and 4 suggest, both price maintenance and slow price erosion

characterize a large portion the price history in many of our markets. For this reason, the

sm definition generates systematic classification errors in a large portion of our dataset.

Further, unlike signals sent under sf, many price postings interpreted as signals under sm

were ‘unintended’ in the sense that a seller expected rivals’ prices to be higher than the

previous period’s maximum price. As seen in column (4b) of Table 1, nearly 16% of the

signals sent under sm (67 of 422) were ‘unintended’ in the sense that a seller posted a

price above the market maximum for the previous period, but below their forecast of

rivals’ maximum price.

14

While the sf signal definition reveals a high frequency of signaling, it also shows

that many signals are ineffective because they are missed by the intended recipients. If a

signaler underestimates the expected maximum price of his rivals, then his signal may

fall below the actual maximum in the upcoming period, thus masking his signal. As

summarized in column (4a) of Table 1 over 28% of signals sent under sf (276 of 982)

were ‘missed’ in the sense that the signal price is below the maximum price charged by

rivals in the subsequent period. Twenty two percent of signals sent under sm (92 of 422)

were similarly ‘missed’.

Given the frequencies of forecasting errors and the systematic error present in the

sm definition during the price erosion phases, it is not surprising that the average simple

correlation between sm and sf is only ρ=0.35, as shown in column (3) of Table 1. This is a

second finding.

Finding 2: A signaling definition based on forecasting (‘sf’) appreciably improves the identification of signals over a definition based on deviations from previous market prices (‘sm’). Definition sm both understates the intentions of sellers to maintain prices or to retard price erosion, and misidentifies as signals price increases when they are below seller’s expectations of rivals’ prices.

Table 1. Aggregate Signaling Activity and Signaling Errors

(1) Signal

Measure

(2) Number

(per Seller)

(3) Correlation

(4) Errors

(4a) Missed Signals (% of Signals)

(4b) Unintended Signals

(% of Signals) sf 982 (20.4) 276 (28.1%)

35.0, =fm ssρ

sm 422 (8.79) 93 (22.0%) 67 (15.9%)

sfl 438 (9.13) 60 (13.6%) 37.0, =

flml ssρ

sml 289 (6.02) 72 (24.9%) 51(17.6%) Key: ‘Missed Signals’ are prices that exceed forecasts, but are below the period’s maximum price. ‘Unintended’signals are prices above the previous period’s maximum price but below forecasts

15

Prior to considering the relationship between signaling activity and overall price

levels, we offer one additional observation. Many signals sent under sf are rather small

deviations above a seller’s forecast of the maximum price to be posted by rivals.

Borrowing terminology from the VCM literature, one might suggest that such instances

be viewed as a sort of conditional cooperation, where a seller ‘cooperates’ by undertaking

an increased risk of being the high pricing seller in a period. A critic might suspect that

eliminating these small differences might make sm and sf similar. This suspicion,

however, turns out not to be true. The bottom two rows of Table 1 summarize aggregate

information regarding ‘large’ signaling variants sfl and sml, where postings are counted as

signals only when they exceed the seller’s forecast (for sfl), or previous period’s

maximum (for sml) by at least $0.50. Notice that, except for the smaller incidence of both

types of signals, a large number of postings interpreted as signals under sml are still

unintended (17.6%) and the average correlation between sfl and sml, remains low (ρ =

.37).

We turn now to the relationship between signaling activity and prices. A simple

regression analysis of the type reported by Durham et al. (2004) provides one simple way

to assess the effect of prices signals on transaction prices. Specifically, for each of the

initial 16 markets, we estimate the following equation

1 1it pi it si it itp c p Iβ β− −= + + +ε (1)

where pit is the mean transactions price in period t={2, … , 120} of market i ={1, … ,

16}. pit-1 is mean the transaction price lagged by one period, itI is an indicator variable

that takes on a value of 1 if at least one seller sent a signal (under definition sf) in the

period, and εit is an i.i.d. error term with variance 2iσ . The mean transaction price

responds positively to a signal if βsi>0. Running such a regression on each of the 16

initial markets we find that βsi >0 in 14 of the 16 cases, using a 5% significance level

(two-tailed test). Thus, as Durham et al. (2004) observed (under sm ), transaction prices

do respond positively to price signals.

A larger question, regards the cumulative effects of signaling activity. If signals

exert any long term impact on prices, some direct relationship should exist between

signaling activity and price levels. We find very little evidence that this is the case.

16

Equation (2) reports results of an OLS regression of signal volume on the mean

transaction price for entire sequences. Specifically,

iV

05.0)01.0(

005.0)63.0(

88.3 2**

−=+=

RVp ii n=16 (2)

Where i it

tp p=∑ denotes the mean transaction price for sequence i. The small

and insignificant coefficient on Vi suggests that signal volumes and price levels are

essentially uncorrelated. The scattergram plotting signal volumes against mean

transaction prices per sequence illustrates visually the weakness of this relationship.

Combined, these observations form our third finding.

Finding 3: Price signals tend to raise transaction prices in the immediately following periods. This effect, however, is short lived. Across sequences, signal volumes are essentially uncorrelated with overall mean transaction prices.

$3.000 50 100 150

Signal Volume

p i = 3.88+ .005V i

Mea

n Tr

ansa

ctio

n Pr

ice

Figure 6. Mean Transaction Prices and Signal Volumes per Sequence

Signaling activity in markets illustrated as the extreme points in Figure 6 provides some

insight into the very weak relation between signal volumes and price levels. Figure 7

illustrates the sequence of contracts in market f2-i, highlighted with a circle in Figure 6.

The market generated the second highest overall mean transaction price, despite a

17

comparatively small volume of 63 signals. As suggested by the sequence of price

postings (‘ ’, ‘ ’ and ‘+’ ) and signals (‘ ’ about price postings) for market f2-i, the

relatively infrequent signals were usually successful at preserving prices at or near the

$6.00 limit.

f2-i

20$3.00

$4.00

$5.00

$6.00

0 20 40 60 80 100 1

Period

Figure 7. Sequence of Price Postings and Signals, Market f2-i. Key: ‘ ’, ‘ ’, ‘+’, price postings by sellers S1, S2 and S3. ‘ ’ a price posting that is a signal under sf.

f1-ii

$3.00

$4.00

$5.00

$6.00

0 20 40 60 80 100 1

Period

20

Figure 8. Sequence of Price Postings and Signals, Market f1-ii. Key: ‘ ’, ‘ ’, ‘+’, price postings by sellers S1, S2 and S3. ‘ ’ a price posting that is a signal under sf.

Consider alternatively, the sequence of price postings in market f1-ii, shown as

Figure 8. This market (highlighted in Figure 6 with a hollow square) had nearly twice the

signal volume of f2-i (106 signals), but very low overall mean transaction prices. Here

again, signals were often posted near the $6.00 limit. However, rivals failed to cooperate.

18

Persistent aggressive pricing by non-signaling sellers undermined signaling efforts at

$6.00 as well as persistent efforts to stave off reductions in prices well below the upper

bound of the pricing range.

5. Cooperative Types and Market Performance.

As a second dimension of this paper, we examine the effect of a basic propensity

to behave cooperatively on market performance. Specifically, we used decisions from

our initial sessions to attempt to identify the propensity of participants to cooperate.

Then we invited ‘cooperative’ and ‘competitive’ cohorts back for a second session.

Combined, Figures 7 and 8 suggest that while signaling activity is an element of

cooperative behavior, signaling volume alone is insufficient to explain price levels. A

second potentially important element of cooperative behavior includes some basic

propensity of participants to follow, or at least not aggressively undercut, price leaders.

Thus, ‘cooperativeness’ must combine a measure signaling activity with measures of the

propensity of a seller to ‘follow.’ Indeed, it is reasonable to anticipate that high signal

values will often occur precisely in cases where price leaders find cooperation difficult to

sustain.

As an index of cooperative propensity, we took a simple average of three factors

(a) the percentage of periods in the forecasting sequence that a seller sent an sf signal, (b)

the percentage of periods a seller either matched the previous period high price or acted

as a price leader in the initial (non-forecasting) sequence, (b) the percentage of periods a

seller either matched the previous period high price or acted as a price leader in the

second (forecasting) sequence.

The index, while admittedly ad hoc nevertheless has some appealing

characteristics. The first of its components assesses a subject’s propensity to act as a

price leader. The second and third components assess a propensity to follow signals.

Using decisions from both the non-forecasting and forecasting sequences captures the

robustness of this cooperative tendency in markets with different participants. Finally,

using a simple average across the three components conforms with the notion suggested

by Figures 6, 7, and 8 that while both cooperativeness and signaling activity are

19

determinants of market performance, perhaps a tendency to follow merits increased

weight.9

Despite some scheduling complications at the end of the spring semester we were

able to recruit from both tails of our index measure. Overall, index values ranged from

1.4 to 52.4 and averaged 20.3. For the nine participants in our ‘competitive’ cohort the

average index value was 9.8, and the highest value was 15.1. In our ‘cooperative’ cohort,

the lowest value was 32.8 and the average index value 38.7

The structure of the second sessions replicated exactly the initial sequences, with

a forecasting sequence following a baseline sequence. In recruiting for these second

sessions participants may have realized that we were interested in specific participants.

However, participants did not know why we were interested in their participation, or that

they were homogeneous with respect to the other people in their cohort. Earnings for

these second two sequences ranged from $27 to $57 (inclusive of a $6 appearance fee)

and averaged about $34.

Inspection of the mean transaction price series for the competitive and

cooperative markets, shown respectively in the upper and lower halves of Figure 9

indicate clearly that types heavily influence price outcomes. Mean transaction prices for

each of the six ‘cooperative’ markets exceed by substantial margins the comparable

prices for each of the six ‘competitive’ markets. Further, the visual weight of the price

spikes in competitive sequences tends to diminish the magnitude of the difference

between the cooperative and competitive groups. Table 2, which lists overall mean

transactions prices for the cooperative and competitive markets, as well as for the initial

markets, clarifies the treatment effect.

As shown in the table, relative to the baseline, transaction prices in the

‘competitive’ cohorts tend to be lower, and prices in the ‘cooperative’ cohort tend to be

higher. The differences are large. Comparing across cooperative and competitive

9 Our multi-dimensional approach is in some respects consistent with Burlando and Guala (2005). Observe that data from the initial sessions did not allow a clean division of participants into the ‘cooperative’, ‘conditionally cooperative’ and ‘free riding’ types considered standard in the VCM literature (e.g., Kurzban and Houser, 2005 or Fischbacher, Gächter and Fehr, 2001). Unlike the VCM context, nearly all subjects send some signals, and, given the cost of signaling, virtually all subjects subsequently undercut their own signals with price reductions. Thus, viewed in terms of the VCM literature nearly all participants in a pricing game are ’conditional cooperators.’ Our cooperation index represents an effort to distinguish among these players.

20

cohorts, the overall mean transaction price for the cooperative sequences, $5.30, exceeds

the comparable mean for the competitive sequences, $3.63, by $1.67, more than half the

admissible price range. The difference is significant using a Mann Whitney test (p<.004).

Competitive Markets

Cooperative Marketscol-b1

$3.00

$6.00

0 60 120

col-b2

$3.00

$6.00

0 60 120

col-b3

$3.00

$6.00

0 60 120

col-f1

$3.00

$6.00

0 60 120

col-f2

$3.00

$6.00

0 60 120

col-f3

$3.00

$6.00

0 60 120

cmp-b1

$3.00

$6.00

0 60 120

cmp-b2

$3.00

$6.00

0 60 120

cmp-b3

$3.00

$6.00

0 60 120

cmp-f1

$3.00

$6.00

0 60 120

cmp-f2

$3.00

$6.00

0 60 120

cmp-f3

$3.00

$6.00

0 60 120

Figure 9. Mean Contract Prices, Competitive Sequences (Top 6 panels) and Cooperative Sequences (Bottom 6 panels).

As the rightmost column in Table 2 indicates, the difference in mean transactions

prices does not dissipate over time. For example, focusing on the last 60 periods, the

difference in mean transaction prices across the cooperative and competitive sequences is

$1.79 ($5.26 - $3.47), slightly larger than the $1.67 overall mean transaction price

difference for the entire sequences.

21

The OLS regression reported as equation (3) more explicitly links type to market

price by regressing the average cooperation index value for the three sellers in each

market on the overall mean transaction prices for our final twelve market sequences.

)07.0()19.0(863.074.506.3 2**** =+= Rcp index (3)

As the regression results indicate, type exerts a strong and significant effect. This is a

fourth finding.

Finding 4. Types affect market performance. Transaction prices are higher in markets populated by cooperative types than in markets populated by competitive types and this effect does not diminish over time.

Table 2. Overall Mean Transactions Prices by Treatment Overall Last 60 Periods Initial Sessions (n=32) 4.02†† 3.98†† ⊕

Competitive (n=6) 3.63** 3.47** ⊕

Cooperative (n=6) 5.30** †† 5.26** ††

††, ** Unequal, p<.01, ⊕ Unequal, p<.05 (One tailed tests)

As a final substantive issue we consider whether or not our type measures are

reasonably stable across sessions. Equation (4) reports an OLS regression of the

cooperation index realization for a seller in the initial session, ‘c1’ on that seller’s

cooperation index realization for the second session ‘c2’ for the 18 subjects who

participated in a second session.

)12.0()35.0(1871.081.0017.0 2

12 ==+= nRcc (4)

Initial and terminal session cooperation index values are strongly correlated. The

coefficient on c1 (0.81) is significant and close to 1. The relative stability of index

measures across sessions is our fifth and final finding.

Finding 5: Participant types are reasonably stable across sessions in the sense that individual cooperative index values in the first sequence are highly correlated with individual cooperative index values in the second session.

Although index measures are highly correlated across sessions, the relationship is

not perfect. The scattergram of cooperation index values for the 18 participants, shown

in Figure 10, illustrates. Although ci values tend to consistently segregate behavior

22

across ‘competitive’ (hollow dot) and ‘cooperative’ (solid dot) treatments, within

treatments initial and terminal index values are not aligned perfectly with 45% line.

The variability of cooperation index values within, but not across cohort types

suggests that rivals actions may affect our measure of cooperativeness. A cooperative

participant in an initially mixed group, for example, may appear to be more cooperative

than in a group of homogenously cooperative competitors. Although we cannot dismiss

the possibility that type is not constant, we consider it more likely that our measure of

cooperativeness is imperfect. The intentions of cooperative players may involve

decisions considerably more complicated than whether or not to send signals, and

whether or not to undercut current prices. Nevertheless, we consider it remarkable that

our measure of cooperativeness was so accurate in predicting second session behavior.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Cooperation Index,1st Session

'Cooperative' Participants

'Competitive' ParticipantsCoop

erat

ion

Inde

x, 2

nd S

essi

on

Figure 10. Cooperation Index Values Across the 1st and 2nd Sessions.

6. Conclusion. This paper examines two factors that affect the success of tacitly collusive

arrangements in posted offer markets, signaling and types. To gain insight into signaling

23

activity and its effects, we modify the standard posted offer market game with a

‘forecasting’ game, in which the seller predicts the maximum price to be posted by his

rivals. This forecasting game allows us to isolate signaling behavior, because in our

design any price above the maximum posted by rivals will result in the sale of zero units.

Thus, any price above a sellers forecast must be a signal. This refined measure of

signaling reveals that sellers attempt to send price signals with a substantially higher

frequency than was measured previously (using a price in excess of the maximum price

in a previous period). Further, a reasonable number ‘signals’ under the standard

signaling measure were mistaken in the sense that sellers mis-forecasted the price

postings of rivals. Nevertheless, even with our refined measure of signaling, we find that

while price signals elicit price responses within a market sequence, on the whole, signal

volumes and overall price levels are uncorrelated. Factors other than signaling drive

pricing outcomes.

As a second dimension, we construct a ‘cooperation index’ to examine the extent

to which a subject’s ‘type’ or basic propensity to behave cooperatively or competitively

supplements signaling activity. We rank participants according to their revealed

cooperativeness. Classifying subjects by their type, we conduct a second session where

participants were collected into cohorts of ‘cooperative’ and ‘competitive’ types, and find

that type very importantly affects performance. Overall price levels in ‘cooperative’

cohort markets were much higher than in ‘competitive’ cohort markets.

The notion that inherent behavioral propensities affect outcomes in games is

certainly not a new idea in experimental economics. Indeed, as observed in the

introduction, this notion now occupies a fairly central place in the VCM literature.

However, to the best of our knowledge ‘type’ has occupied only a minor role in oligopoly

experiments. We believe our results strongly suggest that, at least in some oligopoly

contexts, type may play a primary role in determining market outcomes. Further

laboratory and field experiments in alternative market contexts are needed to more fully

assess the impact of subject type on market competitiveness.

24

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