An experimental evaluation of strategic preemption

International Journal of Industrial Organization 18 (2000) 107–135 www.elsevier.com / locate / econbase

An experimental evaluation of strategic preemption Charles F. Mason*, Owen R. Phillips Department of Economics and Finance, University of Wyoming, Laramie, WY 82071 -3985, USA

Abstract This paper reports the results of a series of two-stage, two-person noncooperative games where one player can strategically preempt the other. In one of our designs, the subgame perfect equilibrium entails complete preemption; in the other, it entails partial preemption. The data show that players tend to completely preempt when it is privately optimal. However, when partial preemption is privately optimal, a non-trivial fraction of players persist in choosing the non-preemptive structure. This may result because of occasional irrational behavior following preemptive play, which induces some dominant agents to play less aggressively.  2000 Elsevier Science B.V. All rights reserved. Keywords: Raising rivals’costs; Experiments; Subgame perfection JEL classification: C91; C92; L12; L13

1. Introduction There is a long-standing tradition that a dominant firm is capable of preemptive actions that increase its market power. Examples of such actions include precommitting to large outputs when there are sunk costs (Dixit, 1979), the investment of capital to create excess capacity (Spence, 1977; Dixit, 1980), and the use of patents to gain a technical advantage (Gilbert and Newberry, 1982). Many other examples exist; the number and diversity of such strategies is evidenced by the amount of attention devoted to their analysis in the literature (see, e.g., Tirole, 1988, chapters 8 and 9; and Gilbert, 1989). When credible,

* Corresponding author. Tel.: 11-307-766-2178; fax: 11-307-766-5090. 0167-7187 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 99 )00036-3

108

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

preemptive actions typically entail some opportunity cost for the dominant firm, while at the same time disproportionately reducing the payoffs to the potential entrant or rival firm(s). In principle there is no significant difference between strategies which seek to prevent potential entry from occurring and strategies which seek to dispatch existing rivals. In either case it is the effect of the preemptive strategy upon the profits in the continuation game that is central. If this effect is sufficiently deleterious to the rivals, the dominant firm becomes a monopolist in the continuation game. If the effect is less severe, the dominant firm increases its market power, but still faces some competition. One specific class of preemptive strategies entails manipulating industry costs. This action binds the dominant firm to a specific cost structure, and so credibly commits it to future actions. When these future actions leave rival firms with sub-normal profits, their best response is to not participate in the industry. Salop and Scheffman (1983) have termed this strategy ‘raising rival’s costs’. Examples of this strategy include: the writing of exclusionary contracts with low cost suppliers, so that the rival must turn to a more costly supplier (Krattenmaker and Salop, 1986); contracting with downstream buyers to cut off profitable distribution outlets to other firms; and the strategic manipulation of government regulations to impose differential compliance costs (Oster, 1982; Salop et al., 1984). Evidence on raising rival’s cost can be found in numerous antitrust case studies.1 Field studies aimed at identifying the importance of strategic preemption have yielded mixed results. Gilbert and Lieberman (1987) and Lieberman (1987) find some evidence that firms used capacity expansion to preempt the expansion of existing rivals or the entry of new firms.2 Masson and Shaanan (1986) find no support for such preemptive action in their study, but they do find evidence that

1

We discuss two illustrative cases in detail. In United Mine Workers vs. Pennington (85 S. Ct. 1585, 1965), Phillips Brothers Coal Company alleged that large coal operations conspired with the United Mine Workers Union to set high wages for all workers represented by the Union at all mines (Williamson, 1968). The large mines had a higher capital / labor ratio, and thus were less impacted by the agreement than small mines. To maintain earnings the smaller mines had to raise coal prices proportionately more than the bigger companies, making the smaller firms less competitive. The benefit to the Union was cooperation from the largest employers on wage negotiations. Although the court did not reach a decision on this case, it did opine that the Union could be in violation of antitrust laws if the allegations were supportable. A second example is Klur’s Inc. vs. Broadway-Hale Stores (359 US 207, 1959). Here, the Klur’s appliance store was blocked from favorably selling selected brands of home appliances because of an agreement with these appliance makers and Broadway-Hale, a rival dealer. The agreement kept manufacturers from selling to Klur’s or only selling at prices higher than those to Broadway. The Court argued that the practice was a group boycott and, therefore, a per se violation of the Sherman Act. See Krattenmaker and Salop (1986) for further discussion. 2 Rather than dominant firms taking strategic action against smaller producers, these papers find that it is typically the smaller firms who ‘preempt,’ where preemption is taken to mean expansion to take advantage of new opportunities. This is rather different from preemption to prevent existing or potential rivals from competing for existing opportunities.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

109

price-cost margins are directly linked to the height of entry barriers. This could represent evidence of limit pricing; an alternative interpretation is that higher equilibrium profits result in industries with higher entry barriers, as in Eaton and Ware (1987). In another study, West (1981) found that the historical pattern of supermarket locations in the Vancouver area supported the hypothesis that established large chains chose location preemptively. However, the pattern he uncovered also was consistent with the clustering of stores, perhaps because of distribution cost.3 Altogether, it is evident that existing industry studies do not provide clear evidence that dominant firms strategically preempt rivals or keep new firms from entering the market. In all these field studies, determining the motives of producers and the causes of changes in a market’s structure are main difficulties. This paper avoids the issue of discerning the motives behind observed behavior by constructing laboratory markets, and observing the behavior of agents under controlled conditions. Investigating the inherent tendencies of a dominant firm to strategically manipulate costs seems ideally suited for experimental markets. In experimental markets the financial environment is controlled so there is no doubt about how a rival’s profits are diminished. Also, the payoffs to producers are made very clear under selected market options. Hence the possible gains from manipulating costs are known in advance. Basic market conditions such as demand and costs are completely controlled in these laboratory environments. What is not known, at least initially, and cannot be controlled for, is the degree to which players are rational, foresighted agents. This is the presence of strategic uncertainty. Our experimental design can be described as a two-stage, two-person noncooperative game. In stage 1, player I (the incumbent) chooses the cost structure: option A, B or C. Player I may have to pay for this choice. Costs are symmetric in structure A, while B and C are increasingly asymmetric. When moving from structures A to C, both players’ costs increase, but I’s increase less. Player I’s cost advantage is so dramatic in cost structure C that the Cournot / Nash equilibrium entails player E (the entrant or rival) selecting zero output. Hence case C represents complete preemption of the smaller rival if the firms are Nash players. In stage II, players I and E simultaneously make choices from payoff tables in the designated option. All payoffs are reported to the players. The subgame perfect equilibrium in this game depends on the amount player I pays for the options. When no costs are attached to the options, the option selected in the subgame perfect equilibrium is C. But when C is sufficiently costly, option B is the subgame perfect outcome. This paper documents the tendency of a dominant producer to choose the

3 West (1981) indicates that the power of these two alternative explanations turns on the manner in which the greater Vancouver area grew over time. With rapid or lumpy growth, his results favor preemption.

110

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

subgame perfect outcome when option C is privately optimal; this is behavior that strategically preempts. We also observe behavior when option C is costly, and option B is the best cost structure for the I player. Under these conditions, a significant percentage of dominant agents choose option A, and do not preempt at all. One explanation for this result is that some of the agents behave ‘irrationally’ as E players. This behavior on the part of the representative smaller firm causes the dominant firm to play less aggressively than in the subgame perfect equilibrium.

2. Experimental design The subject pool for our experiments consisted of students recruited from undergraduate economics and finance classes at the University of Wyoming. Each experimental session involved an even number of subjects. Subjects reported to a room with linked computer terminals at each seat. Individuals were given a set of instructions, provided in an appendix at the end of the paper, that described the experimental procedure; a monitor read these instructions aloud as the participants followed along on their copy. The instructor explained how to read a payoff table, and find earnings at the intersection of the player’s row and the column chosen by ‘the other participant.’ Before starting the experiment, three practice periods were conducted using a sample set of I and E payoff tables.4 A practice period consisted of subjects all playing a designated role, with a monitor playing the role of ‘other person.’ In the first sample trial, the monitor played the role of the I player and subjects played the role of the E player. In the second sample period the subjects played the role of the I player and the monitor played the role of the E player. For both of these trial periods the players’ payoff tables were different; the I player’s table corresponded to relatively lower unit costs and higher profits. In the last sample period the monitor played the role of the I player, with identical I and E payoff tables. After these sample runs, subjects were instructed to study the three payoff table options that would be used when the experiment got underway. These payoff tables also are included in the appendix at the end of the paper. As they studied, subjects were asked to complete a two-page questionnaire that took 7–10 minutes to answer.5 The questionnaire consisted of four questions for each of the three payoff table options. For a specific payoff option, the question

4 These tables, along with the questionnaire discussed below and the experimental data, are available at the URL http: / / www.econ.ku.dk / cie / ijio / exptsum.htm 5 The complexity in this experiment required subjects to think carefully about their rival’s behavior. This questionnaire was designed to aid them in these selections. The alternative is to allow learning to proceed as subjects play the game. In a pilot session, we tried both approaches. While the results of these pilots were qualitatively similar, the session without the questionnaire took 30 min longer to complete. In the interests of brevity, we chose to use the questionnaire in our design.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

111

designated each subject’s role as an E player, and asked them to (i) predict the other player’s choice and (ii) to make their choice. This pair of questions was then repeated with subjects designated as I players. Because we are trying to capture the flavor of a one-shot game, and not an infinitely repeated game, the experiment consisted of a known, fixed number of periods. At the start of each odd-numbered period, the computer randomly designated half the subjects as I players and randomly paired I and E players. At the start of each even-numbered period, roles were reversed and each I player was matched with an E player, who was not the subject’s rival in the preceding period. Subjects never knew their rival’s identity in any period. It was announced at the start of the experiment that individuals would be randomly re-paired at the beginning of each period, and that they could expect to be I players half the time. In all three payoff options inverse demand was linear, with an intercept of 12 and slope of 2 (1 / 4). Firms had constant and possibly different marginal costs across the options. For option A, the marginal cost combinations were c I 5 0 5 c E , where c I (c E ) is the I(E) player’s marginal cost. For option B, the marginal cost combinations were c I 5 0.625 and c E 5 2.50. Finally, for option C, the marginal cost combinations were c I 5 2 and c E 5 7. Subjects were paid in tokens at a conversion rate of 1000 tokens5$1.00. We have rescaled choices by 7 units, so that the choices 1 through 14 listed on the rows and columns of the payoff tables correspond to outputs of 8 through 21. However, a choice of zero always corresponded to an output of zero. The Nash equilibria and associated payoffs for each option are presented in Table 2.6 Option A gives players equal market shares at the Nash equilibrium. Option B is partial preemption. At the Nash equilibrium for this option, player I has a 63% market share. Finally, option C corresponds to complete preemption. At the Nash equilibrium player E chooses 0 on the payoff table, so player I’s market share is 100%. In all cost structures the payoff tables give players the opportunity to not participate at all in the market, by making a choice of 0. Our data come from four experimental sessions. In sessions 1 and 2, I players could select any of the three options at no cost; we shall refer to these experiments as ‘design 1’ in the discussion below. There were 14 subjects in session 1 and 10 subjects in session 2. The choice of options A and B remained free to player I in sessions 3 and 4, but option C had a cost of 400 tokens; these experiments will be

6

It is straightforward to derive the Cournot equilibrium outputs for each option. With option A, each player selects an output of 16, which corresponds to each player choosing 9 and earning 640 tokens. Under option B, the Cournot equilibrium entails q1 517.667 and q2 510.167; after rounding this gives choices of 11 and 3 on the payoff tables. The corresponding payoffs are 788 tokens for the I player and 250 tokens for the E player. (There is a second equilibrium, though only in the ‘weak-best response’ sense; it entails choices of 10 and 4). Finally, with option C the equilibrium outputs are q1 520 and q2 50, or choices of 13 and 0, respectively. Here, earnings are 0 tokens for the E player and 1000 tokens for the I player.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

112

referred to as ‘design 2’ below. There were 14 subjects in each of these sessions. There were 40 repetitions of the game in the first three sessions and 50 repetitions in the fourth session. In theory, the I player should compare the Nash equilibrium payoffs across the three options, and choose that option with the largest equilibrium payoff. Player I’s payoffs in design 1 are highest in option C, so that option is part of this design’s subgame perfect Nash equilibrium. However, the increase in equilibrium payoff between options B and C is smaller than 400, so that option B is the subgame perfect Nash equilibrium choice for design 2. We denote the Subgame perfect Nash equilibrium option choice with an asterisk in Tables 1 and 2. Uncertainty regarding player E’s rationality complicates player I’s decision problem. To illustrate, suppose there is a chance that E will respond to an asymmetric payoff structure (either B or C) by producing more than his or her Nash equilibrium amount, but that E will respond to the symmetric option A by selecting the Cournot / Nash output. This could arise because E has a strong aversion to perceived profit inequities. In this setting, one would expect the I player to form a prediction of the probability that player E is rational, and to then select the option with the largest expected payoff. The possibility of facing an irrational opponent can induce player I to choose option A if the subjective appraisal of E’s rationality is sufficiently low. It is also possible that the I player is irrational. While potential irrationality of the I player may impact the ultimate pattern of play, it is not clear how one should model the first stage choice during which the I player decides the cost structure. One possibility is that I players engage in a form of forward induction. The reasoning goes as follows: if player I selects an asymmetric cost structure, then he or she earns a large fraction of the industry profits. If instead player I chooses the Table 1 Sample frequencies of stage 1 option choices Option Design 1 A B Ca Total no. of choices Design 2 A Ba C Total no. of choices a

Entire experiment

Through round 10

After round 10

177 (36.87%) 55 (11.46%) 248 (51.67%)

127 (52.92%) 27 (11.25%) 86 (35.83%)

50 (20.83%) 28 (11.67%) 162 (67.50%)

480

240

240

313 (49.68%) 246 (39.05%) 71 (11.27%)

144 (51.43%) 99 (35.36%) 37 (13.21%)

169 (48.29%) 147 (42.00%) 34 (9.71%)

630

280

350

Denotes the option choice in the subgame perfect Nash equilibrium.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

113

Table 2 Sample statistics of stage 2 output choices Option

Design 1 A

B

C*

Design 2 A

Player

Nash equilibrium

Entire experiment

Through round 10

After round 10

Choice

Profits

Choice

Profits

Choice

Profits

Choice

9.802 (3.068) 8.508 (3.116) 9.927 (2.782) 5.200 (2.276) 12.57 (1.557) 0.867 (2.468)

638.7 (159.1) 579.0 (155.6) 669.2 (134.5) 265.6 (97.60) 843.4 (252.1) 281.24 (195.5)

9.622 (3.162) 8.268 (3.163) 9.407 (3.634) 5.259 (2.119) 12.01 (2.399) 1.198 (2.472)

646.6 (164.2) 586.4 (161.2) 645.3 (158.2) 287.7 (129.1) 731.7 (256.2) 2118.7 (191.7)

10.26 (2.763) 9.120 (2.903) 10.43 (1.400) 5.143 (2.416) 12.86 (0.634) 0.691 (2.448)

618.4 (143.3) 560.4 (138.5) 692.1 (101.8) 244.3 (41.54) 902.7 (228.8) 261.35 (194.9)

9.939 (2.190) 9.115 (2.385) 10.52 (2.311) 6.000 (3.016) 12.66 (0.731) 1.028 (2.461)

620.6 (108.3) 585.3 (99.59) 644.6 (138.6) 225.0 (93.59) 818.1 (248.5) 296.2 (178.7)

9.549 (2.374) 9.194 (2.657) 9.990 (2.880) 6.505 (3.154) 12.81 (.562) .649 (1.437)

616.0 (121.1) 594.0 (114.1) 616.5 (148.9) 235.3 (116.2) 844.8 (217.4) 270.89 (116.3)

10.27 (1.960) 9.047 (2.123) 10.873 (1.743) 5.660 (2.870) 12.50 (.849) 1.441 (3.173)

624.5 (95.91) 577.9 (84.57) 663.6 (127.8) 218.1 (73.80) 789.1 (275.5) 2123.7 (224.7)

I

9

640

E

9

640

I

11

788

E

3

250

I

13

1000

E

0

0

I

9

640

E

9

640

I

11

788

E

3

250

I

13

1000

E

0

0

B*

C

Profits

* Denotes the option choice in the subgame perfect Nash equilibrium.

symmetric cost structure, player E might expect player I to behave aggressively in the second stage, so as to obtain a similarly large share of industry profits. In this case, player E will choose a smaller output than the Cournot level in the symmetric structure, which allows player I to earn profits above the Cournot level. Alternatively, the I player may feel that he or she is ‘owed’ something by the E player in the symmetric structure, and so tends to produce more than the Cournot level. Either of these examples of irrationality could induce player I to play option A.

3. Overview of results We start our discussion of the experimental results by describing various basic statistics. To this end, we present information for the entire experiment, and then

114

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

divide the results into the first 10 rounds and all rounds after the tenth.7 For each design, Table 1 displays the number of times and frequency that an option was selected in the first stage of the game. Table 2 shows the average quantity choice for each type of player, along with the standard deviation of these choices, in the second stage of the game. These summary statistics are grouped by first stage option choice and by design. Data are reported in ‘rounds’ which combine two periods (i.e., 1 and 2, 3 and 4, and so on). As we noted above, each subject was an I player exactly once in each round, so by focusing on rounds we are able to compare subjects with the same experience. Referring to Table 1, we see that the subgame perfect option (C) was selected slightly more than half the time in design 1, and that there was a significantly larger tendency for I players to choose option C in the second half of the experiment. The null hypothesis that the distribution of choices is the same in each half of the experiment may be tested using a x 2 -test. Under the null hypothesis, the test statistic has a x 2 distribution with two degrees of freedom (Mood et al., 1974, pp. 448–449). In the present application, we compute a test statistic of 56.8, which is substantially larger than the 5% critical value of 5.99. Thus, we reject the null hypothesis with great confidence. We conclude that subjects selected the subgame perfect option choice more frequently as they gained experience. In design 2, the I players chose the subgame perfect option (B) a bit less than 40% of the time. Again there seems to be a tendency to choose this option more frequently as experience is gained; even so, and in contrast to participants in design 1, subjects in design 2 consistently chose option A more frequently than the subgame perfect option. When we compare results from the first ten rounds to behavior after round 10, we cannot reject the hypothesis for design 2 that the distribution of option choices in the early stages was the same as the distribution of option choices in the later stages. The x 2 statistic is 3.8, which is not significant at conventional levels. Stage two output choices and earnings are summarized in Table 2. We observe that player I outputs within a given cost structure are qualitatively the same across designs. In particular, the average I player choice in design 1 is statistically indistinguishable from the average I player choice in design 2, for each of the three cost structures. On the other hand, average E player choices in design 2 are larger than the corresponding choices in design 1, for each cost structure. These differences are statistically significant for structures A and B, with t-statistics of 2.25 and 2.59, respectively.8 However, a comparison of averages before and after

7

In design 1 and the first session of design 2, there are 10 further periods; in the second session of design 2 there are 15 further rounds. 8 In calculating the t-statistics for differences in average choices, we make use of the fact that the variance of the average choice is the sample variance divided by the number of observations. It may be noteworthy that the E players’ average choice over the first 10 rounds differed significantly between the two designs for cost structures A and B, but not for the final rounds.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

115

round 10 reveals that these differences are largely attributable to behavior in the earlier rounds. It is less clear whether E player behavior is persistently different across the two designs; we provide a more careful analysis of this issue in Section 5. It is interesting to compare average E player output choices in the subgame perfect cost structure with the corresponding Nash equilibrium quantity choices for the two designs. In design 1, where the subgame perfect cost structure is C, the average E player choice does not differ much from the Nash equilibrium choice of zero. Furthermore, this divergence appears to be shrinking over time. In design 2, where the subgame perfect cost structure is B, the average E player choice is substantially larger than the corresponding Nash equilibrium quantity. While this divergence is less pronounced after round 10 than before round 10, it persists throughout the entire experiment. The contrast between these two results is crucial for understanding player I option choices. In design 1, outcomes are quite close to the Nash equilibrium, and so the gains to the I player from selecting the subgame perfect cost structure over the symmetric structure are large. In design 2, outcomes are not close to the Nash equilibrium, so I players do not gain much by choosing the subgame perfect cost structure. Whether E players in design 2 pick outputs above the Nash equilibrium level in structure B out of resentment, or in an effort to dissuade I players from choosing the asymmetric option, it is clear that this aggressive behavior is fairly successful at dissuading I players from exploiting their first-mover advantage.9 By contrast, any such attempts are largely unsuccessful in design 1, and so become relatively rare toward the end of the sessions. In light of the averages we discussed above, it is not surprising that I players typically earn less in design 2 than in design 1. In design 2, the typical I player earns profits in cost structure A that are only slightly smaller than profits in cost structure B. Both profit levels are substantially larger than profits from structure C (net of the sunk cost of 400 tokens). This similarity in A and B profitability is somewhat less apparent in the final stages of the experiment, which may explain the slight upward trend in the percentage of I players choosing option B during the final rounds of design 2. By contrast, average I player profits in design 1 were consistently larger in cost structure C than in either of the two alternative cost structures. In order to observe trends, we present a graphical summary of the results as a complete time series. Data are again reported in rounds. Figs. 1 and 2 illustrate the choice of cost structure for the I player in the two designs. In both diagrams, we graph the fraction of I subjects choosing each option, labeled as PRA (proportion

9 In the context of our experimental design, a little uncertainty about the rationality of one’s opponent is likely to go a long way. For example, if player E selects ‘1’ in Table C, player I’s profits at the Nash choice (13) are reduced by 400 tokens, or 40%. The E player forfeits 160 tokens in this venture. If E’s motivation were to ‘punish’ player I for choosing Table C, selecting ‘1’ would be a fairly efficient way of doing so.

116

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

Fig. 1. Option choices in design 1.

A), PR B , and PR C . In these figures, the time series for the option associated with the subgame perfect strategy is the solid line. Fig. 1 illustrates behavior in design 1, and shows that about 90% of the I subjects were choosing option C by round 20 (periods 39 and 40). The remainder were mostly choosing option A. Nash profits for the I player were highest in the C cost structure and, therefore, choosing C was subgame perfect. It apparently took

Fig. 2. Option choices in design 2.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

117

subjects some time to realize that C was most profitable, because at the outset over 80% of the subjects chose option A. It is not until after 10 rounds of choosing a cost structure that option C is chosen by the majority of I agents. Fig. 2 illustrates behavior in design 2. With the 400 token charge for choosing option C, player I’s Nash earnings from Table C drop to 600. The most profitable Nash equilibrium for player I is now associated with cost structure B. As with design 1, most subjects (70%) begin by choosing cost option A. After about 15 rounds roughly 40–50% of the subjects are choosing option B. However, the proportion selecting B does not rise above 70% during the course of these sessions; a substantial fraction (25% or more) persist in choosing option A. Figs. 3 and 4 present information on I player earnings under each of the three options for each round of the game. In these diagrams, the time series labeled as pk represents average earnings by round under option k5A, B, or C. As in Figs. 1 and 2, the time series for the option associated with the subgame perfect strategy is the solid line. Fig. 3 corresponds to design 1, and so parallels Fig. 1; similarly, Fig. 4 parallels Fig. 2. Both diagrams provide evidence of irrationality and convergence tendencies. Upon studying Fig. 3, it is easy to see why option C came to be selected by the majority of our subjects: average earnings are markedly higher with C than either A or B. We note that average payoffs were consistently below Nash levels for all three options, which is consistent with overly aggressive behavior by E subjects. Even so, average earnings under C rise steadily towards the Nash level of 1,000 tokens during the course of the experiment. Fig. 4 facilitates an explanation of the market structure choices in design 2. As in Fig. 3, average earnings under the option associated with the subgame perfect

Fig. 3. Average payoffs to player I in design 1.

118

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

Fig. 4. Average payoffs to player I in design 2.

strategy (here, option B) rise over time, and are larger than the other two options by the end of the experiment. Nevertheless, because of the frequency of aggressive (irrational) play of the E agent, earnings for the I agent tend to be well below the Nash level of 788. For most of the experiment, average earnings under option A are slightly larger than those under option B, which explains why subjects were less enthusiastic about the privately optimal strategy than in design 1. While earnings under option B rose above those under option A near the end of the experiment, this difference was small enough that a significant fraction of subjects persisted in selecting option A. An obvious question is then: can one infer that subjects were ultimately moving toward the subgame perfect strategy? In other words, what is the ultimate proportion of I players that select the subgame perfect option in the first stage of our game? Our econometric analysis below is designed to estimate such asymptotic behavior.

4. Econometric analysis We are principally interested in two issues: do the I players ultimately select that option associated with the subgame perfect equilibrium? And, in the second-stage quantity choosing game, what are the ultimate equilibrium outputs? We answer the first of these questions by treating the vector of frequencies with which each option is selected as a Markov chain, and identifying the asymptotic distribution of choice probabilities. A variation on pooled cross section / time series analysis is utilized to investigate the second question.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

119

4.1. Selection of market structure There are a variety of factors that might influence a subject’s option choice. One imagines that I players choose the option that yields them the largest expected payoff (or utility derived from that payoff). Alternatively, subjects might be motivated by concerns of fairness, as suggested by the vast literature on ultimatum games.10 It also is plausible that player choices are subject to inertia, i.e., that current option choices are linked to their previous option choice, or to the choices made in the corresponding second stage. Finally, we expect that subjects are inclined to experiment with various possibilities in earlier rounds, but settle down in later stages, and so converge towards some equilibrium over time.11 In light of the wide range of possible models, we do not base our analysis on any one learning model. Instead, we follow the approach taken by Friedman (1967), and model the frequencies of option choices as a vector of probabilities. We then regard this probability vector as following a linear Markov chain, so that the current vector is linearly related to the immediately preceding probability vector. Formally, we let P denote the transition matrix, where pjk , the element in the jth row and kth column, is the probability that option j will be selected in round t 1 1 given that option k was chosen in round t. Then the vector of frequencies at time t 1 1, x t 11 , is related to x t as follows: x t 11 5 P x t .

(1)

The asymptotic distribution, x*, satisfies x* 5 P x*. To estimate the asymptotic distribution, we must first estimate the elements in the transition matrix. To this end, we identify all observations where an I player chose option A in his or her last turn as an I player. Let the total number of such observations be nA . In the same manner we define n B and n C , the total number of choices of option B or C, respectively. From the set of observations where option k5A, B or C was selected in the previous round, we determine the number of times option A is then selected; call this number nAk . Similarly, we identify the number of times options B and C are selected; let these numbers be n Bk and n Ck , respectively. Then define pjk 5 n jk /n j ; this is the sample frequency with which an agent who chose option k in some round t then chose option j in round t 1 1. In producing this set of estimated frequencies, we use three samples. In the first, all observations are considered. This gives rise to the estimated transition matrices

10 For more on the relation between ultimatum games and preemption games, see Mason and Nowell (1998). This paper also provides a detailed discussion of the motivation for, and empirical analysis based on, a model that links option choices to anticipated payoffs. 11 In their analysis of learning in games of imperfect information, Kalai and Lehrer (1993) show that play ultimately converges to an underlying Nash equilibrium.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

120

Table 3 Transition matrices and asymptotic distributions Design 1 At21

Asymptotic distribution (x*) Bt21

Ct21

Entire experiment At 0.6379 Bt 0.1092 Ct 0.2529

0.2727 0.3637 0.3636

0.1321 0.0617 0.8062

0.2983 0.1087 0.5930

Through round 10 At 0.6864 Bt 0.1102 Ct 0.2034

0.4167 0.2917 0.2916

0.2027 0.0676 0.7297

After round 10 At 0.5106 Bt 0.0851 Ct 0.4043

0.1786 0.4286 0.3929

0.0922 0.0567 0.8511

Design 2

Asymptotic distribution (x*)

At21

Bt21

Ct21

At Bt Ct

0.7349 0.2289 0.0362

0.2577 0.6701 0.0722

0.1428 0.1905 0.6667

0.4629 0.4002 0.1368

0.4387 0.1112 0.4501

At Bt Ct

0.6574 0.2963 0.0463

0.3205 0.5513 0.1282

0.2333 0.2334 0.5333

0.4634 0.3849 0.1517

0.1731 0.0982 0.7287

At Bt Ct

0.8000 0.1769 0.0231

0.2000 0.7714 0.0286

0.0645 0.1290 0.8065

0.4603 0.4225 0.1172

in the first block listed in Table 3. The second approach uses observations from the first 10 rounds, and so is based on rounds where both t and t 1 1 lie between 1 and 10 (i.e., t 5 1, . . . ,9). The estimated transition matrices from this subset of the database are presented in the second block in Table 3. The third subset we use is based on observations after round 10 (through round 20 in design 1 and the first session from design 2, and through round 25 in the second session of design 2). The estimated transition matrices from this subset of the database are presented in the third block in Table 3. For each sample, we use the estimated transition matrix to compute the asymptotic distribution; this is presented in the column immediately to the right of the corresponding transition matrix. Consider first the transition matrices for design 1. There are three remarks we wish to make based on these estimated matrices. First, the diagonal element associated with the subgame perfect option is larger than the diagonal elements associated with the other two options. Second, we observe a significant amount of attrition away from options A and B, as evidenced by the relatively small estimated values for pAA and pBB . Third, it is apparent that subjects were more likely to migrate into option C than out of option C. The estimated transition probabilities into option C, pCA and pCB , are both relatively large, while the estimated transition probabilities from option C, pAC and pBC , are both relatively small. In light of these remarks, it is not surprising that option C is the most important choice in terms of limiting choice probabilities. In addition, we note that this limiting probability is larger when one restricts attention to the second half of the experiment. Such a focus seems appropriate in light of our desire to identify

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

121

the ultimate choice probability and the apparent differences in choice behavior between the first and second parts of the experiment. Now consider the transition matrices for design 2. Unlike design 1, the diagonal element associated with the subgame perfect option choice is not larger than the other two diagonal elements. In addition, after round 10 the tendency to switch from option B to option A, pAB , is larger than the tendency to switch from A to B ( pBA ). Accordingly, we note that the limiting distribution places more weight on option A than on option B. The results from the Markov chain model are largely consistent with the observations we made in Section 3 above. However, a comparison of the estimated asymptotic distributions based on observations after round 10 to the sample frequencies for these later rounds (the last column in Table 1) reveals some subtle differences for design 1. In particular, the sample frequency associated with option C is somewhat smaller than the estimated limiting probability (0.6528 vs. 0.7077). The estimated limiting probabilities of the other two choices, on the other hand, are each smaller than the sample frequencies. If anything, the picture painted by the initial discussion of basic statistics understates the importance of the tendency to select the subgame perfect option in the later stages of design 1. There is no such evidence of convergence toward the subgame perfect option in design 2. Indeed, the estimated limiting probability associated with option B is only slightly larger than the sample frequency after round 10. One plausible explanation for these results is that the stage 1 option choice is linked to anticipated profits: subjects in design 1 anticipated the subgame perfect option choice would deliver larger profits than the alternatives, while subjects in design 2 were less convinced that the subgame perfect option choice was most profitable.12 There are interesting comparisons between our experiments and earlier studies of predatory pricing. These earlier studies indicate a mixed signal regarding the empirical importance of predatory pricing. As in our design 2, predation is relatively uncommon when the first mover anticipates a relatively small gain (Isaac and Smith, 1985; Harrison, 1988). But like our design 1, when the potential gains are more significant, predatory behavior is quite common (Jung et al., 1994). Perhaps there is a positive threshold return that is required before player I selects the subgame perfect cost structure. If the increase in equilibrium profits between the symmetric structure and the subgame perfect structure is smaller than this

12

For example, in the ‘reinforcement learning’ model subjects predict the profitability of the first stage choice on the basis of average past performance. Under this view, choices that yield higher than anticipated profits become more common in future play (Roth and Erev, 1995). We tested this model using a logit analysis of the option choices, using average past profits for each option as explanatory variables. The results of this analysis, which are available upon request, support the reinforcement learning model.

122

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

threshold, player I takes the relatively safe route of choosing option A. But if the potential gains are large enough, as in our design 1, then the potential for irrational responses by the E player does not undermine the tendency for the I player to pick the subgame perfect option.

4.2. Output choice The next phase of our analysis is the evaluation of subjects’ quantity choices. Here, we segregate by the I or E role. This allows us to compare I and E choices in each option, as well as comparing I (or E) player choices across options. Because of the random re-pairing feature in our experiments, the games are formally equivalent to one-shot games, as opposed to repeated games. We model quantity choices as subject to inertia, in a manner similar to the evolution of option choices in stage 1. If learning takes time, but players ultimately converge to the relevant Nash equilibrium, then imperfect information could cause deviations from ultimate equilibrium behavior in the short term.13 We would then expect to see choices converge to Nash behavior after a sufficient period of time. One can model the evolution of choices over time as a function of their earlier experience. In particular, we model each subject’s period t choice as an I player with cost structure k (5A, B, or C) as a function of the last choice he or she made as an I player and the choice made by his or her last E rival player when make from cost structure k.14 Likewise, each subject’s choice as an E player in structure k is related to his or her last choice as an E player in that structure and the choice made by the associated I player. Let us write subject i’s round t choice playing role r with option k as Q itkr , with k5A, B, or C and r5I or E. Let t9 be the most recent round in which subject i played role r and the cost structure was also k. Write the choice that i made in round t9 as Q it 9kr , and let the choice made by i’s rival in t9 be Q jt 9kr . Then our regression model is Q itkr 5 gkr 1 dkr Q jt 9kr 1 fkr Q it9kr 1 ´itkr ,

(2)

where ´itkr is a mean zero disturbance with E[´itkr ´mskr ] 5 0 if i ± m or t ± s, 2 2 E´ tkr 5 s kr , for k5A, B, C and r5I, E. Thus, we analyze six regression equations.

13

In Mason and Phillips (1998), we develop an evolutionary model of subjects’ predictions, and evaluate the manner in which their beliefs evolve over time within the context of a pre-specified cost structure. A main finding of that paper is that the evolution of subjects’ predictions did lead them to the true underlying Nash equilibrium. 14 This is consistent with a dynamic reaction function or some type of learning. For elaboration on these points, see Mason et al. (1992) or Phillips and Mason (1992).

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

123

Long run, or ‘steady state’, equilibria are obtained for each of the three options in each of the two designs by considering the equations for I and E players in tandem. If Q ek I and Q ek E are the steady state choices for I and E players under option k, they must satisfy (Fomby et al., 1988) Q ek I 5 (gkI 1 dk I Q ek E ) /(1 2 fkI ),

(3)

Q ke E 5 (gk E 1 dk E Q ke I ) /(1 2 fkE ),

(4)

k5A, B, C. From Eqs. (3) and (4) it is easy to calculate these equilibrium values as Q ek I 5 [gkI (1 2 fkE ) 1 dk Igk E ] /D,

(5)

Q eE 5 [dk Egk I 1 gk E (1 2 fk I )] /D,

(6)

where D 5 (1 2 fk I )(1 2 fk E ) 2 fk Idk E . Table 4 reports the results of regression analysis based on this model. We report estimates of gkr , dkr , and fkr for k5A, B, C and r5I, E, along with their standard errors, for both designs. We also tabulate the implied steady state choices, and associated standard errors (calculated in accordance with Corollary 4.2.2 in Fomby et al., 1988; p. 58). Note that the impact of the subject’s own past choice is significantly more important, both statistically and numerically, than the impact of the preceding rival’s choice. This holds true for both types of player in each cost structure, and for both designs. As with the I player’s first stage choice, it is clear that subjects’ output choices are subject to a good deal of inertia. That said, the estimated f coefficients are significantly smaller than one in every case, indicating that subjects’ output choices are not non-stationary processes. Comparing steady state choices across designs, we see that I player choices in cost structures B and C are virtually identical; indeed, one cannot reject the hypothesis of identical steady state choices across treatments for any of the three cost structures. In addition, we note that player I choices are indistinguishable from the one-shot Cournot equilibrium choices in most cases; the exception is the player I choice in cost structure A for design 2, where the choice is slightly larger than the Cournot prediction. As with the sample averages we reported above, there appear to be some slight differences in steady state choices for E players between the two designs for cost structures B and C. The differences in steady state choices between designs are statistically unimportant for all cost structures, which suggests that any differences in behavior between the two treatments tend to disappear over time. E player choices also are statistically indistinguishable from the Nash prediction for structures A and C, but are significantly larger than the Cournot output of 3 in cost structure B; this is true in both designs. We conclude that E behavior was more aggressive than predicted by the Cournot model in the cost structure corresponding

124

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

Table 4 Quantity choice estimates, steady state analysis Parameter

gAI dAI fAI gAE dAE fAE e C AI C eAE gBI dBI fBI gBE dBE fBE C eBI C eBE gCI dCI fCI gCE dCE fCE C eCI C eCE

Design 1

Design 2

Estimate

Standard error

Estimate

Standard error

4.393 20.0362 0.5761 4.393 0.0713 0.4346 9.5952 8.9787 3.521 20.0792 0.4360 5.5451 20.0479 0.1242 10.743 4.7343 11.559 20.0144 0.0927 0.0676 0.0422 0.5411 12.720 1.3176

0.8210 0.0567 0.0697 0.7021 0.0606 0.0718 1.046 1.088 1.252 0.0935 0.1529 .5489 0.0634 0.0582 1.638 0.7009 0.6955 0.0315 0.0548 0.2626 0.0877 0.0622 0.5994 1.899

5.940 20.0065 0.4126 6.327 20.0612 0.3679 10.013 9.0402 5.481 0.0324 0.4735 3.3389 20.0535 0.4978 10.749 5.5023 3.1526 20.0293 0.7554 2.4350 20.1677 0.5177 12.817 0.5922

0.6484 0.0482 0.0517 0.7256 0.0578 0.0718 0.5086 0.6021 0.7114 0.0431 0.0576 0.9322 0.0750 0.0563 1.707 0.9811 0.9968 0.0222 0.0784 4.184 0.3259 0.2340 1.731 1.424

to partial preemption.15 This overly aggressive behavior may well have convinced a number of subjects in design 2 not to pursue partial preemption when they held the role of I player.16 By contrast, there is little indication of such aggressive behavior in cost structure C, and so I players in design 1 were more likely to settle on the subgame perfect option choice.

15

Mason et al. (1992) report similar results from experiments with asymmetric costs and repeated play. There, those subjects with higher costs (akin to our E players) made choices that were larger than their Cournot output. Subjects with lower costs (akin to our I players) responded by choosing outputs that were smaller than the Cournot level, and so earned profits that were less than the Cournot level. The predictive accuracy of the Cournot model in experiments with random re-matching of participants has also been noted by Holt (1985), and Palfrey and Rosenthal, 1994). 16 Our results are also analogous to Ultimatum game experiments, in that our I players decline to fully exploit their first-mover advantage, perhaps for fear that the E player will take an action that drives down the I profits. For further discussion on the relation between Ultimatum game experiments and sequential move preemption experiments, see Mason and Nowell (1998).

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

125

5. Discussion These experiments were explicitly designed to test the proclivities of agents to strategically exploit preemptive power by manipulating industry costs to their advantage. Two findings are of particular interest. First, subjects generally exploit this power, to the extent that they will completely preempt their rivals in situations where it is part of the subgame perfect strategy, as in design 1. Second, a substantial fraction of subjects do not partially preempt their rivals (i.e., keep their rival’s market share small) when it is part of the subgame perfect strategy, as in design 2. Finding that subjects choose option C when it is privately optimal to do so does not provide evidence that dominant firms will preempt in a coldly rational manner; finding that subjects choose option C when it is privately optimal to do so but not when it is suboptimal provides more support for the empirical relevance of the preemption strategy. That ultimately such subjects most frequently select the privately optimal option, namely B, in this latter context confirms the presence of the behavior. Nevertheless, there remains some lingering doubt as to the pervasiveness of strategic preemption behavior, since a non-trivial fraction of subjects selected option A when option B was privately optimal. Finally, there is some evidence that Nash behavior accurately predicts the second stage, quantity choosing equilibrium, though a significant set of subjects appeared to behave irrationally. The combination of privately optimal option selection in stage 1 and Nash outputs in stage 2 is supportive of the subgame perfection refinement. It is of some interest that subjects placed in the E role chose more aggressively when confronted with asymmetric payoffs (i.e., options B and C). The fact that our subjects acted so aggressively may have reflected an attempt on their part to drive I players away from the asymmetric cost structures, which were relatively more favorable for the dominant firm, and into the symmetric design. This points to an interesting complication of partial preemption: since the rival is not dispatched, this agent has the opportunity to retaliate against the dominant firm in later stages. While such behavior is not credible, to the extent that E players can convince I players that such a possibility is sufficiently likely they may induce I players to use their strategic advantage less aggressively. While preemption is profitable for the incumbent in our experimental design, it is never socially optimal. The Cournot equilibrium market output is largest in cost structure A, and smallest in structure C, which implies that consumer surplus declines as one moves from structure A to structure B to structure C (from 405 tokens to 245 tokens to 211 tokens). Likewise, we see from Table 2 that industry profits are largest in structure A and smallest in structure C. The conclusion is that net surplus is largest in structure A and smallest in structure C. Moreover, the difference in total surplus between structures B and C is relatively small (1283 vs. 1211 tokens), while surplus in structure A is markedly larger (1685 tokens). In light of these remarks, it is interesting to consider the implications of a policy that makes it costly for an incumbent to drive a rival from the market. Such a cost

126

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

might be likened to our ‘option cost’ attached to structure C in design 2, since it is in essence a fixed cost to the incumbent. If such a cost makes complete preemption privately suboptimal, while leaving partial preemption as a viable alternative, theory suggests that the first mover will switch from complete to partial preemption. In contrast, our results indicate that the incumbent is more likely to abandon preemption outright. This generates relatively substantial welfare gains, i.e., about a 40% increase in total surplus. Thus, our results suggest that an antitrust stance that actively attacks alleged predators could generate unexpectedly large welfare gains.

Acknowledgements An earlier version of this paper was presented at the Western Economic Association meetings in San Francisco. We thank Tim Cason, Ron Johnson, Stephen Martin, and two anonymous referees for helpful comments, but retain responsibility for any remaining errors. Funding for this project was received through the College of Business, University of Wyoming and the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not reflect the views of these funding agencies.

Appendix A A.1. Instructions This is an experiment in the economics of market decision making. The National Science Foundation and other funding agencies have provided funds for the conduct of this research. The instructions are simple. If you follow them carefully and make good decisions you may earn a CONDIDERABLE AMOUNT OF MONEY which will be PAID TO YOU IN CASH at the end of the experiment. Your earnings in this experiment will depend on the choices you and another person make. This other person, known as ‘the other participant’, is randomly paired with you. You are paired with this person for only one choice period. After choices are made for this period and earnings are recorded, you will be paired with a different person. The identities of the other participants will never be revealed, nor will they ever know who you are. During a choice period you will be labeled as an I or an E participant. For half of the choice periods you will be I, and for the other half you will be E. Both you and the other participant will at the same time choose a value from a table consisting of rows and columns. The two selected values determine the payment made to you and the other participant. At the beginning of each choice period person I selects the tables from which both the I and E people choose. At times

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

127

person I must pay for this choice. The tables are not necessarily the same for each participant, so there may be one for the E person and a different one for the I person. There are three sets of tables from which the I person may choose, they are labeled as sets A, B and C. Whenever you make a choice from your table you always will know the table from which the other person chooses. For every table, the values you may select are written down the left side of the table and are row values. You will always pick a row value. The value selected by the other participant is written across the top of your table. He or she will always pick the column value for your table. The intersection of the row and column value determines your earnings from the table for that period. After recording your earnings on a record sheet you will be paired with someone else, and you may or may not be changed from E to I or vice versa. Earnings are recorded in a fictitious currency called tokens. At the end of the experiment tokens are redeemed for cash at the exchange rate of 1000 tokens5 $1.00. All earnings will be paid to you in cash at the end of the experiment. To begin, you will be given an initial balance of 2000 tokens. You may keep this money plus any you earn. However, earnings can be negative in a choice period. A sample pair of tables for person I and person B is provided on the next page. In the experiment person I will have picked such a pair of tables. The tables are different, although they need not be. The top table shows person I’s earnings and the bottom one person B’s earnings. Each participant, for their table, makes a row choice. The choice can be 0 through 9. Suppose person I picks 4 and person B picks 6, then in the top table person I has earnings at the intersection of row 4 and column 6; they would be 520. Person B has earnings in his or her table at the intersections of row 6 and column 4; the table shows that 250 is earned. Notice that if B has chosen 9 and person I had picked 8, earnings for person B would be 2130. Earnings can be negative. During each period in the experiment only one row choice is made. After everyone has made their choice the computer calculates earnings. Everyone must record their choice and earnings on a record sheet. A sample record sheet is provided at the end. In every period you are randomly paired with a different person and told to be an E or I participant. Under the column labeled ‘Sample 1’ the participant is an I person; he or she chooses from an I table. All participants begin with a starting balance of 2000. Rows (4) and (5), respectively, show how much person I pays for choosing the tables and the adjustment to his or her balance. As shown no payment is made in this sample. On the table, 4 is chosen, while person B on the E table chooses 6. These choices are recorded on rows (6) and (7) of the record sheet. (The computer will inform you of the other participant’s choice.) Earnings at the intersection of row 4 and column 6 on the I table are 520. These earnings are added to the balance to yield an ending balance in row (9), of 2520. In column ‘Sample 2’ the person is made the B participant. On the B table the row choice is 9, the column choice is by I is 8, and earnings are 2130. The balance in row (7) fall to 2390.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

128

An example of the information that will appear on your terminal screen during a choice period is now presented. The numbers shown are based on the I person picking 4 and the B person choosing 6 on the sample table. The time period is 1 and the participant number is 1. When the I person is choosing the tables that determine earnings the following messages appear on the screen: THIS IS PERIOD Please enter your choice of tables (A, B or C). This is the set you have selected, is it correct? If correct enter YBS otherwise enter NO.

1 [A] [A] [YES]

Record this information and type YES to continue. Sample payment tables for person I and person E: payment table for I Person E’s choice 0

1

2

3

4

5

6

7

8

9

Person

0

00

00

00

00

00

00

00

00

00

00

I’s

1

650

525

500

475

450

425

400

375

350

325

choice

2

750

600

570

540

510

480

450

420

390

360

3

840

665

630

595

560

525

490

455

420

385

4

920

720

680

640

600

560

520

480

440

400

5

990

765

720

675

630

585

540

495

450

405

6

1050

800

750

700

650

600

550

500

450

400

7

1100

825

770

715

660

605

550

495

440

385

8

1140

840

780

720

660

600

540

480

420

360

9

1170

845

780

715

650

585

520

455

390

325

4

5

6

7

8

9

Sample payment tables for person I and person E: payment table for E Person I’s choice 0

1

2

3

Person

0

00

00

00

00

00

00

00

00

00

00

E’s

1

450

325

300

275

250

225

200

175

150

125

choice

2

510

360

330

300

270

240

210

180

150

120

3

560

385

350

315

280

245

210

175

140

105

4

600

400

360

320

280

240

200

160

120

80

5

630

405

360

315

270

225

180

135

90

45

6

650

400

350

300

250

200

150

100

50

00

7

660

385

330

275

220

165

110

55

00

255

8

660

360

300

240

180

120

60

00

260

2120

9

650

325

260

195

130

65

00

265

2130

2195

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

129

When the I person is making a choice on the table the following messages appear: Please enter the value you have selected from the I table. This is the value you have selected, is it correct? If correct enter YES otherwise enter NO.

[4] [YES]

A similar message appears for those making a choice from the B table. The table selected is A (or B or C). Please enter the value you have selected from the B table. This is the value you have selected, is it correct?

[6] [YES]

If correct, enter YES, otherwise, enter NO. During the time all of the other subjects are making their choices, the screen will have the message ‘‘We are waiting for other participant to enter their choice.’’ When all choices are typed into the computer, the screen will show the following results for the I participants: This is the value you selected. [4] The option with your table is [A, B or C] You are Person I Your

Other person’s

Choice

Earnings

Choice

Earnings

4

520

6

250

Please record this information on your record sheets. When you have recorded all the information, enter YES to continue. For those choosing from the E table, the screen provides the following information: This is the value you have selected. [6] The option with your table is [A, B or C] You are Person E Your

Other person’s

Choice

Earnings

Choice

Earnings

6

250

4

520

130

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

Please record this information on your record sheets. When you have recorded all information, enter YES to continue. Are there any questions about this procedure? A.2. Summary 1. At the beginning of a choice period you will be randomly paired with another person. The computer will make one person B and one I. I picks the payment tables from which each participant chooses. I may pay a fee for this choice. 2. Each period you must select a row value from your Payment Table. 3. Your earnings from the table will depend on the value you choose and what the other person chooses. 4. The payment you receive from each table can be found at the intersection of the row value you choose and column value chosen by the other participant. Several practiced sessions will be conducted to further acquaint you with the experimental procedure. One of the experimenters will act as the other participant for everyone. If you look at you screen you will see the following message: Welcome! please be seated and wait for you instructions. When you understand all the instructions, enter YES so we may begin. Anytime you are asked to enter information into the computer you will do so by typing what you want to enter and then hitting the ‘ENTER’ key. Words should always be in capital letters. The ‘ENTER’ key is dark grey and is located at the right side of you keyboard beside the quotation marks (‘,’) and the right bracket keys (]). Now enter ‘YES’ so that we may begin. You are now asked to enter your name. After you have typed in your name and hit the ‘ENTER’ key the following message will appear: This is the name you have entered. If it is correct please enter YES, if incorrect NO. Notice that you are given an opportunity to change the information that you have entered. This will allow you to correct any typing errors. If you are satisfied with the information you have entered, enter ‘YES’ and hit the ‘ENTER’ key. You will be given an opportunity to change every entry in a similar manner. After you are satisfied with you name as entered, enter ‘YES’. Now you will be asked for your social security number. REMEMBER THAT WHENEVER YOU ENTER ANY INORMATION INTO THE COMPUTER YOU MUST ALWAYS HIT THE ‘ENTER’ KEY AFTER TYPING IN YOUR INFORMATION. If you do not hit the ‘ENTER’ key the computer will not receive your information. Your identity will remain confidential and will not be used for any purpose other than to account for our expenditures to the funding agencies. Please do not speak to anyone during the experiment. This is important to the validity of the study and will not be tolerated.

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

131

2. Payoff tables Option A: I’s payoffs E’s choice 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14 0

I’s

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

choice

1

800

640

620

600

580

560

540

520

500

480

460

440

420

400

380

2

878

698

675

653

630

608

585

563

540

418

495

473

450

428

405

3

950

750

725

770

675

650

625

600

575

550

525

500

475

450

425

4

1018

798

770

743

715

688

660

633

605

578

550

523

495

468

440

5

1080

840

810

780

750

720

690

660

630

600

570

540

510

480

450

6

1138

878

845

813

780

748

715

683

650

618

585

553

520

488

455

7

1190

910

875

840

805

770

735

700

665

630

595

560

525

490

455

8

1238

938

900

863

825

788

750

713

675

638

600

563

525

488

450

9

1280

960

920

880

840

800

760

720

680

640

600

560

520

480

440

10

1318

978

935

893

850

808

765

723

680

638

595

553

510

468

425

11

1350

990

945

900

855

810

765

720

675

630

585

540

495

450

405

12

1378

998

950

903

855

808

760

713

665

618

570

523

475

428

380

13

1400

1000

950

900

850

800

750

700

650

600

550

500

450

400

350

14

1418

998

945

893

840

788

735

683

630

578

525

473

420

368

315

1

2

3

4

5

6

7

8

9

10

11

12

13

14 0

Option A: E’s payoffs I’s choice 0 E’s

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

choice

1

800

640

620

600

580

560

540

520

500

480

460

440

420

400

380

2

878

698

675

653

630

608

585

563

540

418

495

473

450

428

405

3

950

750

725

770

675

650

625

600

575

550

525

500

475

450

425

4

1018

798

770

743

715

688

660

633

605

578

550

523

495

468

440

5

1080

840

810

780

750

720

690

660

630

600

570

540

510

480

450

6

1138

878

845

813

780

748

715

683

650

618

585

553

520

488

455

7

1190

910

875

840

805

770

735

700

665

630

595

560

525

490

455

8

1238

938

900

863

825

788

750

713

675

638

600

563

525

488

450

9

1280

960

920

880

840

800

760

720

680

640

600

560

520

480

440

10

1318

978

935

893

850

808

765

723

680

638

595

553

510

468

425

11

1350

990

945

900

855

810

765

720

675

630

585

540

495

450

405

12

1378

998

950

903

855

808

760

713

665

618

570

523

475

428

380

13

1400

1000

950

900

850

800

750

700

650

600

550

500

450

400

350

14

1418

998

945

893

840

788

735

683

630

578

525

473

420

368

315

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

132 Option B: I’s payoffs E’s choice 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14 0

I’s

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

choice

1

750

590

570

550

530

510

490

470

450

430

410

390

370

350

330

2

821

641

619

596

574

551

529

506

484

461

439

416

394

371

349

3

888

688

663

638

613

588

563

538

513

488

463

438

413

388

363

4

949

729

701

674

646

619

591

564

536

509

481

454

426

399

371

5

1005

765

735

705

675

645

615

585

555

525

495

465

435

405

375

6

1056

796

764

731

699

666

634

601

569

536

504

471

439

406

374

7

1103

823

788

753

718

683

648

613

578

543

508

473

438

403

368

8

1144

844

806

769

731

694

656

619

581

544

506

469

431

394

356

9

1180

860

820

780

740

700

660

620

580

540

500

460

420

380

340

10

1211

871

829

786

744

701

659

616

574

531

489

446

404

361

319

11

1238

878

833

788

743

698

653

608

563

518

473

428

383

338

293

12

1259

879

831

784

736

689

641

594

546

499

451

404

356

309

261

13

1275

875

825

775

725

675

625

575

525

475

425

375

325

275

225

14

1286

866

814

761

709

656

604

551

499

446

394

341

289

236

184

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0

0

0

Option B: E’s payoffs I’s choice 0 E’s

0

0

0

0

0

0

0

0

0

0

0

0

0

choice

1

600

440

420

400

380

360

340

320

300

280

260

240

220

200

180

2

653

473

450

428

405

383

360

338

315

293

270

248

225

203

180

3

700

500

475

450

425

400

375

350

325

300

275

250

225

200

175

4

743

523

495

468

440

413

385

358

330

303

275

248

220

193

165

5

780

540

510

480

450

420

390

360

330

300

270

240

210

180

150

6

813

553

520

488

455

423

390

358

325

293

260

228

195

163

130

7

840

560

525

490

455

420

385

350

315

280

245

210

175

140

105

8

863

563

525

488

450

413

375

338

300

263

225

188

150

113

75

9

880

560

520

480

440

400

360

320

280

240

200

160

120

80

40

10

893

553

510

468

425

383

340

298

255

213

170

12

85

43

0

11

900

540

495

450

405

360

315

270

225

180

135

9

45

0

245

12

903

523

475

428

380

333

285

238

190

143

95

4

0

248

295

13

900

500

450

400

350

300

250

200

150

100

50

0

250

2100

2150

14

893

473

420

368

315

263

210

158

105

53

0

253

2105

2158

2210

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

133

Option C: I’s payoffs E’s choice 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14 0

I’s

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

choice

1

640

480

460

440

420

400

380

360

340

320

300

280

260

240

220

2

698

518

495

473

450

428

405

383

360

338

315

293

270

248

225

3

750

550

525

500

475

450

425

400

375

350

325

300

275

250

225

4

798

578

550

523

495

468

440

413

385

358

330

303

275

248

220

5

840

600

570

540

510

480

450

420

390

360

330

300

270

240

210

6

878

618

585

553

520

488

455

423

390

358

325

293

260

228

195

7

910

630

595

560

525

490

455

420

385

350

315

280

245

210

175

8

938

638

600

563

525

488

450

413

375

338

300

263

225

188

150

9

960

640

600

560

520

480

440

400

360

320

280

240

200

160

120

10

978

638

595

553

510

468

425

383

340

298

255

213

170

128

85

11

990

630

585

540

495

450

405

360

315

270

225

180

135

90

45

12

998

618

570

523

475

428

380

333

285

238

190

143

95

48

0

13

1000

600

550

500

450

400

350

300

250

200

150

100

50

0

250

14

998

578

525

473

420

368

315

263

210

158

105

53

0

253

2105

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Option C: E’s payoffs I’s choice 0 E’s

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

choice

1

240

80

60

40

20

0

220

240

260

280

2100

2120

2140

2160

2180

2

248

68

45

23

0

223

245

268

290

2113

2135

2158

2180

2203

2225

3

250

50

25

0

225

250

275

2100

2125

2150

2175

2200

2225

2250

2275

4

248

28

0

228

255

283

2110

2138

2165

2193

2220

2248

2275

2303

2330

5

240

0

230

260

290

2120

2150

2180

2210

2240

2270

2300

2330

2360

2390

6

228

233

265

298

2130

2163

2195

2228

2260

2293

2325

2358

2390

2423

2455

7

210

270

2105

2140

2175

2210

2245

2280

2315

2350

2385

2420

2455

2490

2525

8

188

2113

2150

2188

2225

2263

2300

2338

2375

2413

2450

2488

2525

2563

2600

9

160

2160

2200

2240

2280

2320

2360

2400

2440

2480

2520

2560

2600

2640

2680

10

128

2213

2255

2298

2340

2383

2425

2468

2510

2553

2595

2638

2680

2723

2765

11

90

2270

2315

2360

2405

2450

2495

2540

2585

2630

2675

2720

2765

2810

2855

12

48

2333

2380

2428

2475

2523

2570

2618

2665

2713

2760

2808

2855

2903

2950

13

0

2400

2450

2500

2550

2600

2650

2700

2750

2800

2850

2900

2950

21000 21050

14

253

2473

2525

2578

2630

2683

2735

2788

2840

2893

2945

2998

21050 21103 21155

134

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

References Dixit, A., 1979. A model of duopoly suggesting a theory of entry barriers. Bell Journal of Economics 10 (1), 20–32. Dixit, A., 1980. The role of investment in entry-deterrence. Economic Journal 90, 95–106. Eaton, B.C., Ware, R., 1987. A theory of market structure with sequential entry. Rand Journal of Economics 18 (1), 1–16. Fomby, T., Hill, R., Johnson, S., 1988. In: Advanced Econometric Methods, Springer-Verlag, New York. Friedman, J., 1967. An experimental study of cooperative duopoly. Econometrica 35 (3–4), 379–397. Gilbert, R.J., 1989. The role of potential competition in industrial organization. The Journal of Economic Perspectives 3 (3), 107–128. Gilbert, R.J., Lieberman, M., 1987. Investment and coordination in oligopolistic industries. Rand Journal of Economics 18 (1), 17–33. Gilbert, R.J., Newberry, D.M.G., 1982. Pre-emptive patenting and the persistence of monopoly. American Economic Review 71, 514–526. Harrison, G.W., 1988. Predatory pricing in a multiple market experiment: a note. Journal of Economic Behavior and Organization 9, 405–417. Holt, C.A., 1985. An experimental test of the consistent-conjectures hypothesis. American Economic Review 75, 314–325. Isaac, R.M., Smith, V.L., 1985. In search of predatory pricing. Journal of Political Economy 93, 320–345. Jung, Y.J., Kagel, J.H., Levin, D., 1994. On the existence of predatory pricing: an experimental study of reputation and entry deterrence in the chain store game. Rand Journal of Economics 25 (1), 72–93. Kalai, B., Lehrer, B., 1993. Rational learning leads to nash equilibrium (a new extended version). Econometrica 61 (5), 1019–1045. Krattenmaker, T.G., Salop, S.C., 1986. Anticompetitive exclusion: raising rivals’ cost to achieve power over price. Yale Law Journal 96 (2), 209–294. Lieberman, M., 1987. Post-entry investment and market structure in the chemical processing industry. Rand Journal of Economics 18 (2), 533–549. Mason, C.F., Nowell, C., 1998. An experimental analysis of subgame perfect play: the entry deterrence game. Journal of Economic Behavior and Organization 37 (4), 443–462. Mason, C.F., Phillips, O.R., 1998. Dynamic Learning in Two-Person Experimental Games, University of Wyoming working paper, July 1998. Mason, C.F., Phillips, O.R., Nowell, C., 1992. Duopoly behavior in asymmetric markets: an experimental evaluation. Review of Economics and Statistics 74, 662–670. Masson, R., Shaanan, J., 1986. Excess capacity and limit pricing: an empirical test. Economica 53, 365–378. Mood, A.M., Graybill, F.A., Boes, D.C., 1974. In: Introduction to the Theory of Statistics, McGraw Hill, New York. Oster, S., 1982. The strategic use of regulatory investment by industry subgroups. Economic Inquiry 20 (4), 604–618. Palfrey, T., Rosenthal, H., 1994. Repeated play, cooperation, and coordination: an experimental study. Review of Economic Studies 61, 545–565. Phillips, O.R., Mason, C.F., 1992. Mutual forbearance in a conglomerate game. Rand Journal of Economics 23 (3), 395–414. Roth, A.E., Erev, I., 1995. Learning in extensive form games: experimental data and simple dynamic models in the intermediate term. Games and Economic Behavior 8 (1), 164–212. Salop, S.C., Scheffman, D.T., 1983. Raising rivals’ costs. American Economic Review, Papers and Proceedings 73, 267–271. Salop, S.C., Scheffman, D.T., Schwartz, M., 1984. A Bidding Analysis of Special Interest Regulation:

C.F. Mason, O.R. Phillips / Int. J. Ind. Organ. 18 (2000) 107 – 135

135

Raising Rivals’ Costs in a Rent Seeking Society, The Political Economy of Regulation: Private Interests in the Regulatory Process. Spence, A.M., 1977. Entry, capacity, investment and oligopolistic pricing. Bell Journal of Economics 8 (2), 534–544. Tirole, J., 1988. In: The Theory of Industrial Organization, MIT Press, Cambridge, MA. West, D.S., 1981. Testing for market preemption using sequential location data. Bell Journal of Economics 12 (1), 129–143. Williamson, O., 1968. Wage rates as a barrier to entry: The Pennington Case. Quarterly Journal of Economics 85, 85–116.