AN EXPERIMENTAL INVESTIGATION OF PRODUCT POSITIONING AND PRICE COMPETITION IN SPATIAL MODELS WITH PRICE RESTRAINTS

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1 AN EXPERIMENTAL INVESTIGATION OF PRODUCT POSITIONING AND PRICE COMPETITION IN SPATIAL MODELS WITH PRICE RESTRAINTS SUDEEP GHOSH Abstract. This paper uses an experimental design using different spatial models to investigate the relationship between product differentiation and price competition. In such models of horizontal differentiation over product space, it has been hypothesized that with a limited number of entrants, firms have the incentive to product differentiate in order to relax price competition. We also introduce treatments involving vertical restraints in the form of price floors and price ceilings. There has been theoretical work which have predicted that price-floors would have the paradoxical effect of intensifying price competition. Therefore the prediction is for less product differentiation and hence intensified price competition. Similarly price ceilings, by restricting the ability of firms to increase prices might also lead to less product differentiation. We test these predictions and their robustness, by varying price restraints levels and then comparing the results. Keywords: Experimental Economics, Horizontal Differentiation, Vertical Restraints. Department Of Economics & Finance, City University of Hong Kong, Hong Kong. sghosh@cityu.edu.hk I thank Ngai Ho Lam for providing programming assistance with the experiment. I also thank conference participants at 2005 ESA International Meetings and 2006 Asia-Pacific ESA Meetings for comments. Support for the experiment through a Research Grant from City University is acknowledged. 1

2 1. Introduction Product positioning and it s implication on market power has been widely studied in the literature since it was first considered by Edgeworth. One of the commonly used models designed for this purpose is the model of spatial competition, originally due to Hotelling (1929). The location model of Hotelling can be interpreted as a horizontal product differentiation scenario, where firms location corresponds to their product positioning in the space of characteristics that define their products. An implication of such models of horizontal differentiation over product space has been the incentive of firms to product differentiate in order to relax price competition. In this paper we use an experimental design with different spatial models to investigate the relationship between product differentiation and price competition. For a linear spatial model, Hotelling (1929) showed that with two firms the equilibrium would correspond to the principle of Minimum Differentiation, i.e. both firms would both locate at the same position (specifically at the middle of the line). But d Aspremont et. al. (1979) in their paper showed that with linear transport costs, there were multiple equilibria; one with Minimum Differentiation" and another with Maximum Differentiation." On the other hand if the firms were located close to the center (but not at the same location), there did not exist any equilibrium profile of prices. This is due to the fact that with a linear transport cost parameter firm s profit functions are not continuous in location choice. This problem can be solved with the introduction of a quadratic transport cost parameter in which case given a limited number of entrants, Maximal Differentiation is the unique subgame perfect equilibrium in location. But this result that firms have the incentive to maximally product differentiate in order to relax price competition involves a significant coordination problem between firms regarding their location decision, in a linear spatial model. This is due to the fact that there are pair of such equilibria depending upon which firm(s) locate at which end-point of the line. This coordination problem is significant, because the firms could possibly end up with the same location. Minimal differentiation on the other hand though not part of any subgame 2

3 perfect equilibrium but has the advantage that it does not involve a coordination problem. This leads to the problem that any experimentally observed behavior in a linear spatial model that matches Minimal Differentiation," can be attributed to both a cognition" problem of equilibrium behavior and a coordination" problem involving locations. In order to separate the effect of coordination and the cognition problem, we compare results from treatments differing in the timing of location" decisions; where we have simultaneous location choice in a linear spatial design treatment and sequential location choice in a circular spatial design treatment. Economides (1986) showed that for quadratic transport costs there exists a symmetric Maximal Differentiation" equilibrium in locations 1. Now for a circle with two firms, the location space is completely homogenous, i.e. there is no relative strategic advantage for a firm given any locational configuration which in turn implies that there is no disadvantage for a firm in choosing a location first, unlike in a linear space. This sequential location choice also does not change the nature of the above equilibrium. Therefore the design of a circular spatial model with sequential location choices in our experiment was done in order to facilitate coordination and hence separate out the confounding effects of coordination" and cognition." We also test the robustness of the results by varying the psychic" or transportation costs of the consumer. Subsequently, we introduce treatments involving vertical restraints in the form of price floors and price ceilings. There has been theoretical work which have predicted that price-floors would have the paradoxical effect of intensifying price competition, since they would act as a sort of safety net against firms earnings zero profits (negative profits, once we introduce entry costs), ala Bertrand price competition. Therefore the prediction is for less product differentiation and hence intensified price competition. Similarly price ceilings, by restricting the ability of firms to increase prices might also lead to less product differentiation. We test these predictions and their robustness, by varying price restraints levels and then comparing the results. 1 Note that a maximal differentiation equilibrium will be pareto superior to a Minimal Differentiation equilibrium in terms of firms profits, since the latter would lead to zero profits. 3

4 In the case when there are a few firms, Bhaskar (1997) shows that the imposition of price-floors leads to minimum differentiation and hence decline in price. Also the imposition of a price-floor inhibits entry. Unlike the model of horizontal differentiation used in this paper, there is a sizeable literature on the related aspect of Vertical Price Differentiation following Gabszewicz and Thisse (1979, 80), Shaked and Sutton (1982) amongst others. Their the model is one of consumer choice (consumers have different incomes) over differentiated products, where instead of idiosyncratic tastes of consumers over products as in the Horizontal Differentiation case, all consumers now have the same ranking of preferences over the product space. Here Shaked and Sutton (1982) show that firms again product differentiate to soften price competition, but the differentiation is not maximal, i.e. firms choose the immediate rather than extreme positions on the product quality space. Similarly, Ghosh (2003) finds that the imposition of a price-floor leads to a price level uniformly lower than before. Furthermore, only one type of product quality is offered at equilibrium, the highest quality product. This result is similar to Bhaskar (1997) s result in the case of Horizontal Differentiation. In the rest of the paper we first discuss the environment and the model, then the theoretical results, followed by the experimental design and theoretical predictions. We then discuss the experimental results followed by the conclusions. 2. Model We have a line or a circle whose length is normalized to one and on which consumers are uniformly distributed with a positive density. Each consumer buys one unit of the product subject to a reservation utility level. Firms with homogenous product choose a location and a uniform mill price, i.e. firms can t price discriminate based on location since consumers have to bear the transport cost. A consumer will but from the seller whose gross price, i.e. the product price plus transportation cost, is minimum. All firms face a constant marginal cost of c and have no capacity constraints. 4

5 2.1. Linear Space. a b 0 Firm 1 Firm 2 1 As can be seen from the above figure both firms locate on a line, where WLOG firm 1 and firm 2 are located at a distance of a & b respectively from the endpoints of the line and where a 0,b 0;a + b 1. The consumers face a quadratic transport cost function: c(d) = td 2, where d is the distance between the consumer and a firm and t > 0 is a transport cost parameter. The payoffs are identified with the profit earned by the firm less a cost of entry" (if it exists) of ǫ > 0, for those who enter (zero for non-entrants). The solution concept used is the familiar one of (Sub-game) Perfect Equilibrium. The firms play a sequential game whose timing is as follows Sequential Game. Period 0: : Price restraint (if applicable) announced Period 1: : Both firms choose location simultaneously Period 2: : After observing all locations both firms choose a price simultaneously Theoretical Results with No Price Restraints. We use backward induction to find the solution by first considering the Price sub-game. Given a choice of location a by Firm 1 and b by Firm 2 we have the following Nash equilibrium in prices (2.1) (2.2) P 1 (a,b) = c + t(1 a b)(1 + a b 3 ) P 2 (a,b) = c + t(1 a b)(1 + b a 3 ) Now we can solve for the first period choices of locations and thereby characterize the subgame perfect equilibria. Solving for locations we get that firms choose locations in period one such that a = 0 & b = 0, i.e. there is maximal differentiation of 5

6 products. Furthermore, given the above choice of locations, prices are such that P1 = P2 = c + t. Let us consider some implications of the above SPNE. If a = 1 b, then P1 = P2 = c, therefore in general the farther away the firms are from each other the higher the Nash equilibrium prices. With the maximal differentiation equilibrium, there exists a coordination problem between the two firms, since there is pair of such equilibria depending upon which firm locates at which end-point of the line and this coordination problem is significant, because the firms could possibly end up with the same location. Furthermore, minimal differentiation, defined as a = b & a + b = 1, does not involve a coordination problem but is not a subgame perfect equilibrium and leads to P1 = P2 = c and therefore zero profits Theoretical Results with Price Floor = P f c. Profits of firms are no a longer quasi-concave function of location decision. Therefore some locational configurations might be locally optimal even though not part of a subgame perfect equilibrium (i.e. are susceptible to large deviations). If P f > c, then minimal differentiation is always a local optimum. If P f < t + c (the equilibrium price without a price floor), then maximal differentiation is always a local optimum. All locally optimal configurations of location would exhibit either Maximal or Minimal Differentiation and if P f {c,c + t}, then both are locally optimal. Subgame Perfect Equilibrium (1) Maximal Differentiation is subgame perfect iff P f c + t 2 (2) Minimal Differentiation is subgame perfect iff P f c + 25t 72 Let s consider the implications of the above subgame perfect equilibria for price competition. If price floor is low, i.e. P f < c + 25t 72 then equilibrium price is t + c. If price-floor is high, i.e. P f > c + t 2 then equilibrium price is P f If the price-floor is above c + t 2 but below c + t, then it paradoxically reduces equilibrium price. If P f [c + 25t 72,c+ t 2 ], then there are multiple equilibria, with both P f and c + t being 6

7 equilibrium prices. We summarize the above results in Figure 1, which has been adapted from Bhaskar (1997). c + t Equilibrium Price c + 25t 72 c + t 2 Price Floor c + t Figure 1. Equilibrium price with respect to Price-Floor Now let us consider the implications of the above subgame perfect equilibria for product differentiation. If P f < c + 25t 72, we have Maximal Differentiation. If P f > c + t 2, we have Minimal Differentiation. If P f [c + 25t,c + t ], we have multiple equilib ria, with both Maximal Differentiation and Minimal Differentiation as possibilities. Firms earn higher profits in the Maximal Differentiation case, but it s not obvious that the maximal differentiation outcome would occur, since there is a coordination problem associated with it. Therefore minimal differentiation might still be a more likely outcome. Finally, note that none of the subgame perfect equilibria has socially optimal locational configurations, where the socially optimal configuration is given by a = b = Theoretical Results with Price Ceiling = p. Unlike the situation with pricefloors firm s profits are again quasi-concave functions of their locations in the presence of price-ceilings. For any p < t + c, induces firms to choose locations, such that the resulting Nash Equilibrium prices are exactly equal to the price-ceiling. 7

8 Therefore for a price-ceiling of p, the subgame perfect equilibrium induced locations a and b can be found by solving equations (1) & (2) stated earlier, wherein we get a = b = t+c p. Therefore, price-ceilings can be set such that the socially optimal 2t locational configurations are induced as a SPNE, where for any given t and c, the socially optimal location inducing price-floor (p s ) is given by p s = t+2c Circular Space. Now firms locate on a circle, where let a ij and aˆ ij denotes the shortest and the longest distance respectively between two firms i and j, where a ij 0 and a ij + aˆ ij = 1. The consumers face a quadratic transport cost function: c(d) = td 2, where d is the distance between the consumer and a firm and t > 0 is a transport cost parameter. The payoffs are identified with the profit earned by the firm less a cost of entry" (if it exists) of ǫ > 0, for those who enter (zero for non-entrants). The firms play a sequential game whose timing is as follows Sequential Game. Period 0: : Price restraint (if applicable) announced Period 1: : Firms make their entry decision simultaneously Period 1: : Firms choose locations sequentially, where the sequence is decided randomly and firms observe the choices of all firms preceding them before making their own choice Period 2: : Firms observe the locations of each other and then choose prices simultaneously Theoretical Results with No Price Restraints. Under the subgame perfect equilibrium, all firms choose a location equidistant from each other (i.e. equal-spacing between firms) and choose a price (p ) = c + t n 2, where n is the number of entrants. 3. Design All subjects, around 300, participated voluntarily and were enrolled students at City University of Hong Kong. Each subject was paid HK$20 8

9 (1US$ 7.8HK$) for taking part in the experiment and informed of other significant potential earnings depending on their performance in the experiment. The experiment took around 2 hours and subjects earned on average HK$200. There was no screening of the subjects on the basis of year, major etc.in our experimental design, the subjects perform the role of firms and make three decisions: Entry; Location which is used as a proxy for product quality choice; and Price of the product. Consumers (automaton agents in our design) are distributed uniformly across the product quality space, with their location corresponding to their preferences over the product quality Linear Space. Subjects were divided into groups of two serving one market. All consumers are computer automatons and all firms faced a constant marginal cost of production of $2. Each treatment consists of 10 identical rounds, where each subject was matched with the same subject for the first five rounds and then subjects were randomly rematched for the next five rounds. During each round, the subjects had to make two decisions in sequence. (1) Location Decision: In each group both subjects simultaneously chose a location for their firm on a straight line as can be seen from Figure 2. (2) Price Decision: After observing the location of the other firm in the group (red dot on the line) and your own location (blue dot), both firms had to choose a price for their products simultaneously as can be seen from Figure 3. Then the earnings, % of customers served by each firm, prices charged by both firms are revealed to all the group members through a table on the computer screen. The firms then move to the next round, where they play the above game again with the same participant up to a total of five rounds. The subject earnings in each round is their profits for that round, where profits depends upon the price charged by the subject, the cost of producing 9

10 Figure 2. Screenshot of a location decision one unit of the product and the % of consumers served by the subject. The % of consumers buying from each subject depends upon the locations of the two subjects and the prices charged by both subjects in the group. There is a continuum of consumers located uniformly across the whole line, where the two firms have to locate. Each consumer can buy one unit of the product, subject to a reservation level. Each consumer (a computer automaton) calculates the cost of buying the good from each firm, which is given by the sum of the price charged by the firm and the transportation cost involved in buying from that firm. The consumer buys the good from whichever firm itšs cheaper (price + transport costs) to buy from Treatment Variables: (1) Transport Cost Parameter (a) Quadratic Transport Cost: c(d) = td 2 (i) t = 4 (ii) t = 8 10

11 Figure 3. Screenshot of a price decision (2) Price Range (a) No Price Restraint (b) Price Floors (i) p f = 3, 3.7 & 5 for t = 4 (ii) p f = 4, 5.5 & 7 for t = 8 (c) Price Ceiling (i) p = 5 for t = 4 (ii) p = 6 for t = Circular Space. Subjects who chose to enter the game were divided into groups of two/four serving one market. All consumers are computer automatons and all firms faced a constant marginal cost of production of $2. Each treatment consists of 10 identical rounds, where each subject was matched with the same subject for the first five rounds and then subjects were randomly rematched for the next five rounds. During each round, the 11

12 subjects had to make two (three for the entry treatment) decisions in sequence. (1) Entry Decision: All subjects have to decide simultaneously whether they want to enter the game. Subjects who decided to enter have to pay an entry fee specified before. All the participants who enter will then be randomly matched in groups depending on the group size for that game. Each group serves one market. (2) Location Decision: In each group all subjects choose sequentially a location for their firm on a circle on their screen. The order in which the locations are chosen by the group members is selected completely at random, where each successive firm can observe the location choices of all firms that have already chosen a location before. (3) Price Decision: Next, after observing the location of all the other firms in their group (red dots on the line) and their own location (blue dot), each subject have to choose a price for their product simultaneously along with the other firms in the group. Like the earlier line treatment, the earnings, % of customers served by each firm and prices charged by both firms are revealed to all the group members through a table on the computer screen. Also like before, the subject s earnings in each round is equal to their profits for that round, where the profits are now net of entry costs (if any). There is again a continuum of consumers located uniformly across the whole perimeter or circumference of the circle. Each consumer can buy one unit of the product subject to a reservation utility level. Each consumer has to travel on the perimeter of the circle, by the shortest route or path between itself and a firm. A consumer is unable to cut through the inside of the circle Treatment Variables: (1) Transport Cost Parameter: c(d) = td 2 (a) t = 8 12

13 Figure 4. Screenshot of the circle treatment (b) t = 16 (2) Price Range (a) No Price Restraint (b) Price Floors (i) p f = 4 for t = 8 (ii) p f = 6 for t = Theoretical Predictions In this section we look at the theoretical predictions from the subgame perfect equilibrium for our design variables. We first consider the line treatment and then the circle treatment. These results follow directly from our earlier discussion of theoretical results. 13

14 4.1. Line Treatment Transport Cost Parameter: t = 4. In the absence of price restraints we have maximal differentiation (a = 0 & b = 0) with both firms charging a price, P = 6 at equilibrium. With a price floor the equilibrium depends upon the level of price-floor and is given by the following: (1) Price-floor, p f = 3: Since p f < c + 25t 72 = 3.39, hence we have maximal differentiation with both firms charging a price, P = 6 at equilibrium. (2) Price-floor, p f = 3.7: Since c + 25t 72 < p f < c + t 2 = 4, hence we have multiple equilibria, both with maximal differentiation and minimal differentiation. Under maximal differentiation both firms charge a price, P = 6 at equilibrium, while under minimal differentiation both firms charge a price, P = 3.7 at equilibrium. (3) Price-floor, p f = 5: Since p f > c + t 2 = 3.39, hence hence we have minimal differentiation with both firms charging a price, P = 5 at equilibrium. With a price ceiling (p = 5) we have under subgame perfection, a = b = 1 8 with equilibrium price at P = Transport Cost Parameter: t = 8. In the absence of price restraints we have maximal differentiation (a = 0 & b = 0) with both firms charging a price, P = 10 at equilibrium. With a price floor the equilibrium like before depends upon the level of price-floor and is given by the following: (1) Price-floor, p f = 4: Since p f < c + 25t 72 = 4.77, hence we have maximal differentiation with both firms charging a price, P = 10 at equilibrium. (2) Price-floor, p f = 5.5: Since c + 25t 72 < p f < c + t 2 = 6, hence we have multiple equilibria, both with maximal differentiation and minimal differentiation. Under maximal differentiation both firms charge a price, 14

15 P = 10 at equilibrium, while under minimal differentiation both firms charge a price, P = 5.5 at equilibrium. (3) Price-floor, p f = 7: Since p f > c + t 2 = 6, hence hence we have minimal differentiation with both firms charging a price, P = 7 at equilibrium. With a price ceiling (p = 6) we have under subgame perfection, a = b = 1 4 with equilibrium price at P = 6. This is also the social optimal solution. 5. Results We now look at the results from the experimental data. First we look at the linear model and then at the circular model Linear Space. We first look at the results from the treatment with quadratic transport cost parameter of 8 and no price restraint as given in Table 5.1. To look at the location choices, we aggregate the firms individually depending upon their location. Finally we aggregate the firms from the first and tenth decile, second and ninth decile etc., i.e. deciles whose locations are symmetric when observed form either endpoint. We see that a significant number of firms (49%) located in the 5th & 6th decile, i.e. near the mid-point of the line, while a much smaller fraction (11%) located in the 1st & 10th decile, i.e. near the end points of the line. This supports the hypothesis of minimal differentiation over that of maximal differentiation, even though the latter is the unique subgame perfect equilibrium. Also remember that profits are predicted to be higher with maximal differentiation compared to the zero profits under minimal differentiation. But as discussed before this need not just due to a cognitive failure on the part of the subjects. The maximal differentiation solution involves a significant coordination problem since there are two symmetric equilibria (there are two end points that can be potentially chosen by each firm). The minimal differentiation point at the midpoint on the other hand is a focal 15

16 R1 R2 R3 R4 R5 1st & 10th Decile nd & 9th Decile rd & 8th Decile th & 7th Decile th & 6th Decile Av Price (Median) (7.0) 8.09 (6.55) 7.59 (6.5) 7.2 (6.0) 6.1 (5.0) Table 1. Location choices & prices: No Price Restraint & t = 8 point. Also if one firm locates at the midpoint while the other ends up at one of the end points then the latter firm is at a serious strategic disadvantage. For all of this reasons locating at the mid-point might be a very safe decision. The robustness of the minimal differentiation choice is further revealed from the later rounds data as can be seen in Table 5.1. Even in later rounds where firms given the repeated game framework have had more opportunity to coordinate on the end-points, we see no change in the fraction of firms choosing the end-points. Now we look at the pricing decisions. We see that the average price especially in later rounds is significantly less than that of the equilibrium price of $10. This is to be expected since the equilibrium price is under the maximal differentiation condition, which wasonly chosen by around 11% of subjects. Therefore the average price reflects the location choices of firms, where around half the firms chose the location deciles closest to the mid-point while 16

17 the rest were scattered across the board. This can be better seen from Figure 5, which is a scatter plot of the average price in each group and the relative distance between the two firms in the group. Figure 5. Scatter Plot of Average Group Price and Distance The hypothesis that product differentiation relaxes price competition would imply that the scatter diagram should show a linear trend, since more product differentiation means a bigger relative distance between the two firms in a group and hence higher prices on average. We can see from Figure 5 that the evidence is mixed in this regard. We now move to the results with price-floors. High price-floors are predicted to shift the equilibrium from maximal to minimal differentiation. This is supported by the data from Table 5.1, where we can observe that 65-70% of firms were choosing locations in the 5th & 6th decile, while if we combine this with the numbers form the next closest decile this jumps to more that 80%. The price data also matches the theoretical prediction of the equilibrium price equal to the price-floor of 7 extremely well. 17

18 R1 R2 R3 R4 R5 1st & 10th Decile nd & 9th Decile rd & 8th Decile th & 7th Decile th & 6th Decile Av Price (Median) 8.57 (8) 8.02 (7.8) 7.77 (7.4) 7.6 (7.28) 7.39 (7.03) Table 2. Location choices & prices: P ricef loor = 7 & t = 8 The average group price and distance scatter plot from Figure 6 reveals the preponderance of choices by firms of a price of $7. But again the evidence in support of the central hypothesis that product differentiation softens price competition is not very strong, though one must acknowledge the fact that there is a paucity of data with respect to large relative distances between firms in a group. We now move to the treatment with a lower price-floor of $4 compared to $7 before. Now the prediction is for a maximal differentiation equilibrium with price equal to $20. As we can gleam from Table 5.1 that is definitely not the case. On the contrary a very high percentage of choices, around 70-80% are in the category closest to the minimal diffrentiation case. This can again be explained through the coordination issue discussed earlier. The average price which is quite close to the price-floor is what one would expect given that the preponderance of location choices matching the notion of minimal differentiation would heighten price competition and hence bring prices close to the price-floor. 18

19 Figure 6. Scatter Plot of Average Group Price and Distance R1 R2 R3 R4 R5 1st & 10th Decile nd & 9th Decile rd & 8th Decile th & 7th Decile th & 6th Decile Av Price (Median) 6.68 (5.2) 5.54 (5) 5.47 (4.99) 5.12 (4.3) 5.02 (4.01) Table 3. Location choices & prices: P ricef loor = 4 & t = 8 The scatter diagram in Figure 7 just reinforces the evidence from the treatments before. 19

20 Figure 7. Scatter Plot of Average Group Price and Distance R1 R2 R3 R4 R5 1st & 10th Decile nd & 9th Decile rd & 8th Decile th & 7th Decile th & 6th Decile Av Price (Median) 4.49 (4.65) 4.2 (4.0) 3.9 (3.935) 3.72 (3.5) 3.34 (3.0) Table 4. Location choices & prices: P riceceiling = 6 & t = 8 20

21 We finally move to the case of price ceiling, where subgame perfection predicts that we would see the social optimal solution. But as we can observe from Table 5.1, that prediction can be easily rejected. On the contrary the results are what we would expect from before. The social optimal solution like the maximal differential outcome involves a coordination problem, therefore by now one would expect the focal point given by minimal differentiation at the mid-point to be chosen. This is exactly what the data reveals, with around 70% of choices being in the deciles closest to the mid-point.the aggregate price data is also consistent with what we would expect given the location choices. Given the high degree of minimal differentiation, we would expect intense price competition between firms and hence actual prices to be near the marginal cost of $2. Figure 8. Scatter Plot of Average Group Price and Distance 5.2. Circular Space. We now move to the circular space treatment. As mentioned earlier in a circular space we can use the lack of any strategic disadvantage from first-mover s choice of location to make the location choices 21

22 sequential and hence resolve the coordination problem associated with maximal differentiation in the linear space treatment. Therefore any deviation from maximal differentiation can only be attributed to a cognition" problem and not to a coordination problem. Behaviorally, we should expect firms location choices to be more maximally differentiated 2 compared to the linear space treatment. Looking at the data from Table 5.2, where we have quadratic transport cost parameter of 8 and no price restraint, we get strikingly positive but not absolutely conclusive results. Compared to the analogous case of linear space treatment, we do see a significant increase in subjects choosing locations consistent with maximal differentiation. In most rounds more than 50% of location choices corresponded with maximal differentiation as opposed to around 10% in the linear case. But there still is a substantial amount of minimal differentiation going on. Therefore it seems that even though the coordination problem deterring maximal differentiation gets resolved yet the salience of the minimal differentiation location choice still has a significant impact on the location choices. The scatter plot of average group price and relative distance from Figure 9 as before does not support the central hypothesis of product differentiation and prices. Regarding prices we see that the data supports the notion that subjects are able to use the repeated interaction to sustain some kind of collusion and hence keep prices significantly greater than the equilibrium price of $4. Here one should note that groups with minimal differentiation of which there are around 30% as as discussed before, would have an even downward pressure on prices. Therefore the presence of a significant fraction of minimal differentiation choices makes the collusion hypotheis even stronger. With the introduction of a price floor at $4, minimal differentiation is also an equilibrium along with maximal differentiation. Therefore ideally we should observe some switch from the 100% maximal differentiation predicted 2 Note, from an equilibrium viewpoint of course there is no difference in the prediction of location choices both in the linear space and circular space treatments. 22

23 Distance R1 R2 R3 R4 R % 56.82% 47.73% 52.27% 52.27% Rel Freq % 7.95% 6.82% 3.41% 7.95% Rel Freq % 11.36% 9.09% 4.55% 7.95% Rel Freq % 6.82% 15.91% 9.09% 2.27% Rel Freq % 17.05% 20.45% 30.68% 29.55% Rel Freq Av Price (Median) 7.62 (8.0) 7.06 (7.17) 6.75 (6.9) 6.43 (6.0) 5.62 (5.0) Table 5. Location choices & prices: No price Restraint & t = 8 Figure 9. Scatter Plot of Average Group Price and Distance before (without price-floors) to a significant minimal differentitaion now. But 23

24 since contrary to the theoretical prediction we already had a significant presence of minimal differentiation choices before, therefore as can be seen from Table 5.2 we fail to observe a major switch. The price data also supports the lack of any substantial switching by subjects from maximal to minimal differentiation. Distance R1 R2 R3 R4 R % 53.41% 59.09% 43.18% 42.05% Rel Freq % 2.27% 5.68% 9.09% 6.82% Rel Freq % 7.95% 9.09% 4.55% 5.68% Rel Freq % 7.95% 7.95% 11.36% 11.36% Rel Freq % 28.41% 18.18% 31.82% 34.09% Rel Freq Av Price (Median) 7.46 (7.72) 7.18 (7.0) 7.05 (6.99) 6.66 (6.43) (5.0) Table 6. Location choices & prices: P f = 4 & t = 8 6. Conclusion From the results we see that the maximal differentiation hypothesis as advanced in the spatial competition literature is not supported by experimental evidence. On the contrary, minimal differentiation which apart from the fact that it is not supported as an equilibrium location choice (especially for quadratic transport costs) also suffers from the more significant disadvantage that it leads to zero profits, has a substantial presence and is also quite robust as a location choice. Amongst the possible explanations for this deviation, one can readily identify two as being most likely: First, minimal 24

25 differentiation 3 is a strong focal point and hence requires less cognitive effort, especially compared to the cognitive effort required in figuring out the mutual benefit residing in the maximal differentiation choice. Second, there is a significant and somewhat insurmountable coordination problem associated with maximal differentiation, while minimal differentiation has no such problem. In order to separate out the effects of the two competing explanations two design issues were implemented. One, was the repeated interaction design between firms, which theoretically enables firms to resolve the coordination problem associated with maximal differentiation. But as we can see form the data this did not happen. One possible explanation being that due to the repeated interaction, subjects are now less motivated to earn higher profits by trying to maximally differentiate since they can now secure those higher profits by colluding over prices which gets enabled by the repeated interaction. The other and more elegant design implemented to separate the confounding effects of coordination" and cognition," was to introduce the circular space treatment with sequential location choice. In a circle since there is no strategic disadvantage associated with moving first in choice of location, hence the theoretical results supporting maximal differentiation remains intact with sequential location choices. On the other hand sequential location choices resolves the coordination problem that besets maximal differentiation. The results here give a mixed message. On the positive side, there is a substantial switch towards maximal differentiation choices by subjects, actually a clear majority of group location choices correspond to the maximal differentiation location choice. But there still remains a significant level of minimal differentiation location choice which suggests that not all of the minimal differentiation choices from the linear space case can be attributed to the coordination problem. Some of it is ostensibly due to the greater cognitive effort required for subjects to derive the maximal differentiation equilibrium. 3 Especially in case of the mid-point for a linear space 25

26 Regarding the treatments involving price-floors we get decidedly more positive results. The central and quite paradoxical effect of the introduction of price-floors intensifying price competition is significantly supported by the data. Though the mechanism by which it works is probably a bit different in the experiments here. Theoretically, price-floors intensify price competition by reducing product differentiation, i.e. in terms of our experiment by reducing relative distances of location choices between competing firms. this happens because firms are not as worried as before about the potential increase in price competition since the price floor acts as safety net against very low or at the extreme zero profits. But since even without price-floors, we did have substantial minimal differentiation therefore the resultant increase in price competition did not occur from that source. Instead firms were more likely to deviate from collusive pricing by under-cutting since they were now less worried about being punished with a price war as a result of their deviation. 26

27 References d Aspremont, C., J. J. Gabszewicz, and J. F. Thisse. On Hotelling s Stability in Competition." Econometrica, 47(1979), Beckmann, M.J. Location Theory, Random House, New York, Bhaskar, V., The Competitive Effects of Price-Floors." Journal of Industrial Economics, 45 (1997), pp Dolbear, F.T., L. B. Lave, G. Bowman, A. Lieberman, E. Prescott, F. Rueter and R. Sherman. Collusion in oligopoly: an experiment on the effect of numbers and information." Quart. J. Econ, 82 (1968), Dufwenberg, M. and U. Gneezy. Price competition and market concentration. an experimental study." Int. J. Ind. Organ, 18 (2000), Economides N. Minimal nad Maximal Product Differentiation in Hotelling s Duopoly." Economic Letters, 21 (1986), Ellison, G. Learning, local interaction and coordination." Econometrica, 61 (1993), Gabszewicz, J. J. and J. F. Thisse. Price Competition, Quality and Income Disparities." Journal of Economic Theory, 20 (1979), Gabszewicz, J. J. and J. F. Thisse. Entry (and Exit) in a Differentiated Industry." Journal of Economic Theory, 22 (1980), Ghosh, S., An Analysis of the Welfare Effects of Fair-Trade Laws, Working Paper, Hotelling, H. Stability in Competition." Economic Journal, 39 (1929), Salop, S.C. Monopolistic Competition with Outside Goods. Bell J. Econ, 10 (1979),

28 Selten, R. and J. Apesteguia. Experimentally Observed Imitation and Cooperation in Price Competition on the Circle." Games and Economic Behavior, 51 (2005), Shaked, A. and J. Sutton. Relaxing Price Competition Through Product Differentiation." Review of Economic Studies, 49 (1982),