Spatial Strategies in Economics

Charles Boebinger

Sarah Yin

The Question…

Why do restaurants cluster?

Chapel Street:________________________________________________________

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thai taste________________________________________________________

Game Theory Logic…

The Hotelling Location Model (1929): Assumptions:

No product differentiation except for location Consumer will choose closest store Maximize profit by being closest store to most!

Hotelling Model

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A B

A B

Modifying Hotelling

Other Hotelling assumptions: Linear Model – 1 dimension only Uniform Distribution Non-locational attributes not important All customers identical

Our hypothesis

The Hotelling Model works in two dimensions Uniform distribution of customers is not

pivotal

Our Setup

City as a 2D grid Given: Customer Locations Experiment: Subjects act as

stores/restaurants Variations:

Simultaneous vs. Sequential (Real World / Hotelling)

Uniform Distribution / Central Clustering / Corner Clustering

Results – The WinnersCustomer Distribution Period Store # Profit

Simultaneous Uniform Randomness 1 13 22

Uniform Randomness 2 13 21

Uniform Randomness 3 13 10

Central Clustering 5 13 18

Corner Clustering 8 8 24

Sequential Uniform Randomness 11 4 13

Uniform Randomness 12 2 12

Uniform Randomness 13 2 11

Uniform Randomness 14 13 11

Central Clustering 15 1 16

Central Clustering 16 1 13

Central Clustering 17 3, 12 13

Corner Clustering 18 2 13

Corner Clustering 19 12 12

Corner Clustering 20 4, 7 11

Analysis – The Winners As you can see, profit was generally far higher in the

simultaneous round, and one player, number 13, handily dominated. In the ten sequential rounds, 7 different players managed the highest profit in at least one round. This would suggest that no player was able to dominate from any position, although a few players appear multiple times.

The most striking aspect of the sequential data is that the early players had such a strong presence. Players 1, 2, 3 and 4 won 8 of the 10 periods. This could suggest that those players were disproportionately skilled, but given that only 2 appears even three times, the implication appears to be that early position was the key. The other players to appear were on the end (12, 13) and one tie brought about by a player in the middle (7). In fact, only in periods 14 and 19 did a player in the first four positions not at least tie for the lead.

Clustering

What of clustering? Now that we have seen that going first was not a crippling disadvantage, did the hotelling model yield the same result in two-dimensions?

In the few simultaneous rounds we did, the clustering was fairly severe, apparently more than for the sequential rounds.

In Period 11, we see definite clustering, but the winner, player 4, was largely alone. (72, 30)

Period 11

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In Period 12, we see clustering as well, and while the winner, player 2, was still relatively alone, another store is almost nearby. (20, 80)

Period 12

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In Period 13, there is some clustering, but more “lonely” stores. The winner, player 2, has just one nearby competitor. (76, 20)

Period 13

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In Period 14, clustering returns, with the winner, player 13, also having one nearby competitor. (40, 15)

Period 14

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In Period 15, where the density worked towards the center, the winner, player 1, was very close to a number of stores, but was still relatively “lonely.” Given the high central density, it is not surprising to see so much clustering. Also, the four stores who each had a corner eked out moderate profits. (42, 55)

Period 15

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In Period 16, only two players avoided the central cluster, each garnering moderate profits. The winner, player 1, near but not relatively near other players and choosing an area in the central cluster. (41, 50)

Period 16

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In Period 17, players once again ventured beyond the center, but players 3 and 12, the winners, dove right into the middle. (42, 53) and (55, 55)

Period 17

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In Period 18, we moved to a corner-heavy density. Clustering proved extreme, although only player 8 risked the lonely middle and acquired only a low profit. The winner, 2, went to (10, 90)

Period 18

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In Period 19, we again saw plenty of clustering and one brave soul in the middle. That brave soul performed better, but the winner was still the one who went nearer to others, 12, at (88, 15)

Period 19

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In Period 20, we once again saw one person head for the center, again to little effect. The winners still went to the obvious customer clusters, 4 and 7 at (82, 80) and (13, 85)

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Learning Curve?

The need for repetition of periods: Players / Real-life businesses learn to maximize

profits by finding a spatial strategy Players got better as game went on Less standard deviation in profits when

condition was repeated over several periods

Standard Deviation in ProfitsCustomer Distribution Period Standard Deviation in Profit

Simultaneous Uniform Randomness 1 5.32

  2 4.61

  3 4.61

Central Clustering 5 6.58

Corner Clustering 8 6.27

Uniform Randomness 11 3.16

  12 2.77

Sequential   13 2.52

  14 2.57

Central Clustering 15 3.13

  16 2.8

Corner Clustering 17 3.86

  18 4.78

  19 3.07

  20 2.57

First Mover Advantage?

Theory being tested: The first player to move into a market likely has

an insurmountable edge over the competition In the sequential game, Subject 1 always

moved first Double advantage:

Freedom to choose best location When equidistant from customer as another

player, the first mover captures the profit

Results for Player 1

Period Player 1 Max Profit

11 2 13

12 3 12

13 9 11

14 4 11

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16 13 13

17 7 13

18 6 13

19 11 12

20 6 11

…Not much 1st mover advantage except in rounds of central clustering.

Lack of experience High number of players Lack of significance

Private book trader vs. Amazon

Early Mover Advantage?

As noted before, however, players 1-4 as a whole tended to dominate in the sequential rounds. This could imply that after “prime locations” get progressively taken, players are wary of moving too close to one another.

For further consideration

Hotelling is a monopolistic competition model Relaxing more assumptions

More levels of product differentiation, differences in consumer preferences

A 3D / 4D Model? Application to non-spatial dimensions of price, time, etc.

For further consideration

Real life applications on a macro-scale Shopping malls? Gas stations?

Social / Cultural / Political implications Positioning on a spectrum: Social values, political doctrines, etc.