NetLogo User Community Models

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Download If clicking does not initiate a download, try right clicking or control clicking and choosing "Save" or "Download".(The run link is disabled for this model because it was made in a version prior to NetLogo 6.0, which NetLogo Web requires.)

## WHAT IS IT?

This is a simple model of competing restaurants choosing where to locate in a strip shopping mall. The model supports a series of games, outlined below, that students can use to explore the principle of minimum differentiation aka Hotelling's Law .

## HOW TO USE IT

PURPOSE: To gain experintial familiarity with the strengths and weaknesses of the principle of minimum differentiation as a model that explains the observed clustering of retail sellers at a central location.

Open the Location Game and click on "setup".
You are looking down on a strip shoppping mall with 66 potential lunch buyers scattered around the mall neighborhood. There are two sellers of lunch, represented by an orange and a pink patch at opposite ends of the mall. Sellers can change their starting locations by using the two "location" sliders. Other than location, the sellers are identical. Buyers purchase one, and only one lunch each day. A third, blue seller is built into the game as an option. The initial setup eliminates the blue seller by setting their location at 18, outside of the mall.

Click setup.
Click go.
Each time go is clicked, all buyers move one patch. Repeatedly click go to progress through the game.
At noon every day, all buyers begin to move toward the mall. When they reach the mall, they begin to move along the mall in search of a place to eat lunch. The 33 red buyers move to the right. The 33 blue buyers move to the left. When a buyer is directly opposite a seller, they move into the seller location where they are counted as that seller's customer, and then exit the game. Buyers randomly look left or right first; consequently, there is no advantage to being on the left or right side of the mall. When a buyer reaches the end of the mall, they turn aound, change color, and start moving back down the mall in the opposite direction.

The counters and graphs show the cumulative number of buyers each seller receives.

## GAME 1: SOCIALLY OPTIMAL (UNIFORM DISTRIBUTION) SINGLE PLAYER
You are a benevolant dictator charged with choosing where to locate the two sellers of lunch. Your goal is to choose optimal locations so that buyers minimize their cost of travel time. Travel time is represented in the game by the number of "ticks" needed before all buyers have had lunch. The ticks are counted in the upper left portion of the screen. To reflect Hotelling's initial assumption of evenly distributed buyers, click on the "uniform" button after setup to create a uniform starting distribution of buyers.

WHAT IS THE OPTIMAL LOCATION FOR THE TWO STORES?

WHAT IS THE TOTAL NUMBER OF TICKS NEEDED AT THIS OPTIMAL LOCATION? DOES THIS TOTAL MATCH OTHER PLAYERS' RESULTS?

## GAME 2: SOCIALLY OPTIMAL (RANDOM DISTRIBUTION) SINGLE PLAYER
You are still a benevolant dictator charged with choosing where to locate the two sellers of lunch. Your goal is to choose optimal locations so that buyers minimize their cost of travel time. Travel time is represented in the game by the number of "ticks" needed before all buyers have had lunch. The ticks are counted in the upper left portion of the screen. To make the simulation more realistic than Hortelling's assumption of an even distribution, use the simulation's default, random distribution of buyers (Don't click the uniform button.)

WHAT IS THE OPTIMAL LOCATION FOR THE TWO STORES?

WHAT IS THE TOTAL NUMBER OF TICKS NEEDED AT THIS OPTIMAL LOCATION? DOES THIS TOTAL MATCH OTHER PLAYERS' RESULTS?

WHY IS THE TOTAL TICKS COUNT WITH A RANDOM DISTRIBUTION NOT NECESSARILY CONSISTENT WITH OTHER PLAYERS' RESULTS? DOES THIS ALTER THE SOCIALLY OPTIMAL SOLUTION?

## GAME 3: PRINCIPLE OF MINIMUM DIFFERENTIATION: TWO PLAYERS
Two players compete on the same simulation. Each player is a profit-maximizing seller of lunch. The seller with the most buyers ('count-pink" and "count-orange') has the most profit and wins the game. Part of this game is to experience the sequential choices that occur before equilibrium is reached, so the rule is to flip a coin to determine who gets to change location first. After the locations are selected, click through the simulation, and the player with the highest number of buyers must change location first, followed by the other player, followed by a running of the simulation, etc. Because this is a defensive game, going second has advantages.

WHERE DO YOU STOP WANTING TO CHANGE LOCATION?

IF LOCATION IS THE ONLY THING THAT DIFFERENTIATES YOU FROM YOUR COMPETITOR, HAVE YOU MAXIMIZED OR MINIMIZED THAT DIFFERENTIATION? IS THIS CONSISTENT WITH HOTELLING'S PRINCIPLE OF MINIMUM DIFFERENTIATION? (HOTELLING'S LAW)

HOW DOES YOUR PROFIT (NUMBER OF CUSTOMERS) AT THIS EQUILIBRIUM COMPARE TO THE PROFITS FROM THE SOCIALLY OPTIMAL LOCATIONS IN GAME 2?

HOW DOES THE SOCIAL WELFARE (NUMBER OF TICKS NEEDED) IN THIS EQUILIBRIUM COMPARE TO THE NUMBER OF TICKS USED IN THE SOCIALLY OPTIMAL OUTCOME OF GAME 2?

## GAME 4: THREE COMPETING PLAYERS
Hotelling's principle of minimum differentiation is very dependent on a set of strong assumptions. If the assumption of only two sellers is changed to three sellers, what happens? To find out, now three players are all using the same simulation. The third player controls the location of the blue seller. The orange and blue stores cannot choose the same location due to a programming limitation. The goal is to obtain the most buyers.

DO YOU REACH A POINT, AS IN GAME 3, WHERE EVERYONE STOPS WANTING TO CHANGE LOCATION? WHAT DOES THIS SAY ABOUT HOTELLING'S PREDICTION OF THE PRINCIPLE OF MINIMUM DIFFERENTIATION HOLDING TRUE FOR MULTIPLE SELLERS?

## GAME 5: UNEQUAL MARKET POWER AND AGRESSIVE INCUMBENT (TWO PLAYERS, THREE LOCATIONS)
The game returns to two players; however, now one player (the incumbent seller) has the option of opening a second (blue) location after the other player decides on their (new) location. This scenario allows the more realistic assumption of different behaviors to be explored. The game begins with the incumbent player’s (orange) store located at one end of the mall (16). Player two (pink) is now given the option of choosing a location. The incumbent (orange) seller cannot move from their starting location at the end of the mall. To create a more complex behavior, assume the incumbent is irrationally aggressive and will use their power to open an additional (blue) location to try to drive any competition out of the mall. Assume the new (pink) seller will fail (lose the game) if they obtain less than fifteen buyers. The incumbent’s new, blue, second-store location is chosen after the new (pink) seller chooses their location.

IF YOU ARE THE NEW-STORE PLAYER, WHERE DO YOU WANT TO LOCATE? DO YOU EVEN WANT TO TRY TO OPEN YOUR STORE (CAN YOU SEE ANY WAY TO ALWAYS HAVE AT LEAST 15 CUSTOMERS, REGARDLESS OF WHAT THE INCUMBENT DOES?)

## GAME 6: CIRCULAR MALL TWO PLAYERS
This is an opportunity to make a simple modification to the simulation's coding. To modify the program, you need to have downloaded the netlogo software and be running the simulation on your computer.
Click on the "Code" tab of the simulation to access the program. The goal is to change the scenario so that buyers are in a circular mall. That can be accomplished by having the simulation default back to the normal netlogo behavior of turtles "wrapping" around the back of the screen when they reach the edge of the screen. This return to the default "wrapping" is accomplished by eliminating the two lines of code that create the end-of-mall colored patches that tell buyers to turn around. Without these patches, buyers simply wrap around the back of the screen and reappear at the other end of the mall, still moving in the same direction. The two lines of code that need to be eliminated are bracketed by comment lines in the program: ELIMINATE FOR CIRCULAR CODE (START) and ELIMINATE FOR CIRCULAR CODE (STOP). The easiest way to experiment with eliminating code is to place a ";" in front of the code line, thereby turning it into a comment. If this causes a programming error, the ";" can be removed and something else can then be tried.

ONCE THE CIRCULAR MALL IS CREATED, WITH TWO PLAYERS, IS THE PRINCIPLE OF MINIMUM DIFFERNTIATION OBSERVED AS SELLERS SEEK TO MAXIMIZE PROFIT?

## GAME 7 UNCERTAINTY TWO PLAYERS
Even with some of the more realistic assumptions explored in previous games, if an element of uncertainty is introduced into the scenario, the principle of minimum differntiation begins to to again be verified. To see how this can occur, return to GAME 4 scenario of three players in the non-circular strip mall. While players could react to the choices of the other players in GAME 4, now an element of uncertainty is introduced by asking all three players to choose their locations simultaneously so that they don't know what the competition will do. To simulate this, a fourth person acts as gamekeeper and receives the three players' location choices, and then inputs them into the scenario.

GIVEN THE UNCERTAINTY OF NOT KNOWING WHERE THE OTHER TWO PLAYERS WILL LOCATE, WHERE DO YOU CHOOSE TO LOCATE? DOES THIS SEEM TO SUPPORT THE PRINCIPLE OF MINIMUM DIFFERENTIATION?

## CREDITS AND REFERENCES

Author: Dr. Jeffrey E. Russell
Affiliation: Ashland University, Ashland, Ohio

Email: jrussell@ashland.edu