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## Finite Mathematics

by: Briana Cassin

16

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# Finite Mathematics MATH 10120

Briana Cassin
ND
GPA 3.65

Anne Pilkington

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COURSE
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Anne Pilkington
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KARMA
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## Popular in Mathematics (M)

This 0 page Class Notes was uploaded by Briana Cassin on Sunday November 1, 2015. The Class Notes belongs to MATH 10120 at University of Notre Dame taught by Anne Pilkington in Fall. Since its upload, it has received 16 views. For similar materials see /class/232695/math-10120-university-of-notre-dame in Mathematics (M) at University of Notre Dame.

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Date Created: 11/01/15
The Location Game Another common example of where behavior is in uenced by pay off is the Location game The pro ts of a business are often dependent on how close they are to potential customers For example Imagine the following simple model Roger and Colleen both work for the HB ice cream company Their Job is to sell ice cream at a popular beach They can both choose where to set up their booth on the beach each day7 however due to the refrigeration necessary and the amount of ice cream they must keep in stock7 the booth must remain stationary for the day Roger and Colleen both commit to a location for their booth each morning simultaneously and independently They each get a commission of 25 cents per ice cream sold The beach is divided into 11 regions of equal size as shown below 1 2 3 4 5 6 7 8 9 10 11 Roger and Colleen can choose any region each morning On any given day 50 people in each region will purchase an ice cream They will buy the ice cream from the nearest booth If the booths are equidistant from a region7 each booth will get half of the customers from that region Each region yields a commission of 1250 Rather than write out the 11 gtlt 11 pay off matrix and consider strategies Think about the following situations and see if you can gure out the optimum strategy for both Roger and Colleen lf Roger and Colleen situate their booths at Sections 1 and 11 respectively on the rst day7 how could Colleen increase her income on the second day if she thinks Roger will choose section 1 as the location of his booth on Day 2 Which Location would maximize Colleen7s pro ts if Roger always set up his booth in Section 1 What counterstrategy should Roger employ if Colleen pursues this strategy lf Roger always sets up his booth closer to they center say in section 3 where should Colleen set up her booth in order to maximize her pro ts 7 8 9 10 11 If Roger is interested in maximizing his pro ts what should his counterstrategy be Where will equilibrium be reached that is at which locations would you place the booths so that there is no incentive for either party to move We see examples of this behavior with similar stores setting up near each other quite often We can also apply the model to Politics In general voters in a country tend to be diverse Some want government regulation of some industries while others want no government intervention Some want open trade policies while others prefer isolationism In the Us this variation tends to be viewed as a one dimensional political spectrum with liberal minded people on the left and conservative people on the right It is probably true for the most part that a voter will vote for the candidate nearest to their outlook in regard to policy Liberal Conservative The location model suggests that Candidates will locate themselves towards the center of the spectrum This does in fact happen Also it explains why a candidates policies may shift as an election progresses in order to appeal to a wider spectrum of voters

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