5. Along a stretch of a beach are 500 children in 5 clusters of 100 each.(Label the clusters A, B,C,D and E) Two ice cream vendors are decidingsimultaneously where to locate. They must choose the exact locationof one of the clusters. If there is a vendor in one cluster, all 100 childrenin that cluster will buy an ice cream. For clusters without a vendor, 50of the 100 children are willing to walk to a vendor who is one clusteraway, only 20 are willing to walk to a vendor two clusters away, andnone are willing to walk the distance of three or more clusters. Theice cream melts quickly, so the walkers cannot buy for the non-walkers.If vendors choose the same cluster, each will get 50 % of share of thetotal demand for ice cream. If they choose different clusters, then thosechildren for whom one vendor is closer than the other will go to thecloser one,and those for whom the two are equidistant will split 50%each. Each vendor maximizes her sales.(a) Construct the five-by-five payoff table for their location game.(b) Eliminate dominated strategies as far as possible.(c) In the remaining table locate all pure strategy Nash equilibria.(d) If the game is altered to one with sequential moves, where the firstvendor chooses her location first and the second vendor follows,what are the locations and sales that result from the rollbackequilibrium?

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Description: 5. Along a stretch of a beach are 500 children in 5 clusters of 100 each.(Label the clusters A, B,C,D and E) Two ice cream vendors are decidingsimultaneously where to locate. They must choose the exact locationof one of the clusters. If there is a v

A payoff matrix gives all combinations of stragies between two players in a two-person zero sum…

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(a) Construct the five-by-five payoff table for their location game. (b) Eliminate dominated strategies as far as possible. (c) In the remaining table locate all pure strategy Nash equilibria. (d) If the game is altered to one with sequential moves, where the first vendor chooses her location first and the second vendor follows, what are the locations and sales that result from the rollback equilibrium?

(a) Construct the five-by-five payoff table for their location game. (b) Eliminate dominated strategies as far as possible. (c) In the remaining table locate all pure strategy Nash equilibria. (d) If the game is altered to one with sequential moves, where the first vendor chooses her location first and the second vendor follows, what are the locations and sales that result from the rollback equilibrium?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

5. Along a stretch of a beach are 500 children in 5 clusters of 100 each.
(Label the clusters A, B,C,D and E) Two ice cream vendors are deciding
simultaneously where to locate. They must choose the exact location
of one of the clusters. If there is a vendor in one cluster, all 100 children
in that cluster will buy an ice cream. For clusters without a vendor, 50
of the 100 children are willing to walk to a vendor who is one cluster
away, only 20 are willing to walk to a vendor two clusters away, and
none are willing to walk the distance of three or more clusters. The
ice cream melts quickly, so the walkers cannot buy for the non-walkers.
If vendors choose the same cluster, each will get 50 % of share of the
total demand for ice cream. If they choose different clusters, then those
children for whom one vendor is closer than the other will go to the
closer one,
and those for whom the two are equidistant will split 50%
each. Each vendor maximizes her sales.
(a) Construct the five-by-five payoff table for their location game.
(b) Eliminate dominated strategies as far as possible.
(c) In the remaining table locate all pure strategy Nash equilibria.
(d) If the game is altered to one with sequential moves, where the first
vendor chooses her location first and the second vendor follows,
what are the locations and sales that result from the rollback
equilibrium?

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