Gym X and Bodyworks Are Both Going to Open an Exercise

question 93

Essay

Gym X and Bodyworks are both going to open an exercise facility in the local market. Each company may decide to open a facility concentrating on cardio equipment for customers interested in mostly aerobic workouts. Another alternative for each company is to open a facility concentrating on muscle building equipment for customers interested mostly in bodybuilding workouts. The payoff matrix for each company dependent upon their strategies and that of their competitor is given below. Does either player have a dominant strategy? Does the game have any Nash equilibria? What is the maximin strategy of each player in the game?

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Definitions:

Median

The middle value in a data set, which effectively divides the dataset into two halves, with one half having values above the median and the other half below.

Mean

The arithmetic average of a set of numbers, calculated by adding them together and dividing by the number of values.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values, indicating how much the values deviate from the mean.

Range

The difference between the highest and lowest values in a set of numbers, indicating the spread or dispersion of the dataset.