Winning at board games is often determined by identifying and controlling the mo

Question

Winning at board games is often determined by identifying and controlling the most valuable locations on the board. The Miniopoly game board in the figure below represents a scaled down version of the popular board game Monopoly. The board contains eight tiles. Four of these tiles are property tiles indicated by the four colors: Green, Yellow, Red, and Blue. When a player lands on a property tile owned by another player, $100 in rent is paid to the property owner. The four corner tiles are instructional tiles. If a player lands on a corner tile, he or she immediately follows the instructions on that tile. All players start on the START tile and advance clockwise around the board based on the outcome of the spinner. The spinner has the numbers one through four indicating how many spaces a player moves

Red Ave.

Rent $100   

Yellow Ave.

Rent $100

Blue Ave.

Rent $100

Green Ave.

Rent $100

Start

<----------

a) Formulate a Markov chain operations model that could be used to determine which property is the most valuable to own in Miniopoly (i.e., the property that players end their turn on most often).

b) Verify that your model from part (a) meets the conditions to have a steady-state distribution.

c) Use your model from part (a) to determine the most valuable property in Miniopoly.

Red Ave.

Rent $100   

Yellow Ave.

Rent $100

Blue Ave.

Rent $100

Green Ave.

Rent $100

Start

<----------

Explanation / Answer

The blue Avenue is the most valuable property to own as charge has to be paid to the avenue if they enter the tile containing the avenue and the tile before it.

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