Used Game Theory methed to solve in for each Note Situation

Used Game Theory methed to solve in for each

Note :

Situation: Ten tenants of an apartment building are interested in purchasing solar panels to
generate electricity for their apartment. If all tenants have one solar panel on the roof, the
panels receive the maximum incident light leading to maximum power output, but this takes
up all the space on the roof. Tenants are allowed to purchase additional panels but must
share the existing roof space such that each additional panel purchased leads to an overall
eciency decrease of Y % per panel for all panels even those not belonging to the tenant because the panels now must be in a less ecient con guration.

Goal for each tenant: Maximize the power output for their personal array without concern
for cost to purchase the panels, i.e. assume panels are free but must be used, as previously
described, on the roof. Assume it would take 25 panels per tenant to satisfy each tenant\'s
electricity requirements.

Analyze this n-person game where n = 10, X = 250, and Y = 20 and discuss the best strategies for each player. You can treat this game as one of perfect information so the number of panels21 for each player is common knowledge to all players. Analyze the impacts of cooperation between two or more players. Do these optimal strategies change if Y >0is reduced sufficiently?

Solution

When the both X and Y player has equal change to get the success. Then the probability of winning by X is 1/10 is equal to probability of winning in Y is 1/10