Two firms, A and B, have entered the bike sharing market and have to decide on the amount of bikes to provide. Each firm can deploy either 100 bikes or 200 bikes. Assume that it costs both firms $10 per bike to deploy. The firm’s revenue will be $18 per bike if there are 2,00 bikes (in total) in the market; $15 per bike if there are 3,00 bikes in the market, and $11 per bike if there are 400 bikes in the market. (a) Establish the payoff matrix for profit earned and strategies faced by A and B. Solve for the Nash equilibrium. (b) A could invest in a machine that would lower the cost per bike from $10 to $5 (for A only). Other things equal, if A invests in the machine, what will be the Nash Equilibrium of the game? What is the maximum price A should pay for the investment in the machine? Hi, I have the answer sheet but may i request for a more detailed explanation to constructing the matrix as well as part (b)? Thank you.
Two firms, A and B, have entered the bike sharing market and have to decide on the amount of bikes to provide. Each firm can deploy either 100 bikes or 200 bikes. Assume that it costs both firms $10 per bike to deploy. The firm’s revenue will be $18 per bike if there are 2,00 bikes (in total) in the market; $15 per bike if there are 3,00 bikes in the market, and $11 per bike if there are 400 bikes in the market.
(a) Establish the payoff matrix for profit earned and strategies faced by A and B. Solve for the Nash equilibrium.
(b) A could invest in a machine that would lower the cost per bike from $10 to $5 (for A only). Other things equal, if A invests in the machine, what will be the Nash Equilibrium of the game? What is the maximum price A should pay for the investment in the machine?
Hi, I have the answer sheet but may i request for a more detailed explanation to constructing the matrix as well as part (b)? Thank you.
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