Question

Suppose the managers of Superstore and Sobeys must decide independently and simultaneously

whether to print their respective "high price flyer", which we denote strategy H, or their "low price
flyer" which we denote strategy L. If both choose strategy H, each firm would receive a profit of $3
million. If one firm chose H while the other chose L, the profit for the firm that chose H would be $1
million while the profit to the firm that chose L would be $4 million. If both firms choose strategy L, the
profit to each firm would be $2 million.
a) Depict this game as a two-row by two-column matrix, with Superstore being the firm that must choose
the H or L row and Sobeys being the firm that must choose the H or L column. The payoff in each cell is
an ordered pair of numbers, where the first number denotes the profit (in millions of dollars) to Superstore
and second number denotes the profit (in millions of dollars) to Sobeys.
b) What is the unique pair of strategies that would result? Explain why this pair of strategies are mutually
best-response strategies and are, therefore, constitute a Nash equilibrium.
c) Would the firms be maximizing their joint profit? If not, could the firms collude in order to increase
their individual and joint profit? Explain why a collusive agreement would be very difficult to
implement.

Answer 1

The game can be depicted as a matrix with Superstore's and Sobeys' choices represented by rows and columns. The unique pair of strategies that would result as a Nash equilibrium is L-L. The firms would not be maximizing their joint profit, and implementing a collusive agreement would be difficult.

Step-by-step explanation:

The two-firm game can be depicted as a two-row by two-column matrix. In this case, Superstore's choices are represented by the H or L row, and Sobeys' choices are represented by the H or L column. The payoffs in each cell of the matrix are an ordered pair of numbers, representing the profit (in millions of dollars) to Superstore and Sobeys respectively.

The unique pair of strategies that would result as a Nash equilibrium in this game is when both firms choose strategy L. This is because, if Superstore chooses H while Sobeys chooses L, Superstore's profit would be $1 million, but if Superstore chooses L while Sobeys chooses L, Superstore's profit would be $2 million. Similarly, if Sobeys chooses H while Superstore chooses L, Sobeys' profit would be $1 million, but if Sobeys chooses L while Superstore chooses L, Sobeys' profit would be $2 million. In both cases, choosing strategy L is the best response for both firms. Therefore, L-L is the Nash equilibrium.

The firms would not be maximizing their joint profit in this scenario. If they were to collude and agree to both choose strategy H, they would each receive a profit of $3 million and maximize their individual and joint profit. However, implementing such a collusive agreement would be very difficult. The firms are competitors in an oligopoly, where each firm has an incentive to deviate and choose strategy L to earn a higher profit. This is referred to as the prisoner's dilemma where individual self-interest leads to a suboptimal outcome.