Question

1. Suppose Company A is about to play a game with Company B. The following facts are known about the two players. The first Company (Company A) is a row player and uses three different strategies i.e. (Strategy X, Strategy Y and Strategy Z). Whereas the column player (Company B) has two different strategies i.e. (M and N) that can be used accordingly. The payoff matrix is given in the table below. Player A Player B M N X -5 3 Y 3 -7 Z -6 5 Answer the following questions based on the information given above a. Determine the strategies of each firm using graphical technique b. Compute the value of the game.

Answer 1

To determine the strategies of each firm, plot the payoff matrix on a graph and find the intersection of the lines. The value of the game is -7 at the Nash equilibrium.

1. To determine the strategies of each firm, we can plot the payoff matrix on a graph.
2. The row player's strategies are represented on the x-axis, and the column player's strategies are represented on the y-axis.
3. The graph will have three points for the row player (X, Y, Z) and two points for the column player (M, N). We can plot the payoffs in the matrix on the graph and connect them to form lines.
4. The intersection of these lines will represent the strategies of each firm.
   To compute the value of the game, we need to find the Nash equilibrium.
5. This is the point where both firms are playing their best strategies, considering the other firm's strategy. In this case, the Nash equilibrium occurs at the intersection of Strategy X for Firm A and Strategy N for Firm B.
6. The value of the game at this equilibrium is -7.