Assignment 3
1. Some games of strategy are cooperative. One example is deciding which side of the road to drive on. It doesn’t matter which side it is as long as everyone chooses the same side. Otherwise, everyone may get hurt.
Driver 2
Left Right
Driver 1 Left 0,0 -1000 -1000
Right -1000, -1000 0,0
a. Does either player have a dominant strategy? Explain.
b. Is there Nash equilibrium in this game? Explain
c. Why this game is called a cooperative game?
2.
a. What is the firm’s Total Revenue?
b. What is the Total Cost?
c. What is the firm’s Total Profits?
d. If the above monopolist were to behave like a perfectly competitive firm (operating in the long run), determine its output.
1. a. To determine if either player has a dominant strategy, we need to compare the payoffs for each player. In this case, a dominant strategy is a strategy that is the best choice for a player regardless of what the other player chooses.
Looking at the payoffs in the matrix, we can see that for Driver 1, choosing "Left" is always better than choosing "Right" no matter what Driver 2 chooses. Choosing "Right" would result in a payoff of -1000, while choosing "Left" would result in a payoff of 0.
For Driver 2, choosing "Right" is always better than choosing "Left" no matter what Driver 1 chooses. Choosing "Left" would result in a payoff of -1000, while choosing "Right" would result in a payoff of 0.
Therefore, both players have dominant strategies. Driver 1's dominant strategy is to choose "Left", and Driver 2's dominant strategy is to choose "Right".
b. A Nash equilibrium is a situation in a game where each player's strategy is a best response to the other player's strategy. It is a stable state where no player has an incentive to unilaterally change their strategy.
In this game, the only combination of strategies where both players have chosen their dominant strategies is when Driver 1 chooses "Left" and Driver 2 chooses "Right". In this case, neither player can unilaterally change their strategy to improve their payoff.
Therefore, the Nash equilibrium in this game is when Driver 1 chooses "Left" and Driver 2 chooses "Right".
c. This game is called a cooperative game because the players need to cooperate and choose the same side of the road to drive on in order to avoid harm. If both players choose the same side, they will avoid the negative payoffs (-1000) related to choosing the opposite side and ensure a safe outcome for both.
2. a. Total Revenue is calculated by multiplying the price per unit by the quantity sold. In the question, the Total Revenue is not given. You would need to know the price per unit and the quantity sold to calculate the Total Revenue.
b. Total Cost is the sum of all costs incurred in producing the goods or services. The question does not provide information about the costs involved, so it is not possible to determine the Total Cost without that information.
c. Total Profits is calculated by subtracting Total Cost from Total Revenue. Since we do not have the information for either Total Revenue or Total Cost, we cannot calculate the Total Profits.
d. If the monopolist were to behave like a perfectly competitive firm operating in the long run, it would produce the output where marginal cost equals marginal revenue. In a perfectly competitive market, the firm is a price taker and its marginal revenue is equal to the market price. Without the information on the market price or the firm's marginal cost curve, we cannot determine the output in this scenario.