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.
Graph

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.

a. In the given game, neither player has a dominant strategy. A dominant strategy occurs when a player's best choice remains the same regardless of the other player's choice. In this case, both players face a negative payoff if they choose different sides, so it is in their best interest to choose the same side. However, there is no dominant strategy for either player as they have different payoffs for choosing their respective sides.

b. Yes, there is a Nash equilibrium in this game. Nash equilibrium occurs when both players choose their best strategies given the other player's strategy. In this case, the Nash equilibrium is achieved when both players choose the same side, either left or right. If both players choose the same side, neither player has an incentive to unilaterally change their decision since they would incur a negative payoff.

c. This game is called a cooperative game because it emphasizes the importance of cooperation between players in order to maximize their collective benefits. In this specific example, the players need to cooperate by choosing the same side of the road to prevent accidents and ensure everyone's safety. Choosing different sides would result in negative outcomes for both players, highlighting the need for cooperation.

2. Without a specific graph provided, it is difficult to give precise answers to the questions regarding the firm's total revenue, total cost, total profits, and output. To determine these values, it is necessary to have additional information such as the firm's demand curve, cost function, and pricing strategy.

a. Total Revenue is calculated by multiplying the quantity of units sold by the corresponding price of each unit.

b. Total Cost includes both fixed costs (e.g., rent, salaries) and variable costs (e.g., materials, labor) incurred by the firm in the production process.

c. Total Profits can be determined by subtracting the total cost from the total revenue. If the result is positive, it indicates a profit, and if negative, it indicates a loss.

d. If the monopolist were to behave like a perfectly competitive firm in the long run, its output would be determined by the point at which marginal cost equals marginal revenue, as is the case in perfect competition. This output level optimizes efficiency for the firm.

a. In this game, neither player has a dominant strategy because their payoffs depend on the choices made by both players. If Driver 1 chooses Left, Driver 2's payoff is -1000 regardless of their choice, and if Driver 1 chooses Right, Driver 2's payoff is 0 regardless of their choice. Similarly, if Driver 2 chooses Left, Driver 1's payoff is -1000 regardless of their choice, and if Driver 2 chooses Right, Driver 1's payoff is 0 regardless of their choice. Therefore, there is no dominant strategy for either player in this game.

b. There is a Nash equilibrium in this game, which occurs when both players choose Left. In this case, neither player has an incentive to unilaterally deviate from their chosen strategy because any deviation would result in a worse payoff for that player. Both players receive a payoff of 0 if they both choose Left, and any other combination of choices would result in a payoff of -1000 for the player who deviates. Therefore, (Left, Left) is a Nash equilibrium.

c. This game is called a cooperative game because the players have a mutual interest in coordinating their choices to achieve the best outcome for both. The goal is for both players to choose the same side, regardless of whether it is Left or Right. By cooperating and choosing the same side, they can avoid the negative outcome of getting hurt.