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.
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.
No one has answered this question yet.
a. Does either player have a dominant strategy? Explain. There is no choice that either player will always have a higher payoff regardless of what the other player does.
b. Is there Nash equilibrium in this game? Explain
According to the information provided I am assuming that both players know the strategy of each other, so my answer would be yes there is a Nash Equilibrium in this game. If the player prefer not to switch their strategy this is definitely consider Nash equilibrium which are (left, left) or payoff (0, 0) for players one or two. Also assuming each player knows the strategies of the other, then yes, there is no benefit to changing a strategy unilaterally.
c. Why this game is called a cooperative game? Because in this game both players should be cooperative to ensure maximum payoff because, both adopting strategy A, to the highest payoff (say left, left) also players can earn higher payoffs if they work together and drive on the same side of the road.
2.
a. What is the firm’s Total Revenue? Produce were MR=MC, and charge price based on demand. So, total revenue is area A J E 0 (or A * E)
b. What is the Total Cost? Total costs are shown by area B H E 0 (or B * E)
c. What is the firm’s Total Profits? Total profits are area A J H B (or A-B * E)
d. If the above monopolist were to behave like a perfectly competitive firm (operating in the long run), determine its output.
In perfect competition the firm would produce where P = MC, so point N above
1.
a. In this game, neither player has a dominant strategy. A dominant strategy is a strategy that is always the best choice regardless of the actions taken by the other player. In this case, both players have the same payoffs regardless of the side they choose, so there is no dominant strategy.
b. Yes, there is a Nash equilibrium in this game. A Nash equilibrium occurs when no player can improve their payoff by unilaterally changing their strategy. In this game, the Nash equilibrium is when both players choose the same side, either left or right. If one player deviates from this equilibrium and chooses a different side, they will get a lower payoff, which means they have no incentive to switch their strategy.
c. This game is called a cooperative game because both players need to cooperate and make the same choice in order to avoid getting hurt. If they both choose the same side, it doesn't matter which side it is, they will be safe. However, if they choose different sides, they will collide and both get hurt. This game requires cooperation and coordination between the players to achieve the best outcome for everyone.
2.
a. The firm's Total Revenue is calculated by multiplying the price of the product by the quantity sold. Total Revenue = Price × Quantity.
b. Total Cost is the sum of all the costs incurred by the firm in producing a certain quantity of output. It includes both explicit costs (such as wages, rent, and materials) and implicit costs (such as the opportunity cost of the owner's time and capital). To determine the Total Cost, you need to know the different costs associated with production.
c. Total Profits is calculated by subtracting Total Cost from Total Revenue. Total Profits = Total Revenue - Total Cost.
d. If the monopolist were to behave like a perfectly competitive firm in the long run, it would produce the level of output where marginal cost equals marginal revenue. This is because in perfect competition, firms aim to maximize profits by producing the quantity at which marginal cost equals marginal revenue. So, the monopolist would determine the output level based on these conditions.
1. a) To determine if either player has a dominant strategy, we need to compare the payoffs for each player in each possible scenario. In this scenario, the payoffs are represented by the numbers in the matrix.
For Driver 1:
- If Driver 2 chooses Left, Driver 1's payoff is 0 if they also choose Left and -1000 if they choose Right.
- If Driver 2 chooses Right, Driver 1's payoff is -1000 if they choose Left and 0 if they also choose Right.
For Driver 2:
- If Driver 1 chooses Left, Driver 2's payoff is 0 if they also choose Left and -1000 if they choose Right.
- If Driver 1 chooses Right, Driver 2's payoff is -1000 if they choose Left and 0 if they also choose Right.
Based on these payoffs, we can see that there is no dominant strategy for either player. A dominant strategy is one that always yields a higher payoff, regardless of the other player's choice. In this game, no matter what strategy one player chooses, the other player's best response is to choose the same strategy.
b) A Nash equilibrium is a situation in which each player's strategy is the best response to the other player's strategy. To find a Nash equilibrium, we need to look for a pair of strategies where neither player has an incentive to unilaterally deviate.
In this game, the Nash equilibrium occurs when both players choose the Left strategy. If Driver 1 chooses Left, Driver 2's best response is to also choose Left. Similarly, if Driver 2 chooses Left, Driver 1's best response is to also choose Left. In this case, neither player has an incentive to deviate, as switching to the Right strategy would only result in a lower payoff for both players.
c) This game is called a cooperative game because the players need to coordinate and cooperate in order to achieve the best outcome. The strategy that leads to the highest overall payoff for both players is for both of them to choose the Left side of the road. If they choose different sides, it leads to negative payoffs for both players, illustrating the importance of cooperation in this game.
2. a) To calculate the firm's Total Revenue, you need to multiply the price of the product by the quantity sold. If you have information on the price and quantity, you can simply multiply these two values together to obtain the Total Revenue.
b) To determine the Total Cost of the firm, you need to consider all the costs incurred in producing the goods or services. This includes factors such as the cost of raw materials, labor, rent, utilities, and any other expenses related to production.
c) The firm's Total Profits can be calculated by subtracting the Total Cost from the Total Revenue. This represents the amount of money the firm has left over after covering all the expenses. Positive profits indicate that the firm is making money, while negative profits indicate losses.
d) If the above monopolist were to behave like a perfectly competitive firm operating in the long run, it would produce the quantity where marginal cost equals marginal revenue. In a perfectly competitive market, firms are price-takers and have to sell at the market price. Therefore, the output level in the long run would be where the marginal cost curve intersects the market price, which represents the equilibrium output level for a perfectly competitive firm.