graphically distant firms, firm 1 and firm 2
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 2
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QUESTION 2
Two geographically distant firms, firm 1 and firm 2, compete in setting prices, selling the same good.
Suppose the consumers are uniformly distributed on the interval [0,1], and each will buy either one unit or nothing.
Firm 1 is located at 0 and firm 2 at 1. Firms cannot change their locations, only select prices. Firms simultaneously choose prices, firm 1 chooses p1 and firm
2 chooses P2.
Both firms produce at zero cost and must set prices between 0 and 6.
Consumers care about the distance they have to travel to buy the good, but also the price. They get a benefit of 6 from the good if purchased, but also pay a cost
of 2 times the distance traveled to make the purchase. If a consumer is located at x in [0.1] and they purchase from firm 1, their payoff is
6- 2x - P1
and if they purchase from firm 2, it's
6 - 2(1-x) - p2
If they don't purchase, their payoff is zero.
What price do the two firms set in the unique symmetric Nash equilibrium (they both set the same price)? Give your answer to 2 decimal places.
HINT: Find an expression for the "marginal consumer" that is indifferent between going to the two firms given prices (p,,pɔ).
5.00
QUESTION 3
In a mixed strategy Nash equilibrium, it must be that
OEach player gets the same expected payoff from all of her pure strategies.
Each player gets the same expected payoff from all pure strategies which she plays with strictly positive probability.
O Each player randomizes over all of her pure strategies.
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