Game Theory and Strategy End Term: 22 December 2024, Set QDB3 (September 2024 term)

Based on the above data, answer the given subquestions

Enter the Value a = __________

Based on the above data, answer the given subquestions

Enter the Value b = __________

Based on the above data, answer the given subquestions

Enter the Value c = __________

Based on the above data, answer the given subquestions

Enter the Value d = __________

Based on the above data, answer the given subquestions

Enter the Value e = __________

Based on the above data, answer the given subquestions

Enter the Value f = __________

Based on the above data, answer the given subquestions

Enter the Value g = __________

Based on the above data, answer the given subquestions

Enter the Value s1 = __________

Based on the above data, answer the given subquestions

Enter the Value s2 = __________

Based on the above data, answer the given subquestions

Enter the Value s3 = __________

Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. There are three advertisers who are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions

Total valuation of socially optimal allocation will be __________

Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. There are three advertisers who are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions

VCG price for slot a will be __________

Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. There are three advertisers who are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions

VCG price for slot b will be __________

A man dies, leaving an estate worth 500 units. The deceased has two creditors; one’s claim is 400 units, and the other’s claim, 300 units. The division of the estate between them is carried out according to the contested garment principle.
Based on the above data, answer the given subquestions

Creditor 1 with claim 400 units gets

A man dies, leaving an estate worth 500 units. The deceased has two creditors; one’s claim is 400 units, and the other’s claim, 300 units. The division of the estate between them is carried out according to the contested garment principle.
Based on the above data, answer the given subquestions

Creditor 2 with claim 300 units gets

Five bidders with private valuations uniformly distributed between 0 and 1 participate in a sealed bid first price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy answer the given subquestions:

Optimal bid for a bidder with valuation 0.6 will be

Five bidders with private valuations uniformly distributed between 0 and 1 participate in a sealed bid first price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy answer the given subquestions:

The expected revenue of the seller in this auction scenario will be

A machine can be in two possible states viz. Good (G) and Bad (B). It is in the Good state 90% of the time. An item produced by the machine is Defective (D), 1% of the time if it is Good and 10% of the time if it is Bad.
Based on the above data, answer the given subquestions

What is the probability of the item being defective

A machine can be in two possible states viz. Good (G) and Bad (B). It is in the Good state 90% of the time. An item produced by the machine is Defective (D), 1% of the time if it is Good and 10% of the time if it is Bad.
Based on the above data, answer the given subquestions

What is the probability that the machine is good if the item is defective

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions

Consider the market for a single network good as discussed in the lecture and write a different consumer's utility function for joining the network as $U(\theta) = \theta(a + vn^e)$ capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e. consumers differ in their valuation of both the standalone and the network benefits). Here, $a$ is the standalone benefit, $v > 0$ measures the network effect, $n^e$ is the expected number of users joining the network and $\theta$ is uniformly distributed on the unit interval.

Based on the above data, answer the given subquestions

Based on the above data, answer the given subquestions

Based on the above data, answer the given subquestions

Nash equilibrium of this game will be

A cable TV station wants to connect three new customers to its network. The connections to the network are described in the following tree graph:

Calculate the distribution of the costs among the three players if all three decide to connect to the network.
Based on the above data, answer the given subquestions

The cost to be paid by player 1 will be __________

A cable TV station wants to connect three new customers to its network. The connections to the network are described in the following tree graph:

Calculate the distribution of the costs among the three players if all three decide to connect to the network.
Based on the above data, answer the given subquestions

The cost to be paid by player 2 will be __________

A cable TV station wants to connect three new customers to its network. The connections to the network are described in the following tree graph:

Calculate the distribution of the costs among the three players if all three decide to connect to the network.
Based on the above data, answer the given subquestions

The cost to be paid by player 3 will be __________

Based on the above data, answer the given subquestions

How many pure strategy equilibria are there in this game?

Based on the above data, answer the given subquestions

In one of these pure NEs, all three players enter the market

Based on the above data, answer the given subquestions

Suppose 5 numbers are drawn independently from the uniform distribution on the interval [0, 1] and then sorted from smallest to largest. The expected value of the number in second position on the list is

In weighted majority game [7; 5, 4, 3, 1]

Consider following two statements:
1. Crowd can be wrong even if everyone in the crowd is rational and everyone takes the same action.
2. Aggregate behaviour of many people with limited information can sometimes produce very accurate results.
Which statement(s) is (are) true?

Choose the correct alternative