Game Theory and Strategy End Term: 22 December 2024, Set QDB1 (September 2024 term)

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

The fulfilled-expectations demand curve in this setting will be

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

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

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

A market game has two buyers and one seller. Seller 1 has a watch whose worth for him is ₹200 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a watch. The worth of watch is ₹280 for one buyer (player 2) and ₹300 for the other buyer (player 3). Each buyer is interested in paying the lowest price for the watch and unwilling to pay more than the watch's worth to him. Describe the game in coalition form and answer the given sub questions.

Suppose that you receive a piece of e-mail whose subject line contains the phrase “check this out” (a popular phrase among scammers). Based just on this and without looking at the sender or the message content, what is the chance that the message is spam? Suppose that 40% of all your emails are spam and the remaining 60% are emails you want to receive. Suppose that 1% of all spam messages contain the phrase “check this out” in their subject lines, while 0.4% of all non- spam messages contain this phrase.
Based on the above data, answer the given subquestions

What is the total probability of having the phrase “check this out” in subject line of an email?

Suppose that you receive a piece of e-mail whose subject line contains the phrase “check this out” (a popular phrase among scammers). Based just on this and without looking at the sender or the message content, what is the chance that the message is spam? Suppose that 40% of all your emails are spam and the remaining 60% are emails you want to receive. Suppose that 1% of all spam messages contain the phrase “check this out” in their subject lines, while 0.4% of all non- spam messages contain this phrase.
Based on the above data, answer the given subquestions

What is the probability that the message is spam if subject contains the phrase “check this out”?

Based on the above data, answer the given subquestions

The cost to be paid by player 1 will be ________

Based on the above data, answer the given subquestions

The cost to be paid by player 2 will be _________

Based on the above data, answer the given subquestions

The cost to be paid by player 3 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:

Optimal bid for a bidder with valuation 0.75 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

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

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

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