Game Theory and Strategy End Term: 31 August 2025, Set QDB1 (May 2025 term)

Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.

If an item is selected at random, the probability that the item is defective is _____________

Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.

Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ______________

Based on the above data, answer the given subquestions.

What is the best response of roommate 2 if roommate 1 chooses t1 = 0?
t2 =________________

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.

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(θ)=θ(a+νn^(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, ν > 0 measures the network effect, n^(e) is the expected number of users joining the network and θ 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(θ)=θ(a+νn^(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, ν > 0 measures the network effect, n^(e) is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.

The maximum value of p to have buyers will be

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(θ)=θ(a+νn^(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, ν > 0 measures the network effect, n^(e) is the expected number of users joining the network and θ 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(θ)=θ(a+νn^(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, ν > 0 measures the network effect, n^(e) is the expected number of users joining the network and θ 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(θ)=θ(a+νn^(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, ν > 0 measures the network effect, n^(e) is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.

p(n^(e),n) is _____________ (more than one options are correct)

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(θ)=θ(a+νn^(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, ν > 0 measures the network effect, n^(e) is the expected number of users joining the network and θ 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

Calculate the Shapley value of the following game using the procedure for dissolving a partnership

$N = \{1, 2, 3, 4\}$

$\begin{array}{llll} v(1) = 24 & v(2) = 48 & v(3) = 24 & v(4) = 72 \\ v(1,2) = 96 & v(2,3) = 144 & v(1,4) = 120 & v(1,3) = 0 \\ v(2,4) = 0 & v(3,4) = 0 & & \\ v(1,3,4) = 168 & v(1,2,3) = 0 & v(1,2,4) = 0 & \\ v(2,3,4) = 0 & v(1,2,3,4) = 240 & v(\emptyset) = 0 & \end{array}$

Based on the above data, answer the given subquestions.

S1 = ________________

Calculate the Shapley value of the following game using the procedure for dissolving a partnership

$N = \{1, 2, 3, 4\}$

$\begin{array}{llll} v(1) = 24 & v(2) = 48 & v(3) = 24 & v(4) = 72 \\ v(1,2) = 96 & v(2,3) = 144 & v(1,4) = 120 & v(1,3) = 0 \\ v(2,4) = 0 & v(3,4) = 0 & & \\ v(1,3,4) = 168 & v(1,2,3) = 0 & v(1,2,4) = 0 & \\ v(2,3,4) = 0 & v(1,2,3,4) = 240 & v(\emptyset) = 0 & \end{array}$

Based on the above data, answer the given subquestions.

S2 = ________________

Calculate the Shapley value of the following game using the procedure for dissolving a partnership

$N = \{1, 2, 3, 4\}$

$\begin{array}{llll} v(1) = 24 & v(2) = 48 & v(3) = 24 & v(4) = 72 \\ v(1,2) = 96 & v(2,3) = 144 & v(1,4) = 120 & v(1,3) = 0 \\ v(2,4) = 0 & v(3,4) = 0 & & \\ v(1,3,4) = 168 & v(1,2,3) = 0 & v(1,2,4) = 0 & \\ v(2,3,4) = 0 & v(1,2,3,4) = 240 & v(\emptyset) = 0 & \end{array}$

Based on the above data, answer the given subquestions.

S3 = ________________

Calculate the Shapley value of the following game using the procedure for dissolving a partnership

$N = \{1, 2, 3, 4\}$

$\begin{array}{llll} v(1) = 24 & v(2) = 48 & v(3) = 24 & v(4) = 72 \\ v(1,2) = 96 & v(2,3) = 144 & v(1,4) = 120 & v(1,3) = 0 \\ v(2,4) = 0 & v(3,4) = 0 & & \\ v(1,3,4) = 168 & v(1,2,3) = 0 & v(1,2,4) = 0 & \\ v(2,3,4) = 0 & v(1,2,3,4) = 240 & v(\emptyset) = 0 & \end{array}$

Based on the above data, answer the given subquestions.

S4 = ________________

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.

There is a symmetric mixed strategy equilibrium where all three players enter with the same probability (say p). Find the value of p

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 ______________

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 sub-questions:

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 sub-questions:

The expected revenue of the seller in this auction scenario 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. Three advertisers 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. Three advertisers 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. Three advertisers 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; 1, 4, 3, 5]

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