Game Theory and Strategy End Term: 13 September 2026 (May 2026 term)

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(1)=_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(2) =_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(ɸ)=_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(3) =_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(1,2) =_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(1,3) =_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(2,3) =_______

A market game has two buyers and one seller. Seller 1 has a laptop whose worth for him is $2000 and he offers it for sale. Players 2 and 3 are two potential buyers who do not own a laptop. The worth of the laptop is $2,800 for one buyer (player 2) and $3,000 for the other buyer (player 3). Each buyer is interested in paying the lowest possible price for the laptop and is of course unwilling to pay more than the worth of the laptop to him. Describe the game in coalition function form.
Based on the above data, answer the given subquestions.

v(1,2,3) =_______

Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games. This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see what is offered. They both end up at one stand where the ancient board game “Chaturanga” is offered in a second price auction. If they both bid the same, the winner is decided with the toss of a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them are of course very interested, nobody else cares about the old game and participates in the auction. Mohan and Charan know each other well. In particular, they both know the willingness to pay for the game of the other. Mohan is willing to pay ₹80000, while Charan’s maximum willingness to pay is ₹100000. The only admissible bids are 50, 70, and 90 thousand of INR. Represent the situation as a normal form game and answer the given subquestions:

At least one strategy is strictly dominated for Mohan and Charan both.

Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games. This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see what is offered. They both end up at one stand where the ancient board game “Chaturanga” is offered in a second price auction. If they both bid the same, the winner is decided with the toss of a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them are of course very interested, nobody else cares about the old game and participates in the auction. Mohan and Charan know each other well. In particular, they both know the willingness to pay for the game of the other. Mohan is willing to pay ₹80000, while Charan’s maximum willingness to pay is ₹100000. The only admissible bids are 50, 70, and 90 thousand of INR. Represent the situation as a normal form game and answer the given subquestions:

No. of Nash equilibria in pure strategies is

Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games. This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see what is offered. They both end up at one stand where the ancient board game “Chaturanga” is offered in a second price auction. If they both bid the same, the winner is decided with the toss of a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them are of course very interested, nobody else cares about the old game and participates in the auction. Mohan and Charan know each other well. In particular, they both know the willingness to pay for the game of the other. Mohan is willing to pay ₹80000, while Charan’s maximum willingness to pay is ₹100000. The only admissible bids are 50, 70, and 90 thousand of INR. Represent the situation as a normal form game and answer the given subquestions:

For Mohan, playing 70000 weakly dominates playing 90000.

Mohan and Charan, both students of game theory at IIT Chennai, are fans of old board games. This year the Indian-Board-Game-Day, a big fair, is held in Chennai and naturally both go to see what is offered. They both end up at one stand where the ancient board game “Chaturanga” is offered in a second price auction. If they both bid the same, the winner is decided with the toss of a coin (and the winner pays the bid, as the second bid coincides with the first). While both of them are of course very interested, nobody else cares about the old game and participates in the auction. Mohan and Charan know each other well. In particular, they both know the willingness to pay for the game of the other. Mohan is willing to pay ₹80000, while Charan’s maximum willingness to pay is ₹100000. The only admissible bids are 50, 70, and 90 thousand of INR. Represent the situation as a normal form game and answer the given subquestions:

For Charan, playing 90000 strictly dominates playing 50000.

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose:

Based on the above data, answer the given subquestions.

Ms. A will be paired with

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose:

Based on the above data, answer the given subquestions.

Ms. B will be paired with

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose:

Based on the above data, answer the given subquestions.

Ms. C will be paired with

Given the following preference structure, find a stable matching system using the Gale–Shapley algorithm when the men propose:

Based on the above data, answer the given subquestions.

Ms. D will be paired with

B Ri (Pj) will be

Choose the incorrect statement:

Considering two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from the point onward. Every quarter that both firms operate yields each a loss equal to -1, and each quarter that a firm operates alone yields a payoff of 3. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (-1,2) because both firms lose -1 in the first quarter and firm 2 gains 3 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter and N denote exit next quarter. Answer the given subquestions:

There are no strictly dominated strategies in this game.

Considering two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from the point onward. Every quarter that both firms operate yields each a loss equal to -1, and each quarter that a firm operates alone yields a payoff of 3. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (-1,2) because both firms lose -1 in the first quarter and firm 2 gains 3 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter and N denote exit next quarter. Answer the given subquestions:

Weakly dominated strategy in this game is

Considering two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit, then its payoff is 0 from the point onward. Every quarter that both firms operate yields each a loss equal to -1, and each quarter that a firm operates alone yields a payoff of 3. For example, if firm 1 plans to exit at the end of this quarter while firm 2 plans to exit at the end of the next quarter then the payoffs are (-1,2) because both firms lose -1 in the first quarter and firm 2 gains 3 in the second. The payoff for each firm is the sum of its quarterly payoffs. Formulate this as a normal form game considering that E denotes immediate exit, T denotes exit this quarter and N denote exit next quarter. Answer the given subquestions:

Which of the following is a pure strategy Nash equilibrium in this game

Based on the above data, answer the given subquestions.

a=_______

Based on the above data, answer the given subquestions.

Inscript b=_______

Based on the above data, answer the given subquestions.

c=_______

Based on the above data, answer the given subquestions.

d=_______

Based on the above data, answer the given subquestions.

e=_______

Based on the above data, answer the given subquestions.

f=_______

Based on the above data, answer the given subquestions.

S1=_________

Based on the above data, answer the given subquestions.

S2=_________

Based on the above data, answer the given subquestions.

S3 =_________

A man goes bankrupt and his entire estate at the time of bankruptcy is worth 250 units. The man has two creditors; one’s claim is 200 units, the other’s, 150 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 200 units gets

A man goes bankrupt and his entire estate at the time of bankruptcy is worth 250 units. The man has two creditors; one’s claim is 200 units, the other’s, 150 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 150 units gets

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

For what values of CA and CB would there be a Nash equilibrium in which nobody learned the other group’s language? CA should be

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

For what values of CA and CB would there be a Nash equilibrium in which nobody learned the other group’s language? CB should be

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

An outcome is said to be socially efficient if it maximizes total benefits minus total costs. For what values of CA and CB would it be socially efficient for type A’s to learn language B? The condition on CA and CB should be

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

For what values of CA and CB, would there be an equilibrium in which the type A’s learned language B and the type B’s did not learn language A. CA should be

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

For what values of CA and CB, would there be a Nash equilibrium in which the type B’s learned language A and the type A’s did not learn language B. CB should be

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

Another community has 3 linguistic groups, Type A’s who speak language A, Type B’s who speak language B and Type C’s who speak language C. There are 500 Type A’s, 300 Type B’s and 200 Type C’s. Everybody has the same cost C of learning any language other than his or her native tongue. The benefits of being able to speak to and understand any other person in the community is 1 per person. For what values of C would it be true that there is a Nash equilibrium in which nobody learns any language other than their native tongue

In a community of 1000 people, there are 300 type A people whose native language is Language A and 700 type B people with native language B. Everyone can speak and understand his or her native language. A native speaker of Language A can learn language B at cost CA ≥ 0 and a native speaker of Language B can learn language A at cost CB ≥ 0. The value to anyone of being able to speak to and understand another person is 1 per person. Based on the above data, answer the given subquestions.

Another community has 3 linguistic groups, Type A’s who speak language A, Type B’s who speak language B and Type C’s who speak language C. There are 500 Type A’s, 300 Type B’s and 200 Type C’s. Everybody has the same cost C of learning any language other than his or her native tongue. The benefits of being able to speak to and understand any other person in the community is 1 per person. For what values of C would it be true that there is a Nash equilibrium in which nobody learns any language other than their native tongue, but also another Nash equilibrium in which the type B’s and type C’s learn language A.

A cable TV station wants to connect six 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 six players if all six 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 six 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 six players if all six 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 six 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 six players if all six 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_____

A cable TV station wants to connect six 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 six players if all six decide to connect to the network.
Based on the above data, answer the given subquestions.

The cost to be paid by player 4 will be_____

A cable TV station wants to connect six 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 six players if all six decide to connect to the network.
Based on the above data, answer the given subquestions.

The cost to be paid by player 5 will be_____

A cable TV station wants to connect six 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 six players if all six decide to connect to the network.
Based on the above data, answer the given subquestions.

The cost to be paid by player 6 will be_____