Question:
Two people, 1 and 2, are engaged in a joint project. Person πβ{1,2} puts in effort π₯π (0β€ π₯π β€ 1), and incurs cost πΆπ (π₯π ) = π₯π . The monetary outcome of the project is 4π₯1π₯2 which is split equally between them. Considering the situation as a strategic game, the set of all Nash Equilibria in pure strategies is
Two people, 1 and 2, are engaged in a joint project. Person πβ{1,2} puts in effort π₯π (0β€ π₯π β€ 1), and incurs cost πΆπ (π₯π ) = π₯π . The monetary outcome of the project is 4π₯1π₯2 which is split equally between them. Considering the situation as a strategic game, the set of all Nash Equilibria in pure strategies is
Updated On: Oct 1, 2024
- {(0, 0), (1, 1)}
- \(\{{(0,0),(\frac{1}{4},\frac{1}{4}),(\frac{3}{4},\frac{3}{4}),(1,1)\}}\)
- \(\{(0,0),(\frac{1}{2},\frac{1}{2}),(1,1)\}\)
- a null set
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct option is (C): \(\{(0,0),(\frac{1}{2},\frac{1}{2}),(1,1)\}\)
Was this answer helpful?
0
0
Top Questions on Game theory
- In the table below, firm 1 and firm 2 can cooperate to share market profits or compete with each other. The figures in the cells represent the profits in crores of INR. They can either cooperate with each other where they share INR 10 crores equally. Alternatively, they can compete, which lowers the market output to INR 4 crores, which they share equally. If one of the firms competes while the other cooperates, the former obtains INR 10 crore of profit while the other makes zero profit. In equilibrium, firm A and firm B should respectively:
Firm 2 Cooperate Compete Firm 1 5, 5 0, 10 Compete 10,0 2, 2 - CUET (PG) - 2024
- Economics
- Game theory
- In a 3-player game, player 1 can choose either Up or Down as strategies. Player 2 can chose either Left or Right as strategies. Player 3 can choose either Table 1 or Table 2 as strategies.
Which of the following strategy profile(s) is/are Nash Equilibrium?- IIT JAM EN - 2023
- Microeconomics
- Game theory
- An industry has 3 firms (1, 2 and 3) in Cournot competition. They have no fixed costs, and their constant marginal costs are respectively\(c_1=\frac{9}{30} , π_2 =\frac{ 10}{30} , π_3 = \frac{11}{30} .\)
They face an industry inverse demand function π=1βπ, where π is the market price and π is the industry output (sum of outputs of the 3 firms). Suppose that π π is the industry output under Cournot-Nash equilibrium. Then (π π )β1 is equal to _______ (in integer).- IIT JAM EN - 2023
- Microeconomics
- Game theory
Questions Asked in IIT JAM EN exam
- Consider the matrix \( A = \begin{bmatrix} 4 & -1 \\ 12 & -3 \end{bmatrix} \).
The value of the determinant of \( A^5 \) is .......... (rounded off to two decimal places).- IIT JAM EN - 2025
- Linear Algebra
The sum of the payoffs to the players in the Nash equilibrium of the following simultaneous game is ............
Player Y C NC Player X X: 50, Y: 50 X: 40, Y: 30 X: 30, Y: 40 X: 20, Y: 20 - IIT JAM EN - 2025
- Economics and economic theories
- Consider the economy described by the following: \[ Y = C + I + G \quad \text{with} \quad Y = 5000, \, G = 1000, \, T = 1000, \quad \text{and} \quad C = 250 + 0.75(Y - T), \] where \( Y \), \( C \), \( I \), \( G \), and \( T \) are national income, private consumption spending, investment expenditure, government expenditure, and tax revenue respectively. In this economy, private saving is ............
- IIT JAM EN - 2025
- Microeconomics
- Lerner Index (\( L \)), a measure of market power, is defined as \( L = \frac{P - MC}{P} \), where \( P \) and \( MC \) are, respectively, price and marginal cost of a firm. If a profit maximizing firm faces the demand curve \( P^2 Q = 7 \), the value of \( L \) is ............ (rounded off to one decimal place).
- IIT JAM EN - 2025
- Microeconomics
- You are tossing a fair coin repeatedly until a βHeadβ appears. The expected number of tosses required for a βHeadβ to appear is ...........
- IIT JAM EN - 2025
- Probability
View More Questions