Game Theory Questions and Answers

Q: The payoff value for which each player in a game always selects the same strategy is known as :

Such a payoff is called both a saddle point and an equilibrium point.In a two-person zero-sum game with a pure-strategy solution, the payoff at the intersection of the optimal row and column is the minimum of its row and the maximum of its column. Maximin equals minimax there, neither player gains by deviating, and so each player always selects the same pure strategy.Game theory texts call this payoff the saddle point (after the shape of the payoff surface) and also the equilibrium point (because neither player has an incentive to move). Since both names are standard, choosing only one of them is incomplete, and 'none of the above' is wrong.

Q: A company management and the labour unions are negotiating a new three year settlement. Each of these has 4 strategies mentioned below :(I) : Hard and aggressive bargaining.(II) : Reasoning and logical approach.(III) : Legalistic strategy.(IV) : Conciliatory approach.The cost to the company are given for every pair of strategy choice.Labour Union Strategies / Company StrategiesIIIIIIIVI20151235II2514810III402105IV-54110Then the value of the game is :

The value of the game is 12.The entries are costs to the company, so the union (rows) maximises and the company (columns) minimises. Look for a saddle point:Row minima: 12, 8, 2, -5; the largest is 12 (row I).Column maxima: 40, 15, 12, 35; the smallest is 12 (column III).Maximin = minimax = 12, so (I, III) is a saddle point and the game has value 12 in pure strategies: the union bargains hard and the company takes the legalistic line.-5 is the smallest entry, 0 and 2 are other entries of the table; none is both the minimum of its row and the maximum of its column.

The payoff value for which each player in a game always selects the same strategy is known as :

A.saddle point
B.equilibrium point
C.both (A) and (B)
D.none of the above

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

Such a payoff is called both a saddle point and an equilibrium point.

In a two-person zero-sum game with a pure-strategy solution, the payoff at the intersection of the optimal row and column is the minimum of its row and the maximum of its column. Maximin equals minimax there, neither player gains by deviating, and so each player always selects the same pure strategy.

Game theory texts call this payoff the saddle point (after the shape of the payoff surface) and also the equilibrium point (because neither player has an incentive to move). Since both names are standard, choosing only one of them is incomplete, and 'none of the above' is wrong.

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A company management and the labour unions are negotiating a new three year settlement. Each of these has 4 strategies mentioned below :

(I) : Hard and aggressive bargaining.
(II) : Reasoning and logical approach.
(III) : Legalistic strategy.
(IV) : Conciliatory approach.

The cost to the company are given for every pair of strategy choice.

Labour Union Strategies / Company Strategies	I	II	III	IV
I	20	15	12	35
II	25	14	8	10
III	40	2	10	5
IV	-5	4	11	0

Then the value of the game is :

A.12
B.-5
C.0
D.2

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: A

The value of the game is 12.

The entries are costs to the company, so the union (rows) maximises and the company (columns) minimises. Look for a saddle point:

Row minima: 12, 8, 2, -5; the largest is 12 (row I).
Column maxima: 40, 15, 12, 35; the smallest is 12 (column III).

Maximin = minimax = 12, so (I, III) is a saddle point and the game has value 12 in pure strategies: the union bargains hard and the company takes the legalistic line.

-5 is the smallest entry, 0 and 2 are other entries of the table; none is both the minimum of its row and the maximum of its column.

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