Question

Consider the following statements

(1) The set of equilibria does not change after successive elimination of strictly dominated strategies
(2) As (1) but replacing strictly by weakly
(3) The reduced game after successive elimination of weakly dominated strategy must have at least one equilibrium point
(4) The order of elimination of strictly dominated strategies does not affect the set of equilibria
(5) As (4)1 but replacing strictly by weakly

	a.	Only (4) is correct
	b.	None of the other options is correct
	c.	Only (3) and (4) are correct
	d.	Only (1) (3) and (4) are correct
	e.	Only (1) and (2) are correct
	f.	Only (1) and (4) are correct

Consider the following 2-person game

1 2	L	M	R
U	9, 6	5, 4	4, 7
D	x, 5	6, 5	8, y

The set of all values of x and y for which the game is a Prisoner's Dilemma game is

	a.	For no value of x and y the game is a Prisoner's Dilemma game
	b.	None of the other options is correct
	c.	x<9, y<5
	d.	x>9, 5<y<6
	e.	x>9, y>5

Answer 1

The technique called the iterated elimination of strictly dominated strategies is used in solving games that invloves iteratively removing dominated strategies. There are two ways - eliminating strictly dominated strategies which gives a unique nash equilbrium, and eliminating both strictly and weakly dominated strategies which results in a nash equilbrium that may not be the only nash equilbrium in the game (as elimintation of weakly dominated strategies may eliminate some nash equilibrium and because of which order of elimation also matters).

1. correct , 2. incorrect, 3. correct, 4. correct , 5. incorrect

Hence, option d is correct

Prisoners dilemma is the situation where nash equilibrium is the intersection of the two best responses of two players which comes from playing two dominant strategies. And there is always a room for mutual improvement or gains from playing a different strategy.

But in the given game, there is no option that will satisfy the above scenario. (can check by putting values gievn in option c , d, e)There is no point of credible threats.

Hence, option a is correct