Question

4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the iterated elimination of strictly dom- inated strategies solution, if any. (e) [10] Consider the following game: player 2 L с R T 14,4 3,2 4,0 player 1 M 7,0 0,5 1, 12 B 5,0 -1,3 10,8 Find all the Nash equilibria (including mixed strategy ones).

Answer 1

Date..... Topic...... b) Iterated Dominated astrategy over , 1, so debeld COLAS For Player 2 a has do re never the th. player 2 T f G -10,6 10, 0/3, 8 Player I B 9,8 14,8 4,10 C -10 3 5,9 8, 10 0,0 3,10 8,12 G w Now ar has pay oft Mence va Domineked strategy over Over F for Player 2, as it gives it gives high the will never Play Player 2 G .-10,6 3,8 ų, 10 -10, 3 8,10 E Plaget B с D 0,0 8, 12 وينت ليكرام astraty-over_En_DO JE ur hais Dominant Player 2 will never Player, 2 Сл Player 38 4,10 A a С. 8,10 DI Pringle

Live Now for player ! Dhes Dominent strategy over A eso Player I never Play A Player I В Ол 41,10 8.10 4,12 C D av Now Dhes Dominent ostetgy over B, so player! never Play B 1.00 C 9,10 "layeri D 19:12 null Now player ! OVUM estrategy C as hes s sominent it gives higher pay off 10 18,12 so solution is (8,12) pay off c) Nash awilibrium - Nash ewiliorium is a concept within game theory where optimal outcome of a game is where no Player has an incentive to deviate from his chosen strategy one

Plove, C K Player 3, 2 Т" т B 1 0 5, () 0,5 "1, 3 Ч, О 1,72 (0, 0) 2. For a Player ! а) (ті) (ч, ч) Player Nash qm (К,0) (0, 0)
a) A strategy is a dominant strategy for a player if it yields the best pay off ( to that player) no matter what other strategy other player choose.

A iterated elimination of strictly dominated strategy is solving a game by eliminating strictly dominating strategy.

if there is strictly dominating strategy then it lead to help in iterated elimination of strictly dominated strategy.

b) In this case player does not have any strictly domnated strategy but player two has following strategy

1) G has dominated strategy over H

2) G has dominated strategy over F

3) G has dominated strategy over E.

now as we got to know dominated strategy, lets look into the diagram for iterated dominated strategy.