QUESTION 7 Player IlI PlayerII Player A 1,3,3 -1,3,2 8 3,1,0 0,0,4 A 2,3,1 3,1,0

Question

QUESTION 7 Player IlI PlayerII Player A 1,3,3 -1,3,2 8 3,1,0 0,0,4 A 2,3,1 3,1,0 B 3,2,-1 1,3,2 Player l Player l The game above is a simultaneous three player game between players 1,2, and 3 Player 1 chooses between A and B Player 2 between C and D and Player 3 between E and F. In the game above, the strategy profile in which Player 1 plays profle Player 2 plays and Player 3 plays is a Nash Equiibrium QUESTION Player I C D Player A 6,3 2,6 B 43 81 in the game represented in normal torm above, there is a Nash Equlibrium in mixed straleges in which Player 1 plays stratogy A with probabilty stralegy C with probability and Player 2 plays Please, do not write your answer in ractional form i e, if your answer is 1/2 enter 0 5 instead

Explanation / Answer

Q7) player 1 plays B, player 2 plays D and player 3 plays E is a Nash Equilibrium strategy profile beacuse there's no other strategy profile where the players would want to stay put given the strategy of other players.

Q8) If player 2 plays C with probability x and D with probability (1-x) then

the expected payoff of player 1 by playing A= 6x+(1-x)2=4x+2

the expected payoff of player 1 by playing B= 4x+8(1-x)=8-4x

Player 1 will be indifferent between playing A and B when

4x+2=8-4x i.e. x=3/4=0.75

Player 2 plays C with probability 0.75.

Performing the same procedure with player 1 playing A with probability y and playing B with (1-y) gives expected payoffs of player 2 being 3 and (5y+1) by playing C and D respectively.

Thus, y=2/5=0.40. i,e, Player 1 plays A with probability 0.40.

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