Question

Please provide step by step solutions and explanations:

1. Consider the following extensive form game: • Renez par Accepy Reject بيا ليا

(i) List all strategies of player B.

(ii) How many subgames are there? Indicate by making circles in the figure.

(iii) What is the backward induction solution?

(iv) Find all subgame perfect equilibria.

(vi) Find a Nash equilibrium which is not a subgame perfect equilibrium.

(vii) Find a strategy profile which is not a Nash equilibrium.

Answer 1

17 strategis of B af Reneq, par NOB 3 subgames choose Accept as -17-2 tinal node I will So the game becomes . A No - Yes 0 Reneg Pav کا نیا A then B will choose Reneg, as 873 then the game becomes No A yes A so, at first node player I will choose No on-1. So, 100) is the solution and f) sub game perfect equilibrium { No Accept, Reneg} wit Normal form game 4 No Accept Reneg l par If player A 0,0 chooses No Accept No React (0,0) player B may Yes Accept -1,8 I choose Reneg or Par Yes Ryest -2,0 (3,3 player B dooses Reneg then player A will choose No Accept os No Reject, so, (No Accept, Reneg). is a nash equilibrium. Similarly (No Repet, Reng) also a nash equilibrium. If player A choosy Yes Reject A - (0,0 0,0 3,3

Player B will choose par as 300, if player B chooses paw , player A will choose yes Repeat so, Yes Ryect, paw) is also hash equilibrium, So (Yes Ryect, Paw) is a nash equilibrium céhich is not subgame perfect equilibrium, • vil (Yes Accept, Paw) is not a nosh equa.