Question

Player II A 10,3 2,-2 10,-1 B3,-3 4,37,-2 С 2,5 3,0 6,1 Player In the strategic form game above, the set of rationalizable strategies for players 1 and 2 are respectively: a. (A) and (D). b. (A,B) and (D.E. c- A.D and (B,E d. (AB.C) and (D.E.F.

Answer 1

Strategic form games allows both the players to choose simultaneously compared to sequential games where one player moves first and then the other players makes their decisions according to the first player's move.

In the above example, Player I has 3 strategies namely, A, B and C whereas Player II has 3 strategies namely, D, E and F. Lets, first consider that Player I chooses strategy A, then Player II has 3 options either to choose D, E or F. Now, strategy D would give player II 3, strategy E would give him -2 and strategy F would give him -1. So, Player II would naturally chose strategy D when Player I chooses A i.e (A,D). Now, when Player I chooses B, Player II would choose E because D, E and F gives him -3, 3, -2 respectively from where 3 is the highest payoff so we get (B,E). Similarly when Player I chooses C, Player II would choose D because D gives a payoff of 5 which is greater than 0 and 1. So, the strategy chosen would be (C,D).

Now, lets see what player I would choose when Player II chooses D, E and F. When Player II chooses D, Player I would choose A because player I gets a payoff of 10 compared to B where he gets a payoff of 3 and C where he gets a payoff of 2, so the strategy chosen is again (A,D). When Player II plays E, Player II would play B because B yields a payoff of 4 which is greater than 2 and 3. Here again the strategy chosen is (B,E). But when Player II plays F, Player I would play A because 10 is greater than 7 and 6. So, the strategy chosen here is (A,F).

So, the set of rationalizable strategies for player 1 and 2 are respectively Option C) {A,D} and {B,E}.