Game Theory Is there a dominant strategy for either of the two agents? Which strategies can be eliminated be

 

 

answer:

given the matrix,

there is no dominant stratergy as lets see agent 2 in the matrix, now will agent 2 ever prefer Sb3 to Sb2 the answer is that one cannot decide because the payoff for a13 =3 and that of a12=1 but a22=3 and a23=2 though

a13>a12 but a22>a23. The same case follows everywhere for agent 2 and agent 1. hence there is no dominant startergy and no rational player will ever play a dominant stratergy and in this case there is no dominant stratergy.

now a nash equilibrium is a pair of stratergies we use the best response method is that for

for a fixed value of sa1 agent 2 would choose a13 as it gives a payoff of 3 which is greater when agent 1’s response is fixed at sa1. similarly for fixed sa2 agent 2 would choose a21 and for fixed sa3 agent 2 would chose either a31 or a32.

now keeping agent 2’s response fixed, for fixed sb1 agent 1 would chose a21 and for fixed sb2 agent 1 would choose a12 and for a fixed sb3 agent 1 would chose a13. putting the picture together the nash equilibrium is at a21 and a13 as both the agents maximize their payoff given the others response yielding the nash equilibrium

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