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

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

Asked on May 29, 2017 in