Question

John Jackson makes the following offer to his two sons, Dave and Thomas. He says that each of them is to submit a written request for an amount that they want (in whole dollars). They can request $0. Let $ D (respectively, $T ) denote the amount requested by Dave (respectively, Thomas). Each son is to decide on the amount to request without the knowledge of the amount requested by the other brother. If D + T ≤ 20, then they get their requested amounts. In addition, John Jackson doubles the remaining amount, 20 − D − T , and splits the doubled amount equally between the two brothers. If D + T > 20, then both get zero dollars.

Is D=10,T=10 a Nash equilibrium?

Is D=20,T=20 a Nash equilibrium?

Is D=15,T=20 a Nash equilibrium?

Answer 1

suppose, Dave = X and Thomas = Y.

• YES, Is D=10,T=10 a Nash equilibrium.

[ because; if Dave request=$10 and Thomas request=$10 so, so,10+10=20 that is equilibrium. and Dave and Thomas also benefit from the extra double money.]

• Is D=20,T=20 a Nash NOT equilibrium.

[ because; if dave request =$20 and thomas request =$ 20 so, so,20+20=$40 finally the dave and thomas will get $0.]

• Is D=15,T=20 a Nash NOT equilibrium.

[ because; if dave request=$15 and thomas request =$ 20 so, so the same 15+20=$35 the dave and thomas will get $0.]