Question

The Blues and the Bruins are facing a helmet “arms” race. If one team wears helmets, and the other

team does not, then the team without helmets gains a competitive advantage by exploiting better

peripheral vision. If both teams do not wear helmets, neither team faces a “vision” advantage, but they

each sustain heavy head trauma. If both teams wear helmets, there is again no “vision” advantage, but

this time the players in each team are much safer. The payoffs to the two teams for each scenario are

shown in the matrix below with the Blues’ payoff on the left and the Bruins’ payoff on the right in each

cell. The game is played one-shot, simultaneously and non-cooperatively with full information. The

Nash Equilibrium is

Blues

Bruins

Helmets No Helmets

Helmets 7 7 -5 10

No Helmets 10 -5 -2 -2

A. (Blues Helmets, Bruins Helmets).

B. (Blues No Helmets, Bruins No Helmets).

C. (Blues No Helmets, Bruins Helmets).

D. (Blues Helmets, Bruins No Helmets).

E. (Blues No Helmets, Bruins Helmets) and (Blues Helmets, Bruins No Helmets).

Refer back to the table for the arms race.

The maximin strategy for the Bruins is: __________________.

Answer 1

Ans 1)   
Bruins
Helmets No Helmets

Helmets (7,7)    (-5,10)

Blues

No Helmets (10,-5) (-2.-2) (Nash equilibrium)

Both players have dominating strategy as No helmets because for an example if Bruins choose Helmets then best response of Blues is No helmets similarly if Bruins choose No helmets then best response of Blues is No helmets

Similar is the case with Bruins as payoffs are symmetric

Hence Nash equilibrium in one shot game non co-operative game is to play their dominating strategy

hence option B is correct

Ans 2)

In Maximin strategy first we choose highest possible payoff and then minimum out of it therefore for Bruins Maximum payoffs are when played helmets is $7 and Maximum payoff when played No helmets is $-2 now minimum payoff out of it would be -$2

therefore Bruins should choose No Helmets