There are n greater than or equal to 2 airlines. Each airline has the strategy set {1,2,3,4,5,6,7}. Let Si denote the strategy of airline i, and suppose the cost associated with its security measures is 10 x Si.

Assume that the effective security level is determined by the highest security measures chosen by airlines.

We find that airline is payoff is now 50 + 20 max{s1, . . . , sn} 10 si

The available strategy set is si {1, 2, 3, 4, 5, 6, 7} for each player.

a. Find a symmetric mixed strategy equilibrium, where the players are randomizing between strategy 1 and strategy 7. (Hint: assume that the probability of choosing 1 is p, and the probability of choosing 7 is 1-p.)

b. Find a mixed strategy equilibrium where only two players are randomizing between strategy 1 and strategy 7, and all the other players are playing 1. 2

c. (optional) Show that the mixed strategy profile found in b. is indeed a Nash Equilibrium, i.e. show that there is no profitable deviation for any player.