1. Indicate whether a statement below is true or false by writing either T or Fnext to each. If false, give an example where the statement does not hold.

(i) A Nash equilibrium maximizes the sum of utilities of the players in every game.

(ii) If players are rational and each knows others are rational, a Nash equilibrium willbe played. Remember being rational implies a player will never choose a strictly dominatedstrategy and knowing other players are rational means each player knows others will neverchoose a strictly dominated strategy.

(iii) A Nash equilibrium strategy cannot be weakly dominated.

(iv) A Nash equilibrium strategy cannot be strictly dominated.

(v) A game can have more than one Nash equilibrium.