(a) What strategy should Piecrust choose if LaPizza chooses to advertise? Explain using the dollar values in the payoff matrix.
If LaPizza chooses to advertise PieCrust has two option,, to advertise or to not advertise.
Obviously $250 > $180 so PieCrust will choose to advertise also.
(b) What is the dominant strategy, if any for LaPizza? Explain using the dollar values in the payoff matrix.
If PieCrust advertises LaPizza has two choices, to either advertise or not advertise. LaPizza will do better to not advertise as $300 > $200.
If PieCrust does not advertise LaPizza has two choices to advertise or not to advertise. LaPizza will do better to advertise as $500 > $400.
Answer - LaPIzza does not have a dominant strategy (a strategy it would do no matter what PieCrust would do) LaPizza's best strategy is to do the opposite of PieCrust.
(c) In the Nash Equilibrium, determine each of the following.
(i) PirCrust's daily profit.
(ii) LaPizza's daily profit.
A Nash Equilibrium exists when there is no unilateral profitable deviation from any of the players involved. In other words, no player in the game would take a different action as long as every other player remains the same. Nash Equilibria are self-enforcing; when players are at a Nash Equilibrium they have no desire to move because they will be worse off.
Answer - PieCrusts daily profit will be $450 and LaPizza's daily profit will be $300
(d) Suppose the advertising costs decrease by $60 per day. Redraw the payoff Matrix to reflect the effects of the higher advertising costs.