A5 (6 marks) Before the Allied invasion of France in 1944, the Germans had to decide where to place their defenses. They had three choices: they could concentrate their defenses at Calais (GC), concentrate at Normandy (GN), or split their defenses between both locations (GS). The Allies had two choices: they could attack at Calais (AC) or at Normandy (AN). The following payoff matrix assumes this is a zero-sum, single shot, simultaneous game played with the indicated numerical payoffs (where larger positive numbers represent outcomes more favorable and negative numbers indicate losses - so less negative is better).



Assume that this game is played sequentially, with the Allies having the first move. In the rollback equilibrium outcome of this sequential game, (Choose an answer from the list below and enter it on your multi-choice answer sheet) Basically you can solve this game by constructing the game tree for the sequential version of this game, then analyse it using rollback. Here is the relevant game tree. Check the uctv clip for a more detailed explanation.

A4 (6 marks) Consider the following quote from
the a researcher investigating why wearing a bicycle helmet became mandatory
in NZ two decades ago. “Teenagers
are not
likely wear bicycle helmets by individual choice for several reasons - but
the most important one appears to be vanity.
Teens fear the ridicule of other teens. If everyone else wears a helmet they're
tempted to be "cool" by not wearing one. But if no one else wears
a helmet they see themselves as a "sucker" by wearing one . Yet they
seem to realize that they might all be better off wearing helmets than not,
as indicated by the following, typical survey response: “It’s
dumb not to wear a helmet, for safety reason.So if the
school (or the police) made us all wear them we'd definitely all be better
off than if we all didn't wear them. But you look like a nerd if you do!
I don’t—because
the other kids don’t.
I know that’s silly, but most teenagers feel the same way. ” Viewing
the wear helmet–don’t wear helmet choice as though it were
a 2 player simultaneous game, it most closely resembles:On your multi choice
answer sheet for this question write down the identifying letters that
are your answer to this question The words "temptation" and "sucker" should have given the show away - this is the language used in the general idea of a prisoner's dilemma. Whether others wear helmets or whether others don't wear helmets a teens best response is not to wear helmets. ie not wearing helmets is a dominant strategy, for everyone, so is the equilibrium prediction. BUT there is a recognition that if everyone wore helmets they'd all be better off than if no one wore helmets (which is the equilibrium strategy prediction) Presto! the prisoner's dilemma! What you have to check is that the TWO features of a prisoner's dilemma are present: (1) all players have dominant strategies and (2) there is some other feasible combination of strategies in the game where everyone could be better off - ie opportunities for commonality, pareto improvement, mutual beneficial

• (a) a game of chicken
• (b) a pure coordination game
• (c) the textbook's tennis shot game (down-the-line or crosscourt)
• (d) a battle of the sexes game
• (e) a stag hunt game
• (f) a centipede game
• (g) a prisoner's dilemma game
• (h) a trust game.