3. The following game between the EU and UK begins in 2015 when the EU had to decide whether to change the terms of the UK's membership. If the EU says Yes to altered membership for the UK, the game ends and both players get a payoff of 0. If the EU say No, the UK must decide whether to Remain or Leave. If the UK Remains, the game ends and the UK gets a payoff of -5 while the EU gets a payoff of 5. If the UK chooses Leave, the EU must choose either a Weak or Tough negotiating position. After this choice, the UK must decide whether to pursue a Hard or Soft Brexit. If the EU chooses Weak and the UK chooses Soft, the EU gets a payoff of -10 while the UK gets a payoff of 5. Any other combination of Weak/Tough and Hard/Soft will lead to a breakdown in negotiations with the EU getting a payoff of -40 and the UK getting a payoff of -80. (i) (a) Draw the game tree of this game. [3 Marks] (b) Represent this as a normal form game (i.e. a ma- trix) and find all the pure-strategy Nash equilibria. [4 Marks] (c) Find all the Subgame Perfect Nash Equilibria in this game. How many are there? Why should we expect this to be the number of SPNE? [4 Marks] (d) Is it a credible strategy for the EU to play Tough? Is it a credible strategy for the UK to play Hard? Discuss why or why not in each case. [4 Marks] (ii) Suppose instead that if the UK chooses Leave then both players must choose their next moves simultaneously