the policy splits the difference between their policy positions , #11 + m2) and they both win half the time. Find all of the pure strategy Nash equilibria for this game . [HINT : Draw the line and do cases, like in class] 6 Spain and England are deciding whether or not to settle a colony, which each values at v = 2.5. They must take turns deciding whether or not to send more troops, and if so, how many. Each troop cost 1 unit of utility. In other words, England must decide whether to send 0,1,2,...., and then Spain will be given a chance to send more . If Spain chooses not to send more troops ,England wins. If Spain does , then the rst bidder will get another chance to send reinforcements . This continues until one country gives up (there is no actual fighting, and the countries do not pay for the troops that don't actually settle on the colony ) Set up and solve this game using backward induction. 7 Consider the following two games, with > 0: Game 1: 1 10,10. 10.o,1 a2 o,1o,1 0,0,10 Consider a dynamic game as follows: Suppose there are three players. Player 3 first chooses which game players 1 and 2 will play from the previous choices. Players 1 and 2 then proceed to play the game. 1. (5 pts) Write the game as an extensive form game where player 3 moves first, and then players 1 and 2 move simultaneously. 2. (5 pts) Solve this dynamic game by backwards induction. 3. (5 pts) How does the end result of this game depend upon player 3's belief over player 1 and 2's actions 17 4. (5 pts) What happens as -> oo