the policy splits the difference between their policy positions , ;(a:1 + x2} 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 11p (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. Consider the following two games7 with > 0: Game 1 : 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 '3' 4. {5 pts) What happens as a 00