PROBLEM 4 Two weeks from now, Liu Bei will meet with Sun Quan to discuss a potential alliance against a common enemy in an upcoming battle. At some point during the discussion Liu Bei and Sun Quan will simultaneously decide how many of their own warriors to send to combat. To be precise, each of them will choose whether to commit a High number of warriors, or a Low number of warriors. If both send a High number, the probability of winning the battle will be p# = 1, so 100%. If only one of them sends a High number while the other sends a Low number, the probability will be p" = 0.8, i.e. 80%. If both send a Low number of warriors, the probability will be just p = 0.2, so 20%. Winning the battle has a value of X = 100 for both For Liu Bei, sending a High number of warriors has a cost of Chi = 20, regardless of the outcome of the battle, while sending a Low number of warriors has a cost of Chill = 10. For Sun Quan, sending a High number of warriors has a cost of Cun = 50, regardless of the outcome of the battle, while sending a Low number of warriors has a cost of Cun = 20. The following strategic form summarizes the payoffs for every possible outcome. Sun Quan High Low Liu Bei High (PHX - Chiu. PHX - Csun) (pMX - Chu. pMX - Csun) Low (pMX - Chiu pMX - Csun) (pix - Chiu plx - Csun) Part 1 (6 marks). Substitute the parameters provided above into the strategic form and use it to find what the likely outcome of this simultaneous decision will be. Describe the equilibrium. Part 2 (24 marks). Now suppose that Zhuge Liang, a master tactician working for Liu Bei, gives him the following advice: "before going to meet with Sun Quan, start a revolt in the neighboring province of Gan Ning". Liu Bei knows that if a revolt starts in that region it becomes very dangerous to send his soldiers elsewhere. The effect this has on the parameters of the game is that Chiu increases from 20 to 80. Liu Bei has to decide whether to Follow or Dismiss Zhuge Liang's advice before the discussion with Sun Quan. a) Model this decision and the subsequent discussion as a sequential game with simultaneous decision components. b) Should Liu Bei follow Zhuge Liang's advice? Describe, with game theory terminology, the effect that starting the revolt will have on the likely outcome of the discussion with Sun Quan. c) State, with proper notation, what the Subgame Perfect Equilibrium of this game is