Reference no: EM133260131
Game Theory. Havard Lorentzen and Cha Min-Kyu race as professional speed skaters. They each decide whether or not to skate Dangerously (D) or Safely (S). They decide simultaneously at the beginning of the race. There is some chance that the skaters crash and lose the race (resulting in a payoff of 0 for both):
- If both skaters choose S, the probability of a crash is p = 0
- If one skater chooses S and the other chooses D, the probability of a crash is p = 0.2
- If both skaters choose D, the probability of a crash is p = 0.55
A skater who chooses S and does not crash does moderately well, with a payoff of 10. A skater who chooses D and does not crash does very well, with a payoff of 20. Note that any skater's expected payoff is K(1 -p), where K = 10 if the skater chooses S and K = 20 if the skater chooses D, and p is the probability of a crash.
a) Draw the normal form of this game (the matrix) and fill in the expected payoffs.
b) Find all the pure strategy Nash Equilibria of this game.
c) Is there another strategy profile that Pareto domintates the Nash equilibrium (or equilibria if there are multiple)? Briefly summarize the situation.