Chapter 13, Problem 3TY

Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A’s payoff, and the second entry is Animal B’s payoff: Animal A (rows)/Animal B (columns) Hawk Dove Hawk (-5,-5) (10,0) Dove (0,10) (4,4) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. Explain why there cannot be an equilibrium where all animals act as Doves. Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves?

If there are a known finite number of repeated games to be played, the two players will cooperate until the last game, at which point both will try to defect. true or false? explain.

Prove that in a 2 × 2 zero-sum game, if equilibrium strategies exist then one of the players has a dominated strategy.