10.9 Exercises
 Exercise 10.1:

For the hawkdove game of Example 10.11,
where D>0 and R>0, each agent is trying to maximize its utility.
Is there a Nash equilibrium with a randomized strategy? What are the
probabilities? What is the expected payoff to each agent? (These
should be expressed as functions of R and D). Show your calculation.
 Exercise 10.2:

In Example 10.12, what is the Nash equilibrium
with randomized strategies? What is the expected value for each agent
in this equilibrium?
 Exercise 10.3:

In the sequential prisoner's dilemma, suppose there is a discount
factor of γ, which means there is a probability γ of
stopping at each stage. Is titfortat a Nash equilibrium for all
values of γ? If so, prove it. If not, for which values of
γ is it a Nash equilibrium?