Solve Gintis 6.14 Vindication of the Hawk. Chicken (also known as the hawk-dove game) is a two-player game in which each player can choose either attack (A) or remain peaceful (P). Suppose at the start of the game, each player has one util of good stuff. If both players remain peaceful, they each get to consume their stuff. If one is peaceful and the other attacks, the attacker takes the other's stuff. If both attack, they each lose a>0 utils. This gives us the normal form matrix in the diagram below.

	Player 2
Player 1	Strategy	A	P
A	-a -a,	0 2,
P	2 0,	1 1,

Find a mixed strategy Nash equilibrium in which players use completely mixed strategies and the payoff of the game to the players increases when the potential loss from conflict, a, increases. It's OK to use Gambit or Mathematica to explore the space of possible values, but try to get to a general (e.g. algebraic) solution and prove your results.