3. [1|] points} Consider the matching pennies game 1which has a mixed strategy equilibrium but no pure strategy equilibrium. Suppose player 1's payoff from heads [H] is increased by t1 and player 2's payoff from heads is increased by t2 where t1 and 152 are both distributed uniformly {and independently} on [E, E] where E is a small positive number [i.e., signicantly less than 1]. Given t1 and t3 the game is: Player 2 Find cutoffs, c1 and 21 each in the interval [15, E], such that each player chooses heads {H} when their type exceeds their cutoff and chooses tails {T} when their type is below their cutoff. That is, nd a pure strategy Bayesian Nash equilibrium of the game. Note that this implies that the proportion of Player 1 that chooses heads is [E c1 lEEl and that the pmportion of Player 1 that chooses tails is {c1 + 15],?{25}. Similarly.' the proportion of Player 2 that chooses heads is [E ce} and that the proportion of Player 2 that chooses tails is {C2 + EVWE): Deriving the cutoffs isnlt necessary. It's sufcient to correctly guess the cutos and verify that you have found a Bayesian Nash equilibrium