Two animals are fighting over a prey. The prey is worth v to each animal. The cost of fighting is c1 for the first animal (player 1) and c2 for the second animal (player 2). If they both act aggressively (hawkish) and get into a fight, they split the prey in two equal parts but suffer the cost of fighting. If both act peacefully (dovish) then they also split the prey in two equal parts but without incurring any cost. If one acts dovish and the other hawkish, there is no fight and the hawkish gets the prey.
(2.1) Write down the normal form of the game (the bimatrix of strategies and payoffs).
(2.2) Find the Nash Equilibria for all possible parameter configurations and given the following restrictions: v > 0, c1 > c2 > 0, v ?= 2c1 and v ?= 2c2.