Variant of BoS:-
Find all the ESSs, in pure and mixed strategies, of the game.
Bargaining:-
Pairs of players bargain over the division of a pie of size 10. The members of a pair simultaneously make demands; the possible demands are the nonnegative even integers up to 10. If the demands sum to 10 then each player receives her demand; if the demands sum to less than 10 then each player receives her demand plus half of the pie that remains after both demands have been satisfied;
if the demands sum to more than 10 then no player receives any payoff. Show that the game has an ESS that assigns positive probability only to the demands 2 and 8 and also has an ESS that assigns positive probability only to the demands 4 and 6. The next example reexamines the War of attrition, studied previously (pure equilibria). The game entered the literature as a model of animal conflicts. The actions of each player are the lengths of time the animal displays; the animal that displays longest wins.