ii Search Player 2 A B Lo A 1.0 1, 2 4,1 2.1 1,2 1,4 3.0 Player 1 C 0.3 0,1 2,0 2,0 D 2,4 3,2 6,1 0,1 El o iv) R Player 2 A B P A 50,2 2,-1 Re 6,1 2,0 Player 1 Le Fil C 3, 1000,6 Case b) Are any of the equilibria you found in these 4 games in dominant strategies? If yes, which Convert games and which equilibria? for c) Are any of the four games dominance solvable? If yes, which games? d) Are any of the equilibria inadmissible? If yes, which games and which equilibria?1. a) Find all Nash equilibria in pure strategies in the following 4 games. Player 2 A B A 2,2 2,2 Player 2,-2 2,-2 ii) Player 2 A 3,10 4,7 Player 1 B 2,0 4,2 ' Suppose ice cream consumers are distributed along a straight beach of 1km. Each consumer buys 1 ice cream from the closest ice cream cart. if carts are equidistant from a consumer, he will buy from each of them with equal probability. We have seen in lecture what the Nash equilibrium is if2 carts simultaneously choose where to position themselves. Now suppose there are 3 ice cream carts simultaneously deciding where to position themselves. is it a Nash equilibrium for all 3 to position themselves where the median consumer is located? (Explain in no more than two short sentences). 3. There are 2 players. Each has an endowment of 10 dollars and chooses how many dollars to contribute to a public pool, Call x; and X2 the contributions of player 1 and player 2, respectively. If xn he 5, then players 1 and 2 receive a payoff of 10 x; + 1 and 10 k1 + 1, respectively. Otherwise they receive a payoff of 10 x1 and 10 X2, respectively. a) Find a Nash equilibrium of this game. b) Now suppose that if x1 + X2 2 5. players 1 and 2 receive a payoff of 10 x: +10 and 10 )(z + 10, respectively. Find a Nash equilibrium of this game. 4. There are two firms producing a good, firm 1 and firm 2. Both have constant marginal cost of production of 2. There are a total of 10 consumers, each of which will buy at most 1 unit of the good from whichever firm charges a lower price. If both firms charge the same price, each consumer will choose randomly which rm to buy from (so on average each firm will sell to half of all customers): ' The firms compete via Bertrand competition simultaneously setting price but they can only , choose prices that are integers, i.e. 1, 2, 3, 4, etc. This game has three pure strategy Nash equilibria. What are they