open) its potential summer blockbuster movie. There are three possible weeks dur
ID: 1201660 • Letter: O
Question
open) its potential summer blockbuster movie. There are three possible weeks during
which the movies could open. Suppose that the game between the studios can be
modeled as a simultaneous game and that the following matrix shows the payoff
(the profit over the whole summer) that each studio receives for each possible combination
of opening weeks.
(a) How many pure strategy Nash equilibria exist in this game?
(b) Can you compute the Nash equilibrium using the Iterated Elimination of Strictly
Dominated Strategies? If so, show that you can. If not, discuss why.
STUDIO B Week 1 Week 2 Week 3 Week 155, 4570, 5565, 50 65, 6055, 45 55, 55 Week 360, 55 60, 5050, 40 STUDIO Week 2Explanation / Answer
Nash equilibrium was introduced by John von Neumann and Oskar Morgenstern.Here a firm chooses how much output to produce to maximize their own profit when the other firms output is given.In this given game the pure strategy can be calculated in the following way:
a) We know that the best response for both the players will be that no player can do strictly better by deviating thus finding the pure strategy.To start with we can find the best response for studio A for each of the strategies Studio B can play. I will demonstrate this by underlining the best responses . If now Studio B plays in Week 1 , it will get not get the best response in any of the Weeks in Studio A. since in all the 3 rows of week 1 (studio A) ie(55,45),(65,60),(60,55) , Studio A always wins in all situation. Now coming to Week 2 of Studio B , only Studio A wins in all weeks hence here also studio B doesnt win any situation ie (70,55),(55,45),(60,50).Coming to the next column ie week 3 the best response can be taken as Week2 of studio A ie (65,50),(55,55),(50,40), its here that the studio B has a win situtaion for(55,55) which would be the best response. This means when we look out for studio A in week 1 the best win situtaion for studio a would be (65,45),(70,55), (65,50). in all the 3 situation Studio A wins.Coming to week2 the best situtaion for a win would be (65,60), (55,45) , (55,55).Here also in all three situation Studio A has a win win sitution.Now coming to the third week of studio A it is again a win-win situation for studio A in all the three weeks. Now Nash equilibrium is attained when both strategies used by the studios are the best responses to each other. Looking at the studios here only in one situation both the responses are best to each other i.e. (55,55) . Hence the unique pure strategy equilibrium is (55,55), where both have equal chances.In all other responses either studio A or B had a greater advantage over the other one.
b) A dominant strategy for a player is if it yields the best payoff for that player no matter what strategies the other players choose.In the given example STUDIO A dominates in all the WEEKS ie Week 1,2,3. Coming to the Studio B it will not win in any situtaion and thus a iterated ellimination of strictly Dominated strategies will not be possible. since to compute nash equilibrium using dominated strategies , each studio has to be dominant in one situation so that the other can be eliminated and hence we can reach at a point where both can yield a payoff.
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