Question

20 Judy Inc. Option 1 Option 2 Oprah Inc Option X Option Y 10 70 40 L 30 80 No explicou are required for your own low ) List all Nash equilibrin (or widene fo is) b) List all Maximin equilibria (or write one" if none exist) F c) List all Maximax equilibria (or write "none" if none exist) OOSID d) List all cooperative (collusive) equilibria (or write "none" if none exist) Unbox

Answer 1

JUDY INC. OPRAH INC. Option X Option 1 10,20 Option 2 30,80 Option Y 70,60 50,40

a) In the given game there are two Nash Equilibrium as shown above. The highest payoff from the given set of ouctomes is chosen by the player. The two Nash equilibrium are (Option 2, Option X) and (Option 1, Option Y).

b) In a MaxiMin equilibrium the player chooses the maximum paying outcome from the minimum paying outcome choices.

In the given game, out of Option 1 player 1 would choose 10 as it gives the minimum payoff between 10 and 70. Similarly player would choose 30 when to be chosen between 30 and 50 from option 2. From these two payoffs 30 is maximum than 10 and hence final choice would be to choose Option 2.

For player 2, when he has to choose a payoff that gives minimum payoff from playing Option X, the player would choose 20. And when a similar choice has to be made while playing Option Y, the player chooses 40. Now, out of these two, the maximum is gained from 40 and hence the player chooses Option Y as the final outcome.

Hence, the Maximin equilibrium of this game is (Option 2,Option Y).

c) In a Maximax equilibrium the player chooses the maximum paying outcome from the maximum paying outcome choices.

In the given game, out of Option 1 player 1 would choose 70 as it gives the maximum payoff between 10 and 70. Similarly player would choose 50 when to be chosen between 30 and 50 from option 2. From these two payoffs 70 is maximum than 50 and hence final choice would be to choose Option 1.

For player 2, when he has to choose a payoff that gives maximum payoff from playing Option X, the player would choose 80. And when a similar choice has to be made while playing Option Y, the player chooses 60. Now, out of these two, the maximum is gained from 80 and hence the player chooses Option X as the final outcome.

Hence, the Maximax equilibrium of this game is (Option 1,Option X).

d) A cooperative equilibrium is an equilibrium that reaches to the highest joint profit of all the players. Thus, in this game the cooperative equilibrium is (Option 1,Option Y) as it gives the highest joint profits instead of other outcomes .