Nash equilibrium
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1. Some games of strategy are cooperative. One example is deciding which side of the road to drive on. It doesnâ??t matter which side it is as long as everyone chooses the same side. Otherwise, everyone may get hurt.
Driver 2
Left Right
Driver 1 Left 0,0 -1000 -1000
Right -1000, -1000 0,0
a. Does either player have a dominant strategy? Explain.
b. Is there Nash equilibrium in this game? Explain
c. Why this game is called a cooperative game?
2.
Graph
a. What is the firmâ??s Total Revenue?
b. What is the Total Cost?
c. What is the firmâ??s Total Profits?
d. If the above monopolist were to behave like a perfectly competitive firm (operating in the long run), determine its output.
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Solution Summary
This solution analyzes Nash equilibrium in this game and other concepts.
Solution Preview
1. This is an example of a cooperative game.
a. Neither player has a dominant strategy. A dominant strategy is said to exist if the player has an incentive to stick to a particular strategy irrespective of what the other player is doing. This is not the case here. Driver 1 is better off driving to the left when Driver 2 is driving to the left, and to the right when the other is driving to the right. Therefore, Driver 1's decision to drive on a particular side depends on the decision of the other driver. He will not follow a particular strategy irrespective of the other driver's action. By symmetry this applies to Driver 2 too, and hence there is no dominant strategy in this ...
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