Nash equilibrium refers to the optimal outcome of a game where there is no incentive for the players to deviate from their initial strategy. An individual (or player) can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. Given this premise, can there be a no Nash equilibrium?

100 people are choosing between two beaches to go to in the Florida Keys. Beach L is big and never gets crowded, but it is not very nice; the utility from going to Beach L is u(L) = 60. Beach M is much nicer but very small, so it gets crowded; the utility from going to Beach M is u(M) = 100-NM ; NM is the number of people that %3D go to Beach M. 5) The Nash equilibrium number of people that go to Beach L is A) 20 B) 40 C) 60 D) 80 E) 100 5).

Consider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true?     This is a game where players A and B have the same number of strategies.      Player A will get a higher payoff than player B as A moves first.     This is game will only have one Nash equilibrium.     This is a game of perfect information.

The Tampa Tribune and the St. Petersburg Times compete for readers in the Tampa Bay market for newspapers. Recently, both newspapers considered changing the prices they charge for their Sunday editions. Suppose they considered the following payoff table for making a simultaneous decision to charge either a low price of $0.50 or a high price of $1.00.  Tampa’s profits are shown in regular type.  St. Petersburg’s profits are shown in bold. 6. Is there a Nash Equilibrium in this game?  If so, which cell(s) is/are the Nash?  Is/are the Nash Dominant Strategy Equilibrium?

The game, "the battle of the sexes" (discussed in class) has        pure strategy Nash Equilibria and        mixed strategy Nash Equilibrium (again in numbers).  Of these 3 strategy,        are pareto efficient. true or false?

Player 2 1 2 3 1 (0,2) (1,0) (0,2) (0,2) Player 1 2 (1,0) (1,0) 3 (0,2) (1,0) (0,2) 1. Find all pure. strategy Nash equilibria 2. Does the game have a mixed strategy equilibrium? If so, find one. Otherwise, provide an explanation

Explain whether the statement is true or false and explain why? Statement 1: If a game has a Pareto efficient outcome, there exists a Nash equilibrium that leads to this outcome. Statement 2: If someone has linear indifference curves between contingent commodity bundles, then she must be risk averse and the risk premium is positive. Statement 3: Suppose we have a game with three pure strategies. In a (fully) mixed strategy Nash equilibrium, a player is indifferent between her three pure strategies

A large group of players each guesses a number between 0 and 300. The winner is the person whose number is closest to three-fifth of the average guess. What is the Nash equilibrium? Will it be observed? What do you expect for the outcome of this game with next year's 203 class? (Considering that they have similar sophistication to your class but they have not covered game theory yet.)

For various values of X(for player1 and player 2), find all Nash equilibria of the following game with von Neumann-Morgenstern preferences:

For problem 1 and 2, consider the following game : с D A (0,5) (5,-5) B (3, 1) (1, 0) 1. Show that the game above doesn't have a pure Nash equilibrium. 2. Show that the game above has a unique mixed Nash equilibrium, and describe the playing strategy.