7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Caroline are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Antonio chooses Right and Caroline chooses Right, Antonio will receive a payoff of 9 and Caroline will receive a payoff of 8. Caroline Left Right Left 8, 5 8, 7 Antonio Right 3, 6 9, 8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses and Caroline chooses

7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Caroline are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Antonio chooses Right and Caroline chooses Right, Antonio will receive a payoff of 9 and Caroline will receive a payoff of 8. Caroline Left Right Left 8, 5 8, 7 Antonio Right 3, 6 9, 8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses and Caroline chooses

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter15: Oligopoly And Strategic Behavior

Section: Chapter Questions

Problem 17P

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7. Solving for dominant strategies and the Nash equilibrium Suppose Rajiv and Simone are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Rajiv chooses Right and Simone chooses Right, Rajiv will receive a payoff of 5 and Simone will receive a payoff of 5.
5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.
1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?
4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.
1) Suppose that Player A can take two actions, either Up or Down. Player A is thinking to choose Up 50 percent of the time, and Down 50 percent of the time. This type of strategy is called a ____ ? 2) Consider a payoff matrix of a game shown below. In each cell, the number on the left is a payoff for Player A and the number on the right is a payoff for Player B. In order for (Down, Right) to be a unique pure strategy Nash equilibrium, a must be (greater, or smaller) than 3 and b must be (greater, or smaller) than 3. refer to image