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- Describe the prisoner's dilemma
- Define Nash equilibrium. What is the Nash equilibrium of the prisoner's dilemma?
- Name two circumstances in which rational actors playing the prisoner's dilemma game can reasonably be expected not to end up in the Nash Equilibrium
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- Is the solution to the prisoner’s dilemma game a Nash equilibrium? Why? The solution to the prisoner’s dilemma game is a Nash equilibrium because no player can improve his or her payoff by changing strategy unilaterally. The solution to the prisoner’s dilemma game is not a Nash equilibrium because players do not end up in the best combination for both. The solution to the prisoner’s dilemma game is not a Nash equilibrium because both players can improve their payoffs by cooperating. The solution to the prisoner’s dilemma game is a Nash equilibrium because it is a noncooperative game in which both players have to expect that the other is purely selfish.Construct the prisoners dillema game and determine Nash equilibriumConsider the following extensive form game: Find the Nash equilibrium Find subgame perfect Nash Equilibrium Explain why all Nash equilibriums are not subgame perfect
- Table 15.4, Prisoner Dilemma. Suppose the game starts with both Jesse and Frank planning to “Stay Mum” in the lower right cell. Discuss how each player would evaluate the situation and decide whether to change decisions. If each player makes decisions to minimize the penalty, in which cell will this game end? Is there a Nash equilibrium?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?Consider the following game: PLAYER 2 Left Middle Right Up 0,0 2,5 5.4 PLAYER 1 Middle 1,2 7,3 4,3 Down 5,5 3, 1 2, 1 Which of the following statements is true? There are two Nash equilibria, and they are both Pareto efficient. There is a unique Nash equilibrium. There are two Nash equilibria, and they are both Pareto inefficient. There are two Nash equilibria, but only one is Pareto efficient. None of these.
- In the table below, it can be stated that it is the Nash Equilibrium: Regarding the game described by the matrix of possibilities below, it can be stated that the pair constitutes a Nash equilibrium:Problem #4: Bayesian Nash Equilibrium Consider the following game, which has two states of nature shown in the two game tables below: "Harmful" (p = 1/3) "Helpful" (1-p = 2/3) Player 2 X Y 3, 2 Player 2 Y 2, 3 3, 2 1,0 0,1 A 0,1 3,2 A Player 1 Player 1 В 0,1 B a) Assume that Player 1 knows what the true state of nature is when playing this game, but Player 2 does not. Find all of the game's Bayesian Nash equilibria. (Hint: It may help to arrange the game tables appropriately.) b) Now, assume that Player 2 knows the true state of nature, but Player 1 does not. Find all of the game's Bayesian Nash equilibria.Suppose you are interested in applying equilibrium theory to the following game, where 61 = {E,F}. Show that there is Bayesian Nash equilibrium in which player 2 plays a sub-optimal action. Player 2 1,1 GF Player 1 R -1,0 NF 0,0 Nature A 1,0 GE 1- p R -1, –1 NE 0,0
- Review Chapter 15, Table 15.4, Prisoner Dilemma. Suppose the game starts with both Jesse and Frank planning to “Stay Mum” in the lower right cell. Discuss how each player would evaluate the situation and decide whether to change decisions. If each player makes decisions to minimize the penalty, in which cell will this game end? Is there a Nash equilibrium?In game theory, what is a subgame? What is a subgame-perfect Nash equilibrium? If possible, could you please provide an example? Thank you!True or false? If a game has a Nash equilibrium, that equilibrium will be the equilibrium that we expect to observe in the real world. False. People don’t always act in the way that a Nash equilibrium requires. People don’t always make the necessary calculations and they take into account the outcome of others. False. A Nash equilibrium is based on very strict assumptions that rarely hold in the real world. No real-world situation leads to a Nash equilibrium. True. As long as people are rational and have their own self-interest at heart, real-life games will result in the Nash equilibrium. True. Nash’s theory of equilibrium outcomes was derived from real-world interactions. The theory holds true for almost all real-world scenarios.