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- 6) Consider the following signaling game: 20, 5 0,0 10, -10 -10,0 Left Left Right Right Player 2 Player 2 1-a Up Up Nature Player 1-A Player 1-B Туре А — 50% Туре В — 50% Down Down Player 2 1-B Player 2 Left Right Left Right 10,5 0,0 5, -10 0,0 Let's see if it has a pooling equilibrium. Follow the following steps: a. Specify strategies of a possible pooling equilibrium b. Determine player 2’s on-path beliefs for the belief probabilities a and ß as appropriate. You can infer these beliefs from what we know about beliefs in pooling equilibria, and do not have fully calculate them. c. Check whether either player wants to deviate. Is there a pooling equilibrium? d. Determine the off-path beliefs that make the equilibrium hold.1.)D5
- Info for the following two questions: Consider the sequential game below, with two players (1 and 2): 1 a b. (3,5) (4, 2) (5,1) (0, 0) e (0,0) (2, 4) The number next to the black nodes denote which player is picking the action. That is, player 1 starts; player 2 plays next unless player 1 picked c; and player 1 can play again if player 2 picked A. Question 13: What constitutes a pure strategy in this game? O The payoffs associated with the equilibrium outcome. For example, (2,4) describes a pure strategy. 2.Thank you for helping on this!17. In the following bargaining game, a firm (F) and a syndicate (S) have to share the benefits generated by their economic activity. Assume that the benefits are equal to 2 million euros. The game has three stages. Offers are alternating between F, S and F. In each stage, the player who has not offered how to share the benefits has the choice of accepting or rejecting the proposal made by the other player. If she accepts the proposal, the game ends and if she rejects, in the next stage, she will become the proposer. If the players do not reach any agreement, after the third proposal, both of them get a zero payoff. a) What will be agreement reached in equilibrium and in which time period will the agreement be reach if the discount factor of both players is & = 1/4? b) What will be agreement reached in equilibrium and in which time period will the agreement be reach if F has a discount factor 8p = 1/4 and S has 8s = 1/2? c) Compare the two agreements and try to provide an intuitive…
- 7. Which of the following is not true of the “Battle of the Sexes" Game? a. The predicted outcome demonstrates how independent and rational play by players can quickly reach an agreement or a convergence of expectations concerning which strategy will be played by each player in equilibrium. b. The Battle of the Sexes Game can be used to depict a variety of situations where the players' interests do not precisely coincide, except for the fact that they both want to avoid the outcomes that would result from choosing different actions from one another. c. Players do not have a dominant strategy but playing “Boxing" say, is a best response to the other playing "Boxing" even if it doesn't give the player the payoff associated with his or her preferred alternative. d. Played only once, the outcome where each goes to their preferred venue cannot be Nash Equilibrium.3. Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives £20 and player 2 receives £45. If both move left, player 1 receives £15 and player 2 receives £30. If player 1 moves left and player 2 moves right, player 1 receives £40 and player 2 receives £40. a. Draw the above situation in the form of an extensive form game. b. Find the sub-game perfect Nash equilibrium of the extensive form game..What is the probability of getting a king if a card is drawn from a pack of 52 cards?
- 5. Instead of choosing Game A or Game B in the first stage, player 1 chooses either game B or directly which action to play in game A. Game U D L (10,5) (5,10) R (0,0) (0,0) :Game B: L R U (6,6) (0,0) D (0,0) (0,0) (a) Write the game in extensive form. (b) Solve for all SPNEs of the modified game. (c) Do all the SPNEs give intuitively reasonable predictions? Why or why not? (Hint: think about what the modification of the payoff to game A entail for player 2 in that game and how the predictions contrast with the case where the game is chosen first, then the action.)7(9) Solve the following three-stage game through backwards induction. 1 L R 2 L R L R L/ 1\R L/ 1\R L/1\R L/1\R 1,0 -1,3 0,1 -1,0 1,2 2, 1 0,1 -3,4