2. Consider the following "centipede game." The game starts with player 1 choosing be- tween terminate (T) and continue (C'). If player 1 chooses C, the game proceeds with player 2 choosing between terminate (t) and continue (c). The two players choose be- tween terminate and continue in turn if the other player chooses continue until the terminal nodes with (player l's payoff, player 2's payoff) are reached as shown below. Player 1 Player 2 Player 1 Player 2 (3, 3)| (1, 1) (0, 3) (2, 2) (1, 4)
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- Consider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1 (if necessary). At the bottom of the decision tree, the first number represents the payoff of Player 1, while the second number represents the payoff of Player 2. In equilibrium, the payoff of Player 1 is ✓ and the payoff of player 2 is Player 2 L₂ (-1,8) L₁ Player 1 R₂ (100,1) R₁ (1,0)Consider the following game. There are two payers, Player 1 and Player 2. Player 1 chooses a row (10, 20, or 30), and Player 2 chooses a column (10/20/30). Payoffs are in the cells of the table, with those on the left going to Player 1 and those on the right going to player 2. Suppose that Player 1 chooses his strategy (10, 20 or 30), first, and subsequently, and after observing Player 1’s choice, Player 2 chooses his own strategy (of 10, 20 or 30). Which of the following statements is true regarding this modified game? I. It is a simultaneous move game, because the timing of moves is irrelevant in classifying games.II. It is a sequential move game, because Player 2 observes Player 1’s choice before he chooses his own strategy.III. This modification gives Player 1 a ‘first mover advantage’. A) I and IIB) II and IIIC) I and IIID) I onlyE) II onlyTwo players bargain over $20. Player 1 first proposes a split of(n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Find one Nash equilibrium that is NOT a subgame perfect Nash equilibrium. Explain why it is a Nash equilibrium and why it is not subgame perfect.
- in game theory, when are there player 1 and palyer 2 and the payoff function is as follow (if player 1 get to choose first) (u1, u2). my question is if the order change like player 2 get to choose first, will the order of the payoff change as well like (u2, u1)?Consider the following game: Player 1 chooses A, B, or C. If player 1 chooses A, the game ends and each player gets a payoff of $7. If player 1 chooses B, then player 2 observes their choice and plays X or Y. If player 1 chooses B and player 2 chooses X, the game ends. Player 1 gets a payoff of $14 and player 2 gets a payoff of $16. If player 1 chooses B and player 2 chooses Y, the game ends. Player 1 gets a payoff of $17 and player 2 gets a payoff of $14. If player 1 chooses Č, then player 2 chooses secretly to put either a $5 bill or a $20 bill into a sealed envelope. Player 1 does not observe his choice; rather she has two options: Open the envelope and gets whatever bill is inside. If she chooses this, player 2 gets nothing. Give the envelope back to player 2, and get $12 for sure. If she chooses this, player 2 gets the amount in the envelope. Draw the game tree for this game How many strategies does Player 1 have in this game?14. You have baked a cake, but your two dear daughters won't stop fighting on who gets the biggest slice. To settle the dispute, to ask your dear daughter one (DD1) to cut the cake and your dear daughter two (DD2) to choose which piece she wants. (a) Draw the extensive form of the game. Let dear daughter one's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what is on the platter, dear daughter two's strategies might in- clude "Take Big Slice", "Take Small Slice", or "Take Equal Slice". Assign payoffs to dear daughter one and dear daughter two that grow with the size of the slice that they receive. (b) Use backward induction to find the equilibrium outcome of this game. (c) Is the promise to take a small slice by DD2, if DD1 cuts unevenly, credible? Explain carefully. (d) After the rules are announced, dear daughter two says "It is not fair! I want to be the one who gets to cut the cake, not the one who chooses the slice!". Is dear daughter two's complaint valid? You are…
- Consider the following game. There are two payers, Player 1 and Player 2. Player 1 chooses a row (10, 20, or 30), and Player 2 chooses a column (10/20/30). Payoffs are in the cells of the table, with those on the left going to Player 1 and those on the right going to player 2. For example, a payoff 100/200 would mean Player 1 receives 100 and Player 2 receives 200.What is [are] the Nash Equilibrium [Equilibria] of this game?A) (10/10) and (20/20)B) (30/30)C) (10/20) and (20/10)D) (20/20)E) (30/30)3. Three politicians are voting on whether to allow themselves a salary increase of $ 3,500 per year. If they vote in favour of a raise, then they lose some public support, costing them each $ 1,500 per year. The salary increase passes if two or more politicians vote in favour of it. What is this game’s Nash equilibrium (or equilibria)? Explain. There is no need to draw a payoff matrix. (20%[39] Consider the following dynamic game: Player 1 moves first, choosing between strategies A and B. If 1 chooses A, then player 2 moves, choosing between strategies C and D. If 1 chooses B, then 2 chooses between E and F. If 2 chooses E, the game ends. If 2 chooses F, the game continues, with 1 choosing between G and H. The payoffs are indicated in parentheses at the bottom of the game tree, with 1's payoffs 1st and 2's payoffs 2nd. (3.8) (8,3) B E (5.5) G H (2,10) (1.0) Using backwards induction, the solution to the game leads player 2 to choose: A. C B. D C. E D. F
- Consider the following sequential strategic situation, called the centipede game. The game has 100 stages. Two players take turns making decisions, starting with player 1. At stage t = 1,...,99, player 1 (if the stage is odd) or player 2 (if the stage if even) chooses whether to "Terminate the game" or to "Continue the game." If the game is terminated instage t = 1,...,99, the player terminating the game receives a payoff of t, while the other player receives a payoff of zero. Finally, at stage t = 100, player 2 chooses between action A with a payoff of 99 for each player, or action B with a payoff of zero for player 1 and a payoff of 100 for player 2. Draw the game tree for this situation. What is the SPNE?Lee and Cody are playing a game in which Lee has the first move at A in the accompanying decision tree: Once Lee has chosen either aggression or cooperation, Cody, who can see what Lee has chosen, must choose either aggression or cooperation at B or C. Both players know the payoffs at the end of each branch. Lee chooses A Aggression Cooperation Cody chooses 8 Multiple Choice C Cody chooses Aggression aggression: aggression Cooperation Aggression In the equilibrium of this game, Lee chooses Cooperation aggression; cooperation -10 for Lee -10 for Cody 40 for Lee O for Cody O for Leo 40 for Cody 25 for Lee 25 for Cody and then Cody chooses.Consider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1. At the bottom of the decision tree, the first number represents the payoff of Player 1, while the second number represents the payoff of Player 2. For player 2, A stands for Accommodate and F stands for Fight. Player 1 Enter Player 2 A F A Stay out Player 2 F (16,30) (-6,18) In the Nash equilibrium of this game, player 2 earns Player 2 player 1 would play (0,40) (0,20) ✓an incentive to threaten F because, if player 1 believed him then so that player 2 would earn ✓. However, this threat is