Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Player 1 Strategy B с 15, 7 8, 12 a. What is player 1's optimal strategy? D 10, 11 19, 7 O Player 1 does not have an optimal strategy. Strategy A. Strategy B. E 19, 15 12, 3 18, 20 15, 16
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- Consider the game tree below (attached). In this game, each player can mover either Up (U) or Down (D). Player 1 moves first, then Player 2, and Player 3 moves last. Using backwards induction, clearly identify the choice that each player will make at each stage in the tree circle the ultimate outcome (payoff) to the gameConsider 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 onlyPlease find herewith a payoff matrix. In each cell you find the payoffs of the players associated with a particular strategy combination: The first entry is the payoff of player 1, the second entry is the payoff of player2. Player 2 t1 t2 t3 Player 1 S1 3, 4 1, 0 5, 3 S2 0, 12 8, 12 4, 20 S3 2, 0 2, 11 1, 0 Suppose both players select their strategies (S1, S2 or S3 for player 1 and t1, t2 or t3 for player 2) simultaneously and that the game is played once. In your explanation to the questions below, please do refer to the figures in the matrix. Suppose player 2 could move before player 1 (i.e. has a first mover advantage). In your explanation to the questions below, please do refer to the figures in the matrix. What strategy would (s)he select? Is it really an ‘advantage’ for player 2 to move first? Or does player 2 benefit from being the second mover (and hence player 1 moving first)? I.e. for this question, do not make a comparison to the outcome of the…
- Players 1, 2, and 3 are playing a game in which the strategy of player i isdenoted yi and can be any nonnegative real number. The payoff function for player 1 is V1(y1,y2,y3) = y1 + y1y2 - (y1)2,for player 2 is V2(y1,y2,y3) = y2 + y1y2 - (y2)2,and for player 3 is V3(y1,y2,y3) = (10 - y1 - y2 - y3)y3.These payoff functions are hill shaped. Find a Nash equilibrium. (Hint: Thepayoff functions are symmetric for players 1 and 2.)Using the payoff matrix, suppose this game is infinitely repeated and that the interest rate is sufficiently “low.” Identify trigger strategies that permit players 1 and 2 to earn equilibrium payoffs of 140 and 180, respectively, in each periodConsider the following two person game. Player 1 begins the game by choosing A or B. If Player 1 chooses A the game ends and Player 1 receives $100 and Player 2 receives $100. If Player 1 chooses B then Player 2 must choose C or D. If Player 2 chooses C then Player 1 receives $150 and Player 2 receives $250. If Player 2 chooses D then Player 1 receives $0 and Player 2 receives $400. Draw the complete game tree for this situation. Be sure to accurately label the tree and include the payoffs. Using backwards induction (look forward and reason backwards) determine the rational outcome to this game. Given how experimental subjects have behaved in the Ultimatum game, provide a behavioral explanation for why an “average” Player 1 and 2 might deviate from the rational prediction.
- Consider the following representation of a hockey shootout. The shooter can shoot on their forehand, or deke to their backhand, and the goalie can anticipate either move. The number in each cell in the table below represents the percentage chance that the shooter scores for each pair of pure strategies. Anticipate Forehand Anticipate Backhand Shoot Forehand 20 40 Deke Backhand 40 10 In the mixed strategy Nash equilibrium of this game, what is the percentage chance that the player scores? (ie. An 80% chance should be recorded as 80)Consider the following dynamic game. There are two players (P1, P2). Player 2 tries to rob Player 1. If Player 1 pays $100, the game is over with Player 1 (victim) paying $100 to Player 2 (robber) (P1: -$100, P2: +$100). If Player 1 refuses to pay $100, then Player 2 has two choices: one is to hurt Player 1 (P1: -$5,000, P2: -$1,000) and the other is to walk away (P1: 0, P2: 0). Explain how to find an equilibrium in this game.Suppose that Kim and Nene are both in the public eye. They get offers to sell secrets of the other to tabloids. If both keep the secrets, they are both better off than if they get exposed. If only one is exposed, the other person is better off than if no one was exposed. Their payoffs from each option are given in the payoff matrix. Suppose that Nene and Kim play the game over four television seasons, where each season is a new game. Consider the scenarios. Remember, a tit‑for‑tat strategy is one where the person starts by cooperating and then plays whatever strategy the other firm played last. Over four seasons, how much will Nene make if she and Kim both play tit‑for‑tat? $ Over four seasons, how much does Nene make if she always exposes and Kim plays tit‑for‑tat? $ Over four seasons, how much will Nene make if she plays a tit‑for‑tat strategy and Kim always exposes? $ Over four seasons, how much will Nene make if she and…
- A payoff matrix is shown below. With the payoffs in each field indicated in the form (Player 1’s payoff, Player 2’s payoff). Player 2 Left Right Player 1 Up ($1, $1) ($2, $4) Down ($7, $8) ($3, $3) Which of the following is true? The only Nash Equilibrium is Player 1 playing ‘Up’ and Player 2 playing ‘Right’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Left’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Right’. None of the other answers provided are true.Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.Suppose that Teresa and Caroline are both in the public eye. They get offers to sell secrets of the other to tabloids. If both keep the secrets, they are both better off than if they get exposed. If only one is exposed, the other person is better off than if no one was exposed. Their payoffs from each option are given in the payoff matrix. Suppose that Caroline and Teresa play the game over four television seasons, where each season is a new game. Consider the scenarios. Remember, a tit‑for‑tat strategy is one where the person starts by cooperating and then plays whatever strategy the other firm played last. Over four seasons, how much will Caroline make if she and Teresa both play tit‑for‑tat? $_______ Over four seasons, how much does Caroline make if she always exposes and Teresa plays tit‑for‑tat? $________