Consider the following game. Find all Nash equilibria, subgame perfect Nash equilibria, and weak perfect Bayesian equilibria in pure and mixed strategies. a (12, 12) b (12,-8) P1 m (-3,2) P2 (2.7) (22,17)
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- Problem 2. (SPNE 2). Consider the following extensive form game between two players. (1,10) .. D 2 1 B X Y (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)Nn3 Suppose an incumbent monopoly firm currently earns a profit of $50,000 per period. A potential entrant could enter and make a profit of $15,000 per period while also lowering the incumbent’s profit to $20,000 per period. The monopoly firm could seek to engage in predatory pricing, which would lead to both firms earning a loss of $5,000 per period. (a) Is there a Nash Equilibrium in this game? If so, what is it? (b) Discuss how this game might play out in the real world?NE 2). Consider the following extensive form game between two players. (1,10) u D 1 B X (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)
- FOOP 6. (a) For the following extensive-form game: i. Identify the pure and mixed strategy Nash Equilibria. ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in part (a)? Explain (a couple of sentences should suffice). (3,1) A D B C (-2,-2) (2,5) D (0,7)a W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) to(2,0) (4,2) PL (3,5) (4,1) % D P₂ ра с D Using backwards induction on the game tree above, what payoffs would we expect to occur in this game? (2,0) (4,2) (3,5) (4,1)
- Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 10) Firm 1 A B F2 • this strategy profile is F2 Fight Don't fight Fight Don't fight [Select] (20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses don't fight if A, and fight if B. (-10, 30) (25, 15) • this strategy profile i✓ [Select ] (b) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses don't fight if A, and don't fight if B. • this strategy profile is [Select ] (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A and fight if B. not a Nash equilibrium a Nash equilibrium, but not a subgame perfect Nash equilibrium a subgame perfect Nash equilibrium none of the above(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning. Consider a game with N players. Each player chooses Black or White. If a player (b) chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other players does not choose Black. If a player chooses White, she always gets 50. Show that everyone choosing Black and everyone choosing White are both Nash equilibria of this game.Please no written by hand and no emage Two classmates A and B are assigned a group project. Each student can choose to Shirk or Work. If one or more students chooses Work, the project is completed and provides each with credit valued at 4 payoff units each. The cost of completing the project is that 6 total units of effort (measured in payoff units) is divided equally among all players who choose to Work and this is subtracted from their payoff. If both Shirk, they do not have to expend any effort but the project is not completed, giving each a payoff of 0. The instructor can only tell whether the project is completed and cannot determine which students contributed to the project. A. Write down (draw) the normal form game, with payoff in the format of (player A payoff, player B payoff). Note that we assume students choose to Shirk or Work simultaneously. B. Does either player have a dominant strategy? C. Find the Nash equilibrium or equilibria. D. Explain ‘Prisoners’ dilemma’ using the…
- In this game, (80, 50) 52% a) (R, N) b) (R, R) c) (S, N) d) (R, P) S is a Nash equilibrium First Player (20,68) 12% R P Second Player N (90,70) 36%(1) Multi-Party Electoral Competition - In class, we assumed that there are two parties competing in the election. Let us consider the alternative case with three contending parties, A, B and C. Other parts of the game remains the same. In particular, the election is decided by plurality rule, so the party with the largest vote count (share) wins. Moreover, when there is a tie, the tying parties each win with equal probabilities. 1 (a) Consider the action profile where all three parties choose xm = 1/2. Is (1⁄2, ½, ½) a Nash equilibrium? Explain. 2 (b) Now consider the action profile (A, B, C) = (1, 3, 3). Is it a Nash equilibrium? 3' Explain.Question Completion Status: II -10 -20 3. -30 -10 2. -20 3 -30 Write a normal form for this game. How many pure-strategy Nash Equilbria are there in this game? OA1 OB.2 OC3 OD.4 OES OF. More than 5
