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- You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next moveA st SW B st 2,1 5, 15 2. Consider the game of chicken above. SW 11,4 3,5 a. Find all Nash equilibrium in pure strategies. b. Say that player A uses a mixed strategy, where she picks st with prob. 0.55 and sw with prob. 0.45. What is B's expected payoffs from choosing pure st and pure sw? c. Player B uses a mixed strategy and wants A to choose sw. What is the minimum prob. p, for which B needs to play st so A will choose sw.The Dean of a College is looking for a tenured professor to teachin the Core Curriculum. Monetary incentives are needed to get someoneinterested, but how much? The Dean decides to use an auction to do thejob. Two professors, equally qualiÖed, applied for the position. The twoprofessors are invited to covertly submit their bids to the Dean. The Deanwill give the position to the professor who submits the lower bid (if thereis a tie, the job is assigned randomly). The professor who gets the job willbe paid his/her own bid. Each professorís reservation value for teachingthe course is his/her private information. It is common knowledge thattheir reservation values are independently and uniformly distributed over[0;100]: So if a professor with a reservation value of 60 wins with a bid of50, his payoff is 60- 50 = 10: (A) Find a Bayesian Nash equilibrium of the bidding game.(B) Suppose the two professorsíreservation values are 60 and 70, respectively. What are their bids in the Bayesian Nash…
- A occurs if all players in a game play their best strategies given what their competitors do.3. Two players play the following game for infinite times. Cooperate Betray Cooperate 10, 20 -25, 30 Betray 15, -23 -12, -19 For the player to continue to cooperate what would be the ranges of their discount factor, 8, and 82, respectively?GAME ZZZ B1 Player B A1 30, 30 Player A A2 20, 40 B2 40, 20 35, 35 In the Game ZZZ (see table above), all payoffs are listed with the row player's payoffs first and the column player's payoffs second. In this game, neither player has a dominant strategy. the Nash equilibrium does not maximize the total payoff. there is no Nash equilibrium. the Nash equilibrium maximizes the total payoff.
- Game theory 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. Player 2 7. Player 1 A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearlyITERATIVE DOMINANCE Consider the following game in strategic form. a₁ 22 a3 bi 35,52 30,30 28,9 (9,11) (45,47) (47,28) (52,16) (28,9) (30,30) (16,45) (11,35) (35,52) b2 11,35 9,11 16,45 b3 52,16 45,47 47,28 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.)The game to the right is called the dating game. It's origins go back to the early 1950s. Player 2 Bach Stravinsky a. Derive, write out, each player's best response function. Вach 2, 2 0,0 Player 1 Stravinsky 0,0 1, 1 b. Draw the best response functions. c. Identify the pure-strategy Nash equiliria(ium) of this game. What might have raised the eyebrow of economists of the 1950s about the expected outcome of this game?
- Consider this extensive form game. The top number is player 1’s payoff, themiddle number is player 2’s payoff, and the bottom number is player 3’spayoff.a. Describe the general form of a strategy for each player.b. Find the SPNE.4. Find all correlated equilibria of the "Bach or Stravinsky" game. What is the highest symmetric payoff that can be achieved? Can this payoff be achieved with a public signal?し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?
