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Explain what is meant by the last-mover’s advantage.
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- A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete?Alice chooses action a or action b, and her choice is observed by Bob. If Alice chooses action a, then Alice receives a payoff of 5 and Bob receives a payoff of 7. If Alice chooses action b, then Bob chooses action cor action d. If Bob chooses action c, then Alice receives a payoff of 10 and Bob receives a payoff of 5. If Bob chooses action d, then Alice receives a payoff of 0 and Bob receives a payoff of 3. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) O This game has imperfect information. O Alice's backward induction payoff is 5. O This is a promise game. O Alice's backward induction payoff is 0. O This is a prisoners' dilemma. O Bob's backward induction payoff is 5. O Bob's backward induction payoff is 3. O This is a threat game.Question 13. Find the equilibrium in this one-shot simultaneous game. Explain your answer. Is the equilibrium Pareto-optimal? Brian Snooker Film Snooker 5,8 2,6 Anna 1,2 Film 4,4
- what is payoff line for Nash equilibrium?Write the payoff matrix (in dollars) for the coin-matching game between two players. If both coins are heads, R pays C $1.60. If both coins are tails, C pays R $3.20. If the coins differ, R pays C 80c. с R Heads Tails -80 Heads -80 TailsPlayer 2 Strategy A Strategy B Strategy 1 (1,4) (2,3) Player 1 Strategy 2 (6,5) (5,4) Consider the game depicted in the table above. The payout for player 1 is given first in parenthesis, with Player 2's payout second. What is the Nash equilibrium in this game? Strategy 1 and Strategy A Strategy 2 and Strategy A Strategy 2 and Strategy B This game does not have a Nash equilibrium
- A principal can choose to make the allocation of tasks broad (B) or narrrow (N). At the same time an agent can choose to work put in high effort (H) or low effort (L). The payoffs are 20 to the principal and 30 to the agent is the actions chosen are B and L. For all other combinations of actions the payoffs are 0 to both players. Which of the following statements are true? DA Nash equilibrium of the game is (B, H) A Nash equilibrium is (N, L) There is no Nash equilibrium in pure strategies in this game. A Nash equilibrium is (N, H) A Nash equilibrium is (B, L)Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartmentConsider the following story: Charlie finds two fifty-pence pieces on the floor. His friend Dylan is standing next to him when he finds them. Chris can offer Dylan nothing at all, one of the fifty-pence pieces, or both. Dylan observes the offer made by Charlie, and can either accept the offer (in which case they each receive the split specified by Charlie) or reject the offer.If he rejects the offer, each player gets nothing at all (because Charlie is embarassed and throws the moneyaway).(a) Formulate this interaction as an extensive-form game. To keep things simple, players’ payoff is equal to their monetary gain.(b) List all histories of the game. Split these into terminal and non-terminal histories.(c) What are the strategies available to Charlie? What are the strategies available to Dylan? Draw the strategic-form game.(d) Find the pure-strategy Nash equilibria of this game.(e) What do you think will happen?
- A strategy is a decision rule that describes the actions a player will take at each decision point. The normal-form game indicates the players in the game, the possible strategies of the players, and the payoffs to the players that will result from alternative strategies. In the game presented in Table Normal-Form Game, does player B have a dominant strategy? What is the secure strategy for player B in the game presented in Table Normal-Form Game?How do we solve a Sequential-move game?Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
