Player 2 d A Player 1 B 1,3 0,0 4, 2 -1,5 Consider the following stage game: (a) Find the minmax strategies and values for both players. (b) Draw the feasible set and the individually rational set.
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- The first player can choose either U or D. If he chooses U, the second player has a choice of two strategies: L and R. If the second player moves L he obtains 1 and the first player gets 5. If the second player chooses R he obtains 2 units of payoff while the first player receives 1. Following a move D by the first player, both players engage in a simultaneous-move “Bach or Stravinsky” game (as it was described in class). Find the SPE of this game and write it down in a mixed and behavior form.Two friends, Khalid and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. Construct a payoff matrix for the game. Is there a unique Nash equilibrium in this game? Which strategy should a player use to maximize her chances of winning the game?What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)
- Find all NE of the stage game.(b) Consider a two-period game without discounting in which the stage game is played ineach period. Find all pure strategy SPNE.(c) What’s the min-max payoff of each player?(c1) Consider pure strategies only.(c2) Consider all strategies, including the mixed ones.(d) Now suppose the stage game is repeated infinitely many times. Use the Fudenberg-Maskin Folk theorem to find all possible values of payoff that can be supported as aSPNE.Paramter y = 0 What is the highest payoff any player can receive in any subgame perfect Nashequilibrium of the repeated game?Suppose that Alex and Bob complete the project sequentially. Assume that Alex decides his effort level and starts the project first, and then Bob decides his effort level and finishes the project. Present the extensive-form representation of the game (i.e., draw a decision tree which is also referred as the game tree). What is your prediction regarding the outcome of the game? Explain your prediction.
- onsider the game described by the ff table. what is thE best response for the column player if he/she knows that the row player will make the Y move?Consider the strategic form game shown. a. Assume that both players are rational. What happens?b. Assume that both players are rational and that each believes that theother is rational. What happens?c. Find the strategies that survive the ISDS.(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).
- Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.The decision tree below describes the game faced by firm H and firm T. The payoffs are profits in million of US$. The complete plan of action for this game is: H={BL}, T={BL if BL, NB if BS, BL if NB} H={BS}, T={BS if BL, BS if BS, BL if NB} H={BS}, T={BS and NB} H={BL}, T={BS if BL, BS if BS, BL if NB} H={BS}, T={BL if BL, NB if BS, BL if NB}A) Focus on the strategic game at the lower-right side of the gametree. Find all the Nash equilibria for this subgame, including the mixed-strategyones. (b) Find all the subgame perfect equilibria for the entire game, allowingfor both pure and mixed strategies