The payoff matrix for a game ls 5 -1 4 -4 21 2-5 2 (a) Find the expected payoff to the row player If the row player R uses the maximin pure strategy and the column C player uses the minlmax pure stra...
The payoff matrix for a game is 3 -5 2 (a) Find the expected payoff to the row player if the row player R uses the maximin pure strategy and the column C player uses the minimax pure strategy (b Find the expected payoff to the row player if R uses the maximin strategy 40% of the time and chooses each of the other two rows 30% of the bme while C uses the miin ax strategy 50% of the...
6. Given the payoff matrix is the expected value of the game? Which player does the game favor? termine the optimal mixed strategy for player R (rows). What x 2 2 6. Given the payoff matrix is the expected value of the game? Which player does the game favor? termine the optimal mixed strategy for player R (rows). What x 2 2
reel-2, whilplayer does the game favor? 6. Given the payoff matrix ,determine the optimal mixed strategy for player R (rows). What is the expected value of the game? Which player does the game favor? reel-2, whilplayer does the game favor? 6. Given the payoff matrix ,determine the optimal mixed strategy for player R (rows). What is the expected value of the game? Which player does the game favor?
For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 9-3 For row player R: For column player C: Find the value v of the game for row plaver R. Who is the game favorable to? O The game is favorable to the row player. 0 The game is favorable to the column player. O This is a fair game. For the 2 x 2 game,...
8. Consider the two-player game described by the payoff matrix below. Player B L R Player A D 0,0 4,4 (a) Find all pure-strategy Nash equilibria for this game. (b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer (c) Keeping in mind Schelling's focal point idea from Chapter 6, what equilibrium do you think is the best prediction of how the game will be...
2. Consider a static game described by the following payoff matrix: LR a,1 2,6 3,0 2,c B The two numbers in each cell is the payoffs to the row player and the column player, respectively. (a) [6] Find all parameter values of a, b, and c for which the strategy profile (T, L) is a weakly dominant strategy equilibrium. (b) [6] Find all parameter values of a, b, and c for which the strategy profile (T, L) is a pure...
3. Player R has $1, $10, and $50 bills, while player C has $5 and $20 bills. Each randomly chooses a bill and shows it for each play of the game. The one with the larger bill collects the difference between their bill and that of the other player. Build a payoff matrix for this game and determine the optimal pure strategy, if one exists.
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash equilibria of the game. [8 Marks] b). Find the pure-strategy subgame-perfect equilibria of the game. [6 Marks] c). Derive the mixed strategy Nash equilibrium of the subgame. If players play this mixed Nash equilibrium in the subgame, would 1 player In or Out at the initial mode? [6 Marks] [Hint: Write down the normal-form of the subgame and derive the mixed Nash equilibrium of...
Find the row player's optimal strategy r = 21, x2]" in the two-person zero-sum game with the payoff matrix A being given by A= (4 5 1 (216 x1 + x2=1, 21 > 0, and x2 > 0.