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.
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria. Consider two players (Rose as player...
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 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 time while C uses the minimax strategy...
1. Suppose that R and C play a game by matching coins. On each play, C pays R the number of heads shown (0, 1, or 2) minus twice the number of tails shown. Build a payoff matrix for this game and determine the optimal pure strategy, if one exists.
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...
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
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
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?
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.