Game Theory: Will rate for correct and descriptive answers! 2) Here's another game: There are three...
2) Here's another game: There are three players, numbered 1,2, and 3. At the beginning of the game, players1 and 2 simultaneously make decisions, each pulling out a Red or Blue marble. Neither player can see what the other player is choosing. After this choice, the players secretly reveal their marbles to each other without letting player 3 see. If both players choose Red, then the game ends and the payoff vector is(, 0, 0). If both players choose Blue,...
Game Theory: Will rate for correct and descriptive answers! 1 Let's think about the popular game "Rock, Paper, Scissors." On the count of three, two players quickly form their hands into the shape of either a rock, a piece of paper, or a pair of scissors (abbreviate these shapes as R, P, and S, respectively). The players make this choice at the same time and do not know what their opponent is going to choose If the players pick the...
Game Theory: Will rate for correct and descriptive answers! 3) Suppose that we have a game where Si-H, Land S,-(X, Y}. If player I plays H, then her payoff is z regardless of player 2's choice. Player l's other payoff numbers are uI(L,X)-0 and u (L,Y) 10. You can make up any payoff numbers you like for player 2 (we are only concerned with player I's payoff for this question). a. Draw the normal form of this game. Clearly label...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Consider a game in which Player 1 first selects between L and R. If Player 1 selects L, then players 1 and 2 play a prisoner’s dilemma game represented in the strategic form above. If Player 1 selects R then, Player 1 and 2 play the battle-of-the-sexes game in which they simultaneously and independently choose between A and B. If they both choose A, then the payoff vector is (4,4). If they both choose B, then the payoff vector is...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose A or B. The game ends if she chooses A while it continues to Bob if she chooses B. Bob then can choose C or D. If he chooses C the game ends, and if he chooses D the game continues to Alice. Finally, Alice can choose E or F and the game ends after each of these choices. a. Present this game as...
stion 4 10 points Save Answer Player II С 6,6 1,7 D 7,1 3,3 Player l Consider a game in which Player 1 first selects between L and R. f Player 1 selects L, then players 1 and 2 play a prisoner's dlemma game represented in the strategic form above it Player 1 selects R then, Player 1 and 2 play the battie-of the-sexes game in which they simultaneously and independently choose between A and B. If they both choose...
Represent the following strategic interactions using payoff matrix/matrices: Three players are playing the following game: Each of them will put a penny (1 cent in the US) down simultaneously, each choosing between head and tail. If players 1's and 2's penny are on the same side (i.e., both heads or both tails), then player 1 takes over player 2's penny. If player 1's and 2's penny are mismatched (i.e., one head, one tail), player 2 takes over player 1's penny....
4. (a) (10%) A player has three information sets in the game tree. He has four choices in his first information set, four in his second and three in his third. How many strategies does he have in the strategic form? Circle one: (i) 11, (ii) 28 (iii) 48 (iv) 18. (b) (10%) Is it true that the following game is a Prisoners' Dilemma? Explain which features of a Prisoners' Dilemma hold and which do not. (Remember each player must...