4. Ana and Kate are playing the following game. Each one of them chooses a number {1,2,3}. The one who has the highest number wins $10. If they choose the same number, they get $5 each. Represent the game if Ana chooses first and Kate second, find the SPNE of this game. Represent the game if they choose simultaneously and find the NE. Is there any difference?
In this game, we are required to find the NE (Nash Equilibrium) and SPNE (Sub game perfect nash equilibrium). Nash Equilibrium is found by best-response analysis and SPNE by backward induction.There is no difference between the NE and SPNE in this game.
4. Ana and Kate are playing the following game. Each one of them chooses a number...
Problem VI: Consider the following dynamic game: An entrant chooses whether to enter the market or stay out. If he chooses to stay out he will get $0, while the incumbent gets $20. If he enters the market, the entrant and the incumbent play the following simultaneous pricing game: they both choose whether to price high or low. If they both price low, they each get $5. If they both price high, they each get $10. If one prices low...
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....
The following payoff matrix depicts two companies, Lowe's and Home Depot, in an advertising game. The companies will be playing the same game several times. Each company makes its decision without knowing what the other chooses. The payoffs for each firm represent economic profits.Imagine that at the beginning of each week, Home Depot and Lowe's play the game described in the payoff matrix above. Assume there is no known end to the game, so Home Depot and Lowe's will effectively...
Billy and Cam are playing the following game: each player has a coin and decides whether to leave it as heads or tails before showdown (both player reveals their coin simultaneously). If both coins are heads, Billy wins $2. If both are tails, Billy wins $0.50. Otherwise, Cam wins $1. Find the optimal strategy for Billy.
2) Broard Games Rules 1) Game equipment: 1 game broard, 1 deck of playing cards, 25 playing pieces (5 each of 5 colors 2) To start : Each player chooses a color and places the pieces of that color on the matching HOME circle. One player shuffles the deck and places at it face down the space marked CARDS: select a player to play first, the winter of one game goes first in the net. 3) the object of the...
19. A Card Game 19. A Card Game Three students are playing a card game. They decide to choose the first person to play by each selectinga card from the 52-card deck and look- ing for the highest card in value and suit. They rank the suits from lowest to highest: clubs, diamonds, hearts, and spades. a. If the card is replaced in the deck after each student chooses, how many possible configurations of the three choices are possible? b....
You and Ellie are playing a game, in which first Ellie chooses r numbers out of the set 1,2,,n, for 1 S n, and then you independently choose r numbers out of the same set. What is the probability that: (a) Your set of r chosen numbers do not include consecutive values? (b) Your set of r chosen numbers includes precisely one pair of consecutive values? (c) Given Ellie's selection, your numbers are precisely the same as hers? (d) Given...
Two players are playing a game in which each player requests an amount of money, simultaneously. The amount must be an integer between 11 and 20, inclusive. Each player will receive the amount she requests in $s. A player will receive an additional amount of $20 if she asks an amount that is exactly 1 less than the other player’s amount. All of the above is common knowledge. a) Find the set of all pure-strategy Nash Equilibria. b) Suppose we...
5. (10 points) Alice and Barbara are playing a one-stage guessing game. Each must choose a real number between 1 and 4 (inclusive). Alice's target is to match Barbara's number. Barbara's target is to name twice Alice's number. Each receives $10 minus a dollar penalty that is equal to the absolute difference between her guess and her target. Solve this game by iteratively deleting dominated strategies. What will Alice and Barbara choose? 5. (10 points) Alice and Barbara are playing...
4. Political Competition Each of 2 political candidates chooses a policy position x e [0,1: Voters (there is a continuum of them) are uniformly distributed on [0,1]; each votes for whichever candidate chooses a position closest to him. (So for example, if candidate l chooses X1 and candidate 2 chooses x2,then all voters above1 vote for candidate 2, all below with positive probability. A candidate's payoff is 1 if he wins, 0 if he loses. Find all NE of the...