![Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4) si multaneously and independently selects her contribution s E [0, 10]. Each player gets a benefit related to all of the players choices of s,s, but incurs a cost related to her own contribution s In particular, the payoff to each player i is given by: ul (s1 , s2, s3, s.) = si + s2 + s3 + 84-0.5s (a) Find best response functions for all players. (b) Find all Nash equilibria (if any). (c) Are there any dominated strategies? (d) Are there any dominant strategies?](http://img.homeworklib.com/questions/fff0c190-a045-11eb-a1fd-dd1429b02062.png?x-oss-process=image/resize,w_560)
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Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4)...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y,...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies S = {U,D), S2 L, R, S3 - {A, B). The payoffs are summarized in the following payoff matrices: Table 3: Payoff Matrices P3 P3 plays A P2 P3 plays B P2 U|3,3,8 1,2,-2 D 0,9,6 -4,13 , -2 ,1 U 11,-1,2 9,5,12 DI 0,1,4 3,-1 , 3 P1 where in an cell the payoff x , y , z corresponds to P1, P2...
A game involving two players with two possible strategies is a prisoner's dilemma if each player...
A game involving two players with two possible strategies is a prisoner's dilemma if each player has a dominant strategy and: Select one: a. neither player plays their dominant strategy. b. each player's payoff is higher when both play their dominated strategy than when both play their dominant strategy. c. each player's payoff is lower when both play their dominant strategy than when both play their dominated strategy. d. there is a Nash equilibrium that yields the highest payoff for...
Consider an investment game among 2 players. Each player can either invest, i, or not invest,-i....
Consider an investment game among 2 players. Each player can either invest, i, or not invest,-i. If a player does not invest, her payoff is 0 regardless of whether the other invests or not. If a player invests, she gets 1 if the other invests but -1 if at least one of the others does not. a. What are the pure Nash equilibria? b. What is the Pareto dominant pure Nash equilibrium? c. What is the Risk dominant pure Nash...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
1. Find the Nash equilibria of the two-player strategic game in which each players set of...
1. Find the Nash equilibria of the two-player strategic game in which each players set of actions (strategies) is the set of nonnegative numbers and the players payoff functions are ui(a1, a2)- a1 (a2-a1) and u2 (a1, a2) = a2 (1-al-a2).
Some notes: A hundred players are participating in this game (N 100). Each player has to...
Some notes:
A hundred players are participating in this game (N 100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players". Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Q4 Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any)...
A game is a strategic interaction between two players. Each player has their own sets of...
A game is a strategic interaction between two players. Each player has their own sets of actions called the strategies. Each strategy comes with a definite outcome, these outcomes are tied to some profit or loss called the payoff. One of the favorite examples of game theory is the Prisoners' dilemma. In this game, two partners of crime are caught by police and held in different cells being interrogated separately. Both have two options, either to confess or be silent....
1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1)...
1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1) have any dominated strategies? (b) Does P2 (player 2) have any dominated strategies? (c) Suppose l2 beleves that Pl is rational, should P2 believe P1 will ever play B? (d) Suppose player P2 rales out the possibility that Pl plays B, is there a dominated ECON 306 Page 2 of 12 2018 strategy for player P2? (e) Can yoa find any more eliminated strategies...
A hundred players are participating in this game (N = 100). Each player has to choose...
A hundred players are participating in this game (N = 100). Each player has to choose an integer between 1 and 100 in order to guess “5/6 of the average of the responses given by all players”. Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins. (a) Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any). No additional...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies S = {U,D), S2 L, R, S3 - {A, B). The payoffs are summarized in the following payoff matrices: Table 3: Payoff Matrices P3 P3 plays A P2 P3 plays B P2 U|3,3,8 1,2,-2 D 0,9,6 -4,13 , -2 ,1 U 11,-1,2 9,5,12 DI 0,1,4 3,-1 , 3 P1 where in an cell the payoff x , y , z corresponds to P1, P2...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
1. Find the Nash equilibria of the two-player strategic game in which each players set of actions (strategies) is the set of nonnegative numbers and the players payoff functions are ui(a1, a2)- a1 (a2-a1) and u2 (a1, a2) = a2 (1-al-a2).
Some notes:
A hundred players are participating in this game (N 100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players". Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Q4 Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any)...
1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1) have any dominated strategies? (b) Does P2 (player 2) have any dominated strategies? (c) Suppose l2 beleves that Pl is rational, should P2 believe P1 will ever play B? (d) Suppose player P2 rales out the possibility that Pl plays B, is there a dominated ECON 306 Page 2 of 12 2018 strategy for player P2? (e) Can yoa find any more eliminated strategies...
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