Give an example of an ((extensive form)) game with 2 players. In all steps each player...
Give an example of an ((extensive form)) game with 2 players. In all steps each player has two options. Player I decides in step 1 and step 3. Player II decides in step 2. Player 2 has perfect information. In step 3 player I has forgotten the decision in step 1 and has imperfect information in step 2.
Homework Answers
In step 3, there is
information set joining 4 nodes
The circled one shows that Player is unsure about actions of player 2, imperfect information about player 2 choices
The dotted Information set shows that Player 1 has forgotten his choice of actions in step 1
Add Answer to:
Give an example of an ((extensive form)) game
with 2 players. In all steps each player...
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2...
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2 (0, 4) (4,0 (4, 0) (0, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy (Bayesian Nash equilibrium (equilibria) b) Does a pure strategy perfect Bayesian equilibrium exist? If so, show it (or them). If not, prove it.
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice....
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice. If player 1 chooses H, then player 2 must choose A or B. Player 1 does not get to observe this choice by player 2, and must then choose X or Y. If A and X are played, the payoff for player 1 is 1 and for player 2 it's 5. If A and Y are played, the payoff for player 1 is 6...
A) Consider the extensive form game of complete and imperfect information above. The number of pure...
A) Consider the extensive form game of complete and imperfect
information above. The number of pure strategy Nash Equilibrium in
the game is? (Please, type only numerical values, for example: 0,
1, 2, 3,....)
B) Consider the extensive form game of complete and imperfect
information above. The following strategy profiles are Subgame
Perfect Nash Equilibrium (Select all that apply)
a) (WY, AD)
b) (WY, AC)
c) (ZX, AD)
d) (ZY, BC)
e) (ZY, BD)
...
In the extensive form representation of the game between Player 1 and Player 2, Player 1...
In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has______________ pure strategy Nash equilibria and__________ pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is___________ . (Please, enter only numerical answers like: 1, 2,...
5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the...
5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the belief that the player 2's decision node after Player 1 chooses Ais reached. Player 1 (2, 2) Player 2 a, 0) (3, 1 (a) Find the conditions on parameter values (a and b) such that (B,X) witlh 0 is the perfect Bayesian equilibrium, if any (b) Find the conditions on parameter values (a and b) such that (C,Y) is the strategy profile of the...
Above is the Russian roulette ex. shown in class In a version of the game Russian...
Above is the Russian roulette ex. shown in class
In a version of the game Russian roulette, made infamous in the movie The Deer Hunter, two players are faced with a six-shot pistol loaded with one bullet. The players ante $1000, and player I goes first. At each play of the game, a player has the option of putting an additional $1000 into the pot and passing, or spinning the chamber and firing (at his own head). If player I...
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...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
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...
3. The extensive form of a 2-person game is as follows: () (1019 (a) What are...
3. The extensive form of a 2-person game is as follows: () (1019 (a) What are the pure strategy sets for players I and II? (b) Derive the normal (strategie) form of the game. (c) Use backward induction to find the sub-game perfect Nash Equi libria of the game. There are 2 SPNEs.) (d) Is there any other Nash Equilibrium?
or 5. 1. Consider the following game tree. In this tree, a player, say Player 3,...
or 5. 1. Consider the following game tree. In this tree, a player, say Player 3, has an information set with three nodes, I, II, and III in it. Explain whether each of the following is true or false. (a) Node I is Player 3's decision node, but node II is Player 2's decision node. (b) Player 3 has three actions at node III and two at node I (c) Player 3 has exactly two actions at node III, labeled...
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2 (0, 4) (4,0 (4, 0) (0, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy (Bayesian Nash equilibrium (equilibria) b) Does a pure strategy perfect Bayesian equilibrium exist? If so, show it (or them). If not, prove it.
A) Consider the extensive form game of complete and imperfect
information above. The number of pure strategy Nash Equilibrium in
the game is? (Please, type only numerical values, for example: 0,
1, 2, 3,....)
B) Consider the extensive form game of complete and imperfect
information above. The following strategy profiles are Subgame
Perfect Nash Equilibrium (Select all that apply)
a) (WY, AD)
b) (WY, AC)
c) (ZX, AD)
d) (ZY, BC)
e) (ZY, BD)
...
5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the belief that the player 2's decision node after Player 1 chooses Ais reached. Player 1 (2, 2) Player 2 a, 0) (3, 1 (a) Find the conditions on parameter values (a and b) such that (B,X) witlh 0 is the perfect Bayesian equilibrium, if any (b) Find the conditions on parameter values (a and b) such that (C,Y) is the strategy profile of the...
Above is the Russian roulette ex. shown in class
In a version of the game Russian roulette, made infamous in the movie The Deer Hunter, two players are faced with a six-shot pistol loaded with one bullet. The players ante $1000, and player I goes first. At each play of the game, a player has the option of putting an additional $1000 into the pot and passing, or spinning the chamber and firing (at his own head). If player I...
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...
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...
3. The extensive form of a 2-person game is as follows: () (1019 (a) What are the pure strategy sets for players I and II? (b) Derive the normal (strategie) form of the game. (c) Use backward induction to find the sub-game perfect Nash Equi libria of the game. There are 2 SPNEs.) (d) Is there any other Nash Equilibrium?
or 5. 1. Consider the following game tree. In this tree, a player, say Player 3, has an information set with three nodes, I, II, and III in it. Explain whether each of the following is true or false. (a) Node I is Player 3's decision node, but node II is Player 2's decision node. (b) Player 3 has three actions at node III and two at node I (c) Player 3 has exactly two actions at node III, labeled...
Most questions answered within 3 hours.
-
You're examining some of the tiny printing on one of the newer
twenty-dollar bills. A 1.5...
asked 33 seconds from now -
Discuss several common sources of secondary data coming from
government sources.
asked 2 minutes ago -
This is a basic java program where you convert units using only
loops, control statements and...
asked 2 minutes ago -
A sample survey at a supermarket showed that 204 of 300 shoppers
regularly use cents-off coupons....
asked 47 minutes ago -
1. Find the area under the standard normal curve that lies
outside the interval between z=...
asked 19 minutes ago -
In ________ mode, the interpreter reads the contents of a file
that contains Python statements and...
asked 34 minutes ago -
1.
The second-order rate constant for self-reaction of hydroxyl
radicals
2 OH → H2O + O...
asked 24 minutes ago -
What is the most important factor leading to improved resource
efficiency over the long run?
asked 21 minutes ago -
Defend the effectiveness of teamwork in an organization.
(Use no more than 30 words)
asked 22 minutes ago -
Promotional strategies can assist in moving a product through
the channel of distribution. (a) Briefly explain...
asked 23 minutes ago -
Discuss why new and improved security measures are not enough to
stop online crime, What is...
asked 28 minutes ago -
A person whose weight is 516 N is being pulled up vertically by
a rope from...
asked 41 minutes ago