Find pure nash equilibria, Game Theory

Assignment Help:

Find Pure Nash Equilibria

1. Consider a two-player game in which player 1 chooses the strategy x1 from the closed interval [-1, 1] while player 2 chooses the strategy x2 from the same closed interval [-1, 1]. Player 1's utility function is x21/2 + x1x2 and player 2's utility function is x2 2/2 - x1x2. Find and plot the best- response function of each player (against any pure strategy of the opponent). Is there a pure strategy Nash equilibrium of the game?

2. Consider a game in which player 1 chooses rows, player 2 chooses columns and player 3 chooses matrices. Only Player 3's payoffs are given below. Show that D is not a best response for player 3 against any combination of (mixed) strategies of players 1 and 2. However, prove that D is not dominated by any (mixed) strategies of player 3.

1561_find all pure Nash Equilibria 1.png

3. Consider the following three-player game and find all pure Nash Equilibria. Can you find any Nash equilibrium in which exactly two of the three players play a pure strategy while the other plays a mixed strategy (such as (B, R, ½X ½Y)). Explain by considering all possible cases.

2288_find all pure Nash Equilibria 2.png

4. Show that the following game has two types of NE: (i) player 1 chooses D, 2 chooses C with probability at least 1/3 and player 3 chooses L, and (ii) where player 1 chooses C, player 2 chooses C and 3 chooses R with probability at least ¾.

1360_find all pure Nash Equilibria 3.png


Related Discussions:- Find pure nash equilibria

Full equilibrium strategy example, (a) A player wins if she takes the tota...

(a) A player wins if she takes the total to 100 and additions of any value from 1 through 10 are allowed. Thus, if you take the sum to 89, you are guaran- teed to win; your oppone

Game playing in class, GAME PLAYING IN CLASS There are several games t...

GAME PLAYING IN CLASS There are several games that are appropriate for use on the first or second day of class. These games are simple but can be used to convey important poin

Game theory equilibrium exercise, Exercise 1 a) Pure strategy nash equi...

Exercise 1 a) Pure strategy nash equilibrium in this case is Not Buy, bad ( 0,0) as no one wants to deviate from this strategy. b) The player chooses buy in the first perio

Simultaneous game, A simultaneous game is one during which all players buil...

A simultaneous game is one during which all players build choices (or choose a strategy) while not information of the methods that are being chosen by different players. Although t

Find the nash equilibria of game - bimatrix of strategies, Players 1 and 2 ...

Players 1 and 2 are bargaining over how to split one dollar. Both players simultaneously name shares they would like to keep s 1 and s 2 . Furthermore, players' choices have to be

Volunteer''s dilemma , Scenario As described by William Poundstone, imag...

Scenario As described by William Poundstone, imagine that you just notice that electricity has gone out for your entire neighborhood. the electrical company can send somebody to

Draw the strategic form game - nash equilibrium, 1. Consider a two-player g...

1. Consider a two-player game where player A chooses "Up," or "Down" and player B chooses "Left," "Center," or "Right". Their payoffs are as follows: When player A chooses "Up" and

How to make game, I wanna know the language to make games

I wanna know the language to make games

Coalitional game and matching markets, 1. This question and the next is bas...

1. This question and the next is based on the following description. Consider the coalitional game (referred to as Game 1) given by: N = {1,2,3,4}; v(N) = 3, v{i} = 0, i = 1,...,4,

Mixed strategy, A strategy consisting of potential moves and a chance distr...

A strategy consisting of potential moves and a chance distribution (collection of weights) that corresponds to how frequently every move is to be played. A player would solely use

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd