Find pure nash equilibria, Game Theory

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

Posted Date: 2/15/2013 12:15:12 AM | Location : United States







Related Discussions:- Find pure nash equilibria, Assignment Help, Ask Question on Find pure nash equilibria, Get Answer, Expert's Help, Find pure nash equilibria Discussions

Write discussion on Find pure nash equilibria
Your posts are moderated
Related Questions
1.a.out 2 1 Here is the grid that has been generated: 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0

Matches or different objects are organized in 2 or a lot of piles. Players alternate removing some or all of the matches from anyone pile. The player to get rid of the last match w

Ordinal payoffs are numbers representing the outcomes of a game where the worth of the numbers isn't vital, however solely the ordering of numbers. for instance, when solving for a

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

A non-cooperative game is one during which players are unable to form enforceable contracts outside of these specifically modeled within the game. Hence, it's not outlined as games

saaaaaaasfffffffffffffffffffaaaczzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

What are the important forms of product differentiation? There are three significant forms of product differentiation, which are: 1. Differentiation through style or type –


Something in a very game is Mutual information if all players realize it. A seemingly straightforward concept, mutual information is insufficient to research most games, since it's

A sequential game is one during which players build choices (or choose a strategy) following an exact predefined order, and during which a minimum of some players will observe the