Draw the strategic form game - nash equilibrium, Game Theory

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 player B chooses "Left" player A gets $5 while player B gets $2. When player A chooses "Up" and player B chooses "Center" they get $6 and $1 correspondingly, while when player A chooses "Up" and player B chooses "Right" player A gets $7 while player B gets $3. Moreover, when player A chooses "Down" and player B chooses "Left" they get $6 and $2, while when player A chooses "Down" and player B chooses "Center" they both get $1. Finally, when player A chooses "Down" and player B chooses "Right" player A loses $1 and player B gets $1. Assume that the players decide simultaneously (or, in general, when one makes his decision doesn't know what the other player has chosen).

(a) Draw the strategic form game.

(b) Is there any dominant strategy for any of the players? Justify your answer.

(c) Is there any Nash equilibrium in pure strategies? Justify your answer fully and discuss your result. When an action is never chosen by a player it is because this action is DOMINATED by another action (or by a combination of other actions). Dominated strategies are assigned a probability of 0 in any Nash Equilibrium in mixed strategies. Given this observation answer the following parts of this problem:

(d) Find the best response functions and the mixed strategies Nash Equilibrium if each player randomizes over his actions.

(e) Show graphically the best responses and the Nash Equilibria (in pure and in mixed strategies).

Posted Date: 3/22/2013 6:40:42 AM | Location : United States







Related Discussions:- Draw the strategic form game - nash equilibrium, Assignment Help, Ask Question on Draw the strategic form game - nash equilibrium, Get Answer, Expert's Help, Draw the strategic form game - nash equilibrium Discussions

Write discussion on Draw the strategic form game - nash equilibrium
Your posts are moderated
Related Questions
Consider the electoral competition game presented in Lecture 6. In this game there are two candidates who simultaneously choose policies from the real line. There is a distribution

"Assurance game" is a general name for the game more commonly known as "Stag Hunt." The French philosopher, Jean Jacques Rousseau, presented the subsequent circumstances. Two hunte

The best reply dynamic is usally termed the Cournot adjustment model or Cournot learning after Augustin Cournot who first proposed it in the context of a duopoly model. Each of two

A class of games of imperfect data during which one player (the principal) tries to supply incentives to the opposite (the agent) to encourage the agent to act within the principal

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

This version of Twenty-one is a card game played between a player and the dealer (the computer). The aim of the game is to accumulate a higher point total than the dealer but witho

1  A, Explain how a person can be free to choose but his or her choices are casually determined by past event 2  B , Draw the casual tree for newcomb's problem when Eve can't pe

PROBABILITY AND EXPECTED UTILITY Most students know the elementary combinatorial rules for probability algebra and need only a refresher with some exam- ples. We have used card

Write a bouncing ball video game. The game is similar to the one described and depicted in The balls bounce within the screen where the two horizontal walls are fixed. The two v

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