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
The following is a payoff matrix for a non-cooperative simultaneous move game between 2 players. The payoffs are in the order (Player 1; Player 2): What is/are the Nash Equil

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,

the first three words are ''''the boys'' down''''. what are the last three words?

Backward induction is an iterative procedure for resolving finite general form or sequential games. First, one decides the finest policy of the player who makes the last move of th

A game tree (also referred to as the in depth form) may be a graphical illustration of a sequential game. It provides data concerning the players, payoffs, strategies, and also the

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

A type of trigger strategy sometimes applied to the repeated Prisoner's Dilemma during which a player responds in one amount with identical action her opponent utilized in the last

GAME 1 Claim a Pile of Dimes Two players Aand B are chosen. The instructor places a dime on the table. Player A can say Stop or Pass. If Stop, then A gets the dime and the gam

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

Find the pure-strategy Nash equilibrium Alice is on vacation in Wonderland and considers trying a special mushroom sold by the caterpillar. She cannot tell upfront if the mush