Ordinally symmetric game, Game Theory

Ordinally Symmetric Game Scenario

Any game during which the identity of the player doesn't amendment the relative order of the ensuing payoffs facing that player. In different words, every player ranks the payoffs from each strategy combination within the same order.

Description

A game is ordinally symmetric if the ordinal ranking of 1 player's payoffs is corresponding to the ordinal ranking of the transpose of the opposite player's payoffs. If the transpose of the opposite player's matrix is equivalent (not simply ordinally equivalent), then the sport is cardinally symmetric (or simply symmetric).

Outcome

The result that obtains from a selected combination of player's methods. each combination of methods (one for every player) is an outcome of the sport. A primary purpose of game theory is to work out that outcomes are stable, within the sense of being Nash equilibria

Example



Player 1



A

B

Player 2

A

1,5

0,6

B

3,1

4,8

Note that player 1's strategies are the matrix:

1

0

3

4

which transposed gives the following matrix (ranks in parentheses):

1 (3rd)

3 (2nd)

0 (4th)

4 (1st)

which is ordianlly equivalent to player 2's strategy matrix:

5 (3rd)

6 (2nd)

1 (4th)

8 (1st)

General Form



Player 2



L

R

Player 1

U

a,w

b,y

D

c,x

d,z

such that the ranking of a,b,c,d is equivalent to the ranking of w,x,y,z, respectively.

 

Posted Date: 7/21/2012 4:39:29 AM | Location : United States







Related Discussions:- Ordinally symmetric game, Assignment Help, Ask Question on Ordinally symmetric game, Get Answer, Expert's Help, Ordinally symmetric game Discussions

Write discussion on Ordinally symmetric game
Your posts are moderated
Related Questions
About assignment The goal of this assignment is for the student to propose a new game of your own and to be able to present their ideas in clear and convincing manner. This pro

A game is one among complete data if all factors of the sport are common information. Specifically, every player is awake to all different players, the timing of the sport, and als

Consider two quantity-setting firms that produce a homogeneous good. The inverse demand function for the good is p = A - (q 1 +q 2 ). Both firms have a cost function C = q 2 (a


(a) Draw a table representing the Prisoner?s Dilemma game. (b) Give a story inspired by real life for the prisoner?s dilemma game that is di¤erent from the story about the two crim

The interaction among rational, mutually aware players, where the choices of some players impacts the payoffs of others. A game is described by its players, every player's methods,

Equilibrium payoffs a) The reward system changes payoffs for Player A, but does not change the equilibrium strategies in the game. Player A still takes the money at the fir

A strategy is strictly dominant if, no matter what the other players do, the strategy earns a player a strictly higher payoff than the other. Hence, a method is strictly dominant i

Leadership in an Oil Production Game Students can be broken into pairs to play this game once, witheach student's representing one country; then each shouldswitch partners and

1. (a) True or False: If a 2x2 game has a unique pure strategy Nash Equilibrium, then both players always have dominant strategies. (b) Draw a table representing the Prisoner.s Dil