Free Ans.1 Essay Sample

The most interesting game according to my perspective is the most famous and most analyzed game the “Prisoner’s Dilemma” an 2×2 game in strategic form that appears to be very common in the real world and which has nasty outcome. It is one of only seven with a unique and inferior Nash equilibrium and the only symmetric member of the family. the most impressive of all the features of this game is that when the Prisoner’s Dilemma flaps its up further we get the Battle of Sexes and when it flaps with wings towards the origin we get Stag Hunt and the Coordination games. That means it is the most unique game which include all other seven games in it.
Q2) choose any of the 7 non-boring symmetric games and create a payoff matrix for it with values that differ from the standard 1,2,3,4 used in chapter of the most recent version of the text.?

Ans) Out of seven non-boring symmetric games lets consider the version of ‘chicken ‘ pictures in figure below:-

A payoff matrix for Chicken
Like all forms of the game, there are three strategies Nash equillibria. The two pure strategy Nash equillibria are (D, C) and (C,D). There is also mixed strategy equilibrium where each player dares with probability 1/3. It results in expected payoff of 14/3= 4.667 of each player. In this payoff matrix it is shown that the player A and player B tries to do dare for chicken so the possible outcome will be nobody is daring that shown by values (0,0) and when player A dares for chicken then the values are (7,2) and now if take the column then the player B dares for chicken then values are opposite of player A there is (2,7). Then the possible outcome for all the values will be at (6,6).

Qns2) Sketch your values in payoff space?

Ans)
(2,6) (7,6)
(2,0)
(0,7)
This is the sketch of the “chicken game” making a quadrilateral diagram , game 411. Showing the points (2,0);(2,6);(7,6) and (0,7), by joining the lines a structure is from shaping a quadrilateral.

Qns4) By swapping values in your payoff matrix or sketch, convert the game to one of its neighbours.?

Ans)
(2,6) (7,6)
(2,7)
(0,2)
The above given sketch of the chicken game can converted into its neighbor that is Prisoner’s Dilemma by changing the dimensions of (0,7) to (2,7). Therefore to keep the game symmetrical we have to dgrag the tip of the upper left wing right into the top-center cell. These are produced by swapping 0 for the 2 in the payoff matrix for both players. The result of this “symmetric game called “Prisoner’s Dilemma , game 311.

Ans. 5

story to fit the payoffs developed above
On the basis of above payoff, now I will make up story to fit payoff I have developed in question 2nd. I will Prisoner’s Dilemma here as it has been used as an interpretive framework to explain the real world situations.
Here in the case of Prisoner’s Dilemma game I modeled the use of performance enhancing drugs in professional sports tournament. In the game Players are athletes and the possible strategies used are using performance enhancing drug or not. If one athlete use drug and his opponent does not, first one will definitely get advantage in the sports tournament, but that athlete will suffer from long term harm and possibility of get caught.
If the athletes are playing sport where it is difficult to detect the use of drug then the downside is viewed as smaller factor than the competitions benefit, and this situation is captured in numerical payoffs as given below:

Athlete 2

Athlete1
The best outcome we can say here us with payoff of 2 as it is to use drug when the opponent does not use it, because there your chances of winning is more. However payoff to both the athletes using drug (which is 6) is worse than the payoff where both are not using drug (which is 0). Though in both the cases you are equally matched with your opponent but in the former case you are also causing harm to yourself. Where using drugs is a strictly dominant strategy and various situation happens where we saw that payers are using drugs even though they know the drawback of using it.

Ans. 6

Here we have to create an example of ordinally symmetric payoff which is not symmetric in terms of the actual payoff. If ordinal ranking of one player’s payoff is similar to the ordinal ranking of the transpose of opponent player’s payoff then it is said to be ordinally symmetric game.
If one player’s payoff can be expressed as a transpose of the other player’s payoffs then that is a symmetric game and ordinally symmetric we want other player’s matrix have to be ordinally equivalent.

Example:

1st Player
X Y
X

2nd Player

Y

Here first player’s strategies are the matrix

After transpose the matrix will be look like (ranks in parentheses)
Which is ordinally equivalent to 2nd players strategy matrix
Ans. 7
Y
*(1,8)
*(5,6)
*(3,4)
X
(1,0)
The most famous and most analyzed game in the world is the prisoner’s dilemma- an 2 X 2 game in strategic form that appears to be very common in the ”real” world, and which has a nasty outcome.
And hence by taking previous answers reference the sketch for this dilemma is drawn