Optimal Strategies for Rowboy: Game Theory Question | Find Value & Fairness

In summary, the game with payoff matrix [4,2,0,-1,5,-2], [-2,-3,2,5,0,4], [5,-3,4,0,4,7], [1,3,3,2,-6,5] has an optimal column strategy of [1/2, 0, 0, 1/2, 0, 0] for Columngirl. To find the optimal strategies for Rowboy, only the first and fourth columns need to be considered. The optimal row strategy is [1/2, 1/2, 0, 0] and the value of the game is L(x, y) = w =
  • #1
dglee
21
0
In the game with payoff Matrix

[4,2,0,-1,5,-2]
[-2,-3,2,5,0,4]
[5,-3,4,0,4,7]
[1,3,3,2,-6,5]

Columngirl's strategy of [1/2,0,0,1/2,0,0] is optimal. Describe all the optimal strategies for Rowboy. Find the value of the game and show that this game is not fair.

Thing is i can't find any optimal value for Rowboy

here is his strategie Rowboy's strategy

Min{W}
-4y1+2y2-5y3-y4+w>=0
-2y1+3y2+3y3-3y4+w>=0
-5y2-2y4+w>=0
-5y1-4y3+6y4+w>=0
2y1-4y2-7y3-5y4+w>=0
y1+y2+y3+y4=1
y1,y2,y3,y4>=0

L(x,y)=w=5/2
 
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  • #2
You are given that the optimal column strategy is [1/2, 0, 0, 1/2, 0, 0]. Any optimal row strategy must be optimal against that so you really only need to consider the first and fourth columns. (I get, as optimal row strategy, [1/2, 1/2, 0, 0].
 
  • #3
I tried that but then i can't show that L(x,y)=w=5/2 which makes the game unfair. If i use Rowboy's strategie as [1/2,1/2,0,0] i get the game is at w=3/2 which doesn't equal to 5/2. I know that is a feasiable strategy but its not optimal.
 

Related to Optimal Strategies for Rowboy: Game Theory Question | Find Value & Fairness

1. What is game theory and how is it relevant to the Rowboy game?

Game theory is a branch of mathematics and economics that studies decision-making strategies in situations where the outcome is influenced by the decisions of multiple individuals. In the context of the Rowboy game, game theory can be used to determine the optimal strategies for players in order to achieve the best possible outcome.

2. What is the objective of the Rowboy game?

The objective of the Rowboy game is to find the value and fairness of the game, which can be achieved by using game theory to determine the optimal strategies for players.

3. How does game theory determine the optimal strategies for the Rowboy game?

Game theory uses mathematical models, such as the Prisoner's Dilemma, to analyze the different strategies that players can use and determine which one will result in the best outcome for all players. It takes into account factors such as the potential gains and losses for each player and their possible actions.

4. What is the importance of finding the value and fairness of the Rowboy game?

Finding the value and fairness of the Rowboy game can help players make informed decisions and avoid being taken advantage of by other players. It also promotes a sense of fairness and cooperation among players, leading to a more enjoyable and balanced gameplay experience.

5. Can game theory be applied to other real-life situations?

Yes, game theory has applications in various fields such as economics, political science, and biology. It can be used to analyze and predict decision-making in situations involving multiple individuals, such as negotiations, conflicts, and resource allocation.

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