# Tagged Questions

31 views

### Game Theory - Setting Up Column Player's Optimal Stategy

Above is my question. Could someone please help me with the first part? I should be ok once I have set up the linear programming problem, but I don't even know what $x_1, x_2 \ \text{and} \ x_3$ are ...
27 views

57 views

### Game Theory in relation to economics and sociology [closed]

I know some algebra and calculus, and have been reading about Linear Programming/Game Theory. How are the models in this field, even the infinite calculus models, usable in macro economics. Even ...
53 views

### Linear Programming with Matrix Game

It seems from an easy google of "learning linear programming" that a common way of learning it is to work with Matrices that represent "games" for two players. Here is one I have stumbled across. We ...
560 views

### Solving a 2*3 game with graphical method in game theory

Solve the following game. $$\begin{pmatrix} 1 & 2& 3 \\ 4 & 2 & 1 \\ \end{pmatrix}$$ Since this is a $2\times3$ matrix I used the graphical method ...
233 views

### Prove the dominant strategy of Game Theory

A row $r$ of the payoff matrix is said to dominate a row $s$ if $a_{rj}\geq a_{sj}$ for all $j$ = 1,2,......,$n$. Similarly, a column $r$ of the payoff matrix is said to dominate a column $s$ if ...
56 views

### Duals of Linear Programs

We are trying to find the dual of the following linear program. $$\max_x \ ax_1 \ + x_2$$ such that: $$v_1x_1 - v_2x_2 \geq b_1 \\ v_1x_1 - v_2x_2 \geq b_2 \\ x_1 \geq 0 \\ x_2 \geq 0$$ ...
157 views

### Duality and the Minimax Theorem

I review LP duality by reading Lecture 7: The LP Duality Theorem. I get the idea how to find the dual LP from primal LP, but my basic knowledge is not enough for finding dual LP for the LP in chapter ...
168 views

### Strictly Dominated and Never Best Response in LP

There is a well known notion of Strategic Dominance in Game Theory. I am interested in elimination of strictly dominated strategies by Linear Programming and in LP for definition of never best ...
66 views

### Finding a dual Linear-Program

We are trying to prove Von-Neumann's MINIMAX Theorem namely $$\max_{x\in\Delta_{n}}\min_{y\in\Delta_{m}}y^{T}Ax=\max_{x\in\Delta_{n}}\min_{1\leqslant i\leqslant n}(Ax)_{i}$$ (Here $\Delta_k$ is the ...
37 views

### Is it necessary to state that $y_i \leq 1$

In a class test for Linear Programming, my professor deducted some marks because I missed the condition $y_i \leq 1$ in the mixed strategy games solution. $y_i$ stands for the probability of any ...
281 views

### Finding the payoff matrix of a game

A two player zero-sum game can be represented by a $m\times n$ payoff matrix $M$ having $m$ rows and $n$ columns with values in $[0,1]$. The value $M(x,y)$ represent the payoff given to player $1$ ...
73 views

### Criterium for Nash-Equilibrium from Nash's Paper

I am reading Nash's original paper "Non-cooperative games" from 1951, which could be found here: Non-Cooperative Games, Nash (1951) Now I have a question to criterion (2) on the second page. There ...
1k views

Consider the following game matrix $$\begin{array}{l|c|c} & \textbf{S} & \textbf{G} \\ \hline \textbf{S} & (-2,-2) & (-6, -1) \\ \hline \textbf{G} & (-1,-6) ... 2answers 482 views ### GameTheory, Solve for optimal strategies by solving a system of linear equations In a book on game theory I saw the following example of a game, a modified version of Roshambo (or Rock-paper-scissors), which is described by the following payoff-matrix:$$ \begin{array}{c|c|c} ...
I have $n$ tasks that I wish to delegate to $m$ independent individuals, where $m$ is a factor or divisor of $n$. Each of the tasks $T_{1} ... T_{n}$ is independent. From the following two extremes, ...