0
votes
0answers
22 views

Finding matrices values

I was trying to teach myself some things about saddle points. This is a little more advance when it comes to finding the number for each matrices and a value $v$ $($say $v=(1/3), (1/3), (1/3))$ ...
4
votes
0answers
95 views

Saddle Points on Matrices

Let $n$, $m$ be positive integers. Suppose that $A$ is a $2$ x $n$ or an $m$ x $2$ matrix and that it has a saddle point. Show that among the saddle points of $A$ there exists at least one which ...
1
vote
0answers
34 views

Two person zero sum problem, help/guidance needed..

I'm a computer science student and I have this problem I need to solve for my games theory course. I don't have an example to follow, or use as guidance, and my colleagues are not very helpful( as in, ...
1
vote
0answers
20 views

Matrix multiplication in game theory doesn't add up? Min y^T*Ax

I'm studying game theory and something seems weird to me. My book says y is the probability of the row player and x is the probability of column player, both x and y are vectors. A = [a$_i$$_j$] is ...
0
votes
2answers
55 views

Solution to $n$ by $n$ game of lights out

How can I solve an $n$ by $n$ game of Lights Out?
1
vote
2answers
56 views

Maze Connectivity

Given a grid maze which is an n × m rectangle maze where each cell is either empty, or is a wall. One can go from one cell to another only if both cells are empty and have a common side. Initially we ...
1
vote
2answers
126 views

Problem regarding filling squares inside a $n\times n$ grid.

Assuming a $n\times n$ square grid, what is the most number of squares that can be filled in such that there are no completed rows, columns, or diagonals? Is there a formula to calculate this? ...
9
votes
2answers
512 views

Determine the winner of a tic tac toe board with a single matrix expression?

Assume a tic-tac-toe board's state is stored in a matrix. $$ S=\begin{bmatrix} -1 & 0 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1 \\ \end{bmatrix} $$ Here, $X$ is mapped to $1$, $O$ is ...
7
votes
1answer
355 views

Determinant game - winning strategy

I came across this problem while looking at Putnam problems a while ago: "Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008 x 2008 array. Alan plays ...
1
vote
2answers
362 views

Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
0
votes
1answer
76 views

How do we prove that e = RPC, in game theory?

Here e is the expected value of the game for the row player, P is the payoff matrix from the perspective of the row player, R is the row matrix containing the probabilities for each of the row ...
5
votes
2answers
132 views

Question regarding technicalities in the paper Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent

For people on this board I have a probably pretty modest question, but since I'm not a mathematician (just an economist), I'm having trouble. The full pdf can be found here: ...
1
vote
1answer
112 views

Reducing an infinitely large matrix to a finite matrix using domination

I'd very much appreciate it if anyone with any familiarity of game theory could help out a newbie. I came across the following problem doing homework in an introductory game theory course: ...