# Math Help - What does this vector expression mean

1. ## What does this vector expression mean

Hi,

I have attached image because I do not know how to type math symbols on this site.

Anyway, I am studying game theory and the topic is transereable utility games in coalitional form.

Note that the professor says, that an additive game is determined by a vector a is element of a set of real numbers to the power of N. I am sure the superscript is to denote the size of vector a, am I right?

I want to know what he means by that expression. Does he mean that "a" is a tuple of size N (N is the number of players in the game) where each element comes from the set of real numbers?

I have looked on wikipedia. Wiki explains the other vectors but not this kinda notation of vectors.

2. Originally Posted by hasinque
Anyway, I am studying game theory and the topic is transereable utility games in coalitional form.
Whats that?

Originally Posted by hasinque
Note that the professor says, that an additive game is determined by a vector a is element of a set of real numbers to the power of N. I am sure the superscript is to denote the size of vector a, am I right?

I want to know what he means by that expression. Does he mean that "a" is a tuple of size N (N is the number of players in the game) where each element comes from the set of real numbers?
Yes,you are right about the notation, though I dont know anything about the subject you are talking about

P.S: Was it like this : $a \in \mathbb{R}^n$ ?

3. Yes Matt, it is the same, just look at the picture I posted. Exactly the same notation. so what does it mean PRECISELY?

Transefereable utility game in coalitional form: transefereable utility means that the pay offs are the same for every person/agent and that anyone can transfer it to anyone he wants.

In coalitional form means that groups of people/agents can achieve higher pay-offs (in terms of money and anything u can imagine) by co-operation.

4. Originally Posted by hasinque
Yes Matt, it is the same, just look at the picture I posted. Exactly the same notation. so what does it mean PRECISELY?
Exactly like you said. It means 'a' is an n-tuple, with each co-ordinate being real. What else do you want to know about it?

5. Thanks!

Hmm, now something that I want to know out of my own interest. Suppose we have vector

$a = (1, 2, 3, 10, 55, 77, 100)$

Is this the 7-dimensional vector?

Is it true that the graph of this vector is impossible to draw because we cannot visualize 7 dimensions?

6. Originally Posted by hasinque
Thanks!

Hmm, now something that I want to know out of my own interest. Suppose we have vector

$a = (1, 2, 3, 10, 55, 77, 100)$

Is this the 7-dimensional vector?

Is it true that the graph of this vector is impossible to draw because we cannot visualize 7 dimensions?
Yes