Application of Sequences in Economics

Question

I have an example of sequences in one-dimension space (e.g. An investment opportunity promises you a payment of £1000 at the end of each of the next 10 years, If the interest rate is 5%, what would be the present value?

P=1000/1,04+1000/1,04^2+...+1000/1,04^10)

What would be a good example of sequences in economics in a two-dimensional space?

Thanks

Answer 1

Any strategy profile on a non-cooperative 2 person-game.

Take for example a static 2-person game, where $I$ as the set of players in a game (where $|I|=2$), and for simplicity let's assume that we are dealing only with pure strategies, such that $A_i$ denotes the respective set (and $a_i$ the generic element), and $u_i$ is the Von Neumann-Morgenstern utility function.

Therefore, a strategy profile $a=(a_i,a_j)$ is a tuple of 2 element (the respective strategies chosen by $i$ and $j$), such that $a \in A:= \times_{i \in I} A_i$.