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If you are interested in the applications of game theory in economics then I would recommend Ken Binmore's book "Playing for Real." By the way: every modern textbook on game theory that you pick up will be mathematical. Only the most elementary books for popular audiences are non-mathematical.

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Get a book and start working through it. I recommend On Numbers And Games by John Conway. Like Thomas said, you don't need too much math background to understand game theory, and if you miss something you can look it up while working through a book.

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1) To show there is a Nash equilibrium, we show that no player can unilaterally deviate and improve his situation. When $n_{1} = n_{2} = 25$ and $n_{3} = 50$, the edges $(a, b), (c, d)$ have weight $1.75$. So suppose an ABD player chooses ACD instead. Then that player is adding $1$ to the edge $(c, d)$, increasing his cost of using that route. By symmetry, ...

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By your logic the total differential equation should start with $3 \ddot{V}_0$. But I think you misinterpreted the Superposition Theorem. It states that if you have $y_i$ output for $u_i$ input, then you will have $\sum_i y_i$ output for $\sum_i u_i$ input, for a given system, i.e. for a single differential equation. What you have is 3 independent ...

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Any situation in which you have a collection of tasks, some of which need to be completed prior to others (e.g. must take French I before taking French II) can be modeled as a directed acyclic graph (the graph should be acyclic because it doesn't make sense to have mutual dependencies). You can then use topological sorting to determine an appropriate order ...

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Let's write $n$ instead of $4$ for the number of locations. Given you specification, the only thing you need (or can!) to decide on is the coefficients on the linear correspondence: $$M_{ij} = A - KD_{ij} \qquad\text{for }i\ne j$$ Once $A$ and $K$ are known, you can compute all of the off-diagonal elements of $M$, and then find the diagonal by  M_{ii} = ...

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