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Represent an economic transaction with {M, X, V}, where M is currency, X is some good or service, and V is violence.

For a music cd, there's three parties involved, though the third is sometimes not explicitly accounted for.

1:{-M, +X, 0}

2:{+(1-p)M, -X, 0}

3:{+pM, 0, V}

(aside: money, you see, plays a nice role of making it a 3-tuple instead of an infinite-tuple)

The first two elements of a tuple have the constraint that they must sum to nullity across all the other parties involved. You can't make labor or goods appear out of thin air.

Violence, however, doesn't have that constraint. You can always throw in more violence, and it's always a positive amount.

(Why doesn't 3 just set p = 1? It certainly could, but that isn't the optimal proportion to maximize sum(M). The incentive structure breaks down: Laffer bites with a vengeance. So there's some other optimal p 0<p<1 that maximizes sum(M) over all clients--what that value is is simply an empirical question.)

So let's look at a market of violence, with multiple suppliers:

1:{-(q+r)M', 0, 0}

2:{+qM', 0, V'}

3:{+rM', 0, V''}

where q + r = p' and M' is the total value that 1 provides at p' where p' maximizes M'.

This satisfies the required constraints, but it's not a stable equilibrium. q+r is that same optimal value p from before, but with a twist: it's not set by only one agent trying to maximize sum(M) but by two trying to maximize their own. There's no reason for 2 not to go for (q+e) instead of q, and the same is true of 3. Taking only q and r as varying qualities, and you rapidly end up at q + r = 1, which means no one gets anything.

In practice, what happens is that 2 and 3 have their own separate transaction since they can foresee that upcoming equilibrium:

2:{0, 0, V'}

3:{0, 0, V''}

That itself is unstable: assuming that V' > V'', the new equilibrium is

2:{0, 0, V'}

Leading to

1:{-p'M', 0, 0}

2:{+p'M', 0, V'}

I lose you at the part where you essentially claim that violence is free or unlimited. In reality, violence is very costly and risky. In this sort of analysis, I don't see why violence would be considered a separate variable, rather than simply one cost factor for both sides of the transaction, just like the cost of advertising, or paying employees.

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