If you really want to keep the rest of the sentence as it is, I would add it parenthetically after intend:
"Since I intend, with this volume, to demonstrate to historians the usefulness of economic or game theory approaches, I ..."
The problem is that the sentence is overloaded.
Since it is obvious that it is the author's intention, the passive would probably be more appropriate:
"Since this volume is intended to demonstrate to historians the usefulness of economic or game theory approaches, I ..."
Another problem is that a clause with "since" may make an important intention of the author appear incidental. Unless you have discussed this intention previously, it might be preferable to use a main clause and express the causality or purpose differently. "This volume . . .; so/therefore/for this reason . . ."
Use of "because" rather than "since" would be another way of making the reason less incidental (but bear in mind that a few readers, having misunderstood some advice, may think that one should not begin a sentence with because).
It depends a bit on the context.