Optimal pricing for Crypto-Currency Exchanges
You are missing the key element, transfer fees.  If the transfer fees are large enough, then the marginal cost to move between exchanges just needs to stay inside the gross bid-ask spread.  It can probably move outside that spread because there is an additional risk for one who moves between exchanges.  Not all exchanges move back and forth between real world bank accounts equally well, nor do all have equal trading depth.  Additionally, the time value of money between the exchanges is probably sufficient to eat up any arbitrage.  It may be worth giving up arbitrage profits if they are traded for the time value of money profits.  If the arbitrage is small and the cost is great, you can carry a wider bid-ask spread and get away with it as a market maker.

It sounds like you need decision theory and not game theory unless you are considering the behaviors of the other actors as part of the game.  You should start with de Finetti's Coherence Principle.  It is a weaker principle than the "no arbitrage" principle.  In its weakest form, it only states that odds are coherent if a bookie cannot take a sure loss in all states of nature through the clever combination of bets either by a single or by multiple actors.

What makes it weaker is that it never says that no arbitrage opportunity exists, but it would imply that if it did exist, then the market makers would capture all or nearly all the profits.  I would be surprised to find that the exchanges did not profit greatly from the arbitrage opportunities on each other's exchanges.  They are perfectly placed and have deep inventory that they could borrow from their customers.  They probably allow some to go by to get speculators into their markets.  They are profit maximizers.