The standard way of matching orders in the Opium Network is through off-chain relayers.
A relayer collects orders, matches them in the best possible way and broadcasts them to Opium for execution. Users sign their order with their private key, which allows the Opium Network to withdraw funds from their balance that are needed to execute the order.
A relayer, most likely, demands a relay-fee from the traders for his services and if he sees fit, will also act as an arbitrageur or affiliate. For example, if several complex orders cannot be filled directly, he can make separate deals and earn an arbitrage profit.
An affiliate looks for the best prices in the market at other relayers and redirects users' orders to the relayer that offers the best price. An affiliate does not broadcast orders to the blockchain himself. For his services, an affiliate will most likely demand an affiliate fee. If he sees fit, he can also act as an arbitrageur and make a profit.