I can answer some of these questions, but I won’t go into specifics about the percentages since I can only really give you insight into one company with any confidence.
On the SSP side the revenue model is based on a percentage of revenue flowing to the publisher. This works well as it lines up the SSP’s incentives with the publisher. The more money the publisher makes – the more money the SSP makes. SSP’s are generally geared toward serving the publishers so that alignment makes for a good relationship.
On the DSP side I know of two prevalent revenue models. The most prevalent has profits tied to a percentage of spend. This is taking money the same way the SSPs do, so it requires the advertisers that use the DSP to trust that all the algorithms and technology is: A – getting them a good price, and B – fulfilling the requirements of the campaign in the most optimal way. The major DSPs seem to have a good handle on these two elements and appear to be doing fine, even though the financial model doesn’t inherently lend itself to support “A”.
The second DSP profit model is more of a fee based scenario where there’s a flat CPM for services. This has the advantage of eliminating any buyer’s agent conflict where fees are calculated as a percentage of spend, but it limits the upside for the DSP and might reduce their incentive to go after high-profile customers who are willing to pay high prices for quality inventory. There are probably internal sales scenarios to combat that tendency at any DSP employing this pricing model.
You could consider an arbitrage model as something that is out there as a third DSP model as well. There may be buyers using DSP style technology that bid up to a predefined CPM for their buyers and then take the difference between the bid and the charge price as a profit. Whether or not this provider can be considered a true DSP can be debated, but I’ll leave the “defining” job to the IAB.
In terms of differentiating between desktop display and mobile – I don’t know of any different or unique profit models being employed other than what I’ve laid out