I have a blog that has a good following within my specific industry. I have until now kept it Ad free but now wish to entertain offers.
I currently have three separate offers each with a different budget. I do not wish to leave anything on the table so I want to work with all three. The problem is our industry is small and the three parties are fierce competitors.
As I already have my potential clients I do not wish to introduce a third party such as Google but would rather commission a developer to build me a simple CPM system that provides both myself and the three Advertisers a transparent view of the impressions their Ads are getting.
All three parties agree on the same price per thousand impressions (CPM) however as mentioned they have different budgets. My problem is that the highest bidder who is spending considerable more won't agree on equitable round-robin distribution of Ads. He believe he deserves priority on account of spending more and the fact he approached me first. He is proposing he gets the first 1 million impressions before the next bidder should even gets a chance to spend which I don't think the other two bidders would find acceptable. All are paying the same amount per impression so I can understand the other bidders arguing that their money is just as good as his. What can I do mathematically speaking to ensure I am being fair ?
Well "fair" is not a mathematical term, so no mathematics can guarantee fair.
Since the CPMs are the same, I assume that a higher budget means more ads.
Rather than showing the ads in round robin order, you might give preference to the higher budgets. For example, if the ratio of the budgets is $5:3:2$ you might show each $10$ ads in those proportions.
The actual ratios will probably not be such nice numbers. Since you are showing many ads, you can get the desired distribution by choosing which ad to show randomly each time, with probabilities in proportion to the budgets.