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I've seen that the reporter fee is dynamic and proportional to the amount of open interest in the system, but the deterministic link between REP price and fees remains unclear.

For example, if open interest is equal to 500 million USD, but REP market cap is 1 billion, the dynamic fees would increase forever until the condition: (Open Interest * Multiplier == REP market cap) is true?

And by how much would the fee increase? Examples with concrete numbers would be appreciated.

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You have the formula basically right, you can get a bit more detail at https://augur.stackexchange.com/a/362/13. You are also correct that the reporting fee would continue to increase until the condition is true. The assumption is that as fees go up, it increases the value of REP in the same way that as dividends for a stock go up, the value of the stock increases.

The fees increase/decrease via the following formula:

new_fee = old_fee * target_market_cap / actual_market_cap

So if the target market cap is 5,000,000 and the actual market cap is 6,000,000 then the fee would adjust to 5/6 of whatever it is right now.

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