Blueberry comments on Unknown knowns: Why did you choose to be monogamous? - Less Wrong
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To be more accurate, you can set whatever price you want, and the other person needs to choose between paying the price and ending the monopoly (by violating the monogamy agreement or ending the relationship). But in the real world people are often very reluctant to end long-standing relationships quickly.
I probably should have said that you can probably get a higher price than you could get in the absence of a monopoly.
People shouldn't be missing the point that many people like to have a monopoly and its part of the reason many enter monogamus relationships.