Suppose I am willing to buy a contract which I believe has a 15% chance to settle to $100 and 0 otherwise. The EV of this contract is therefore 15. How much should I buy this for?
I would answer at most 15 (in order to ensure I make money on this contract). But going beyond this, how can the price on (0, 15) be determined? Is it arbitrary? Should the price be altered until other people are willing to make a trade with me? How can we make a better answer to this than "at most 15"? Suppose that we are trading against other people who do not necessarily agree on how much this contract may be worth.
To make this more concrete, we were playing a trading game which was a toy model of a real trading scenario. I believed the scenario above, and I did not know which price on (0, 15) to quote, so I just quoted a pretty much arbitrary price until someone was willing to trade. How can I do better?