When modeling the incentives to change probabilities of events, it probably makes sense to model the payoff of changing probabilities of events and the cost of changing probabilities of events separately. You’d expect someone to alter the probabilities if they gain more in expectation from the bets than the cost to them of altering the probabilities. If someone bets on an event and changes the probability that it occurs from p to q, then their expected payoff is qp−1 times their investment, so if, in a prediction market in which there are n possible outcomes, the expected payoff you can get from changing the probability distribution from (p1,...,pn) to (q1,...,qn) is proportional to maxi(qipi)−1.
Modeling the cost of changing a probability distribution seems harder to model, but the Fisher information metric might be a good crude estimate of how difficult you should expect it to be to change the probability distribution over outcomes from one distribution to another.
When modeling the incentives to change probabilities of events, it probably makes sense to model the payoff of changing probabilities of events and the cost of changing probabilities of events separately. You’d expect someone to alter the probabilities if they gain more in expectation from the bets than the cost to them of altering the probabilities. If someone bets on an event and changes the probability that it occurs from p to q, then their expected payoff is qp−1 times their investment, so if, in a prediction market in which there are n possible outcomes, the expected payoff you can get from changing the probability distribution from (p1,...,pn) to (q1,...,qn) is proportional to maxi(qipi)−1.
Modeling the cost of changing a probability distribution seems harder to model, but the Fisher information metric might be a good crude estimate of how difficult you should expect it to be to change the probability distribution over outcomes from one distribution to another.