Joint-outcome prediction markets for climate risks

If an order changes the market maker’s exposure from qi to qi+wi (for i = 1,� � �,m) the mar- ket maker quotes an asking price given by C q þ w ð Þ C q ð Þ ¼ b log X m i¼1 eðqi þwiÞ=b ! b log X m i¼1 eqi =b ! An elegant feature of the LMSR marker maker is that the reward participants receive is lin- ear in the logarithmic scoring rule [22]. This is a strictly proper scoring rule that, if the partici- pants’ utilities are linear in the number of credits they accumulate, will incentivize participants to reveal their true beliefs about the probabilities of each outcome [26]. That is, the LMSR is “incentive compatible”. To illustrate the relationship between the market maker and the logarithmic scoring rule, consider the situation where a single participant believes the probability of outcome i occur- ring is fi (i = 1,� � �,m). They will buy outcomes until the prices set by the market maker equal Fig 1. Prices in the market for U.K. average daily high temperature and total monthly rainfall for July 2018 on 15th May 2018. The grid shows the partitioning of the joint-outcome space into 5,207 separate outcomes, each covering a 0.2˚C interval in temperature and 5mm in rainfall. The extreme intervals for temperature and the maximum interval for rainfall are open intervals. The black dots show values of temperature and rainfall for each July since 1908. https://doi.org/10.1371/journal.pone.0309164.g001 PLOS ONE Joint-outcome prediction markets for climate risks PLOS ONE | https://doi.org/10.1371/journal.pone.0309164 August 30, 2024 6 / 14