Joint-outcome prediction markets for climate risks

order may correspond to a fraction of that order, x<xmax, so x had to be determined for each order. The price of the contract after x contracts are filled is P x ð Þ ¼ Pm i¼1 wieðqiþxwiÞ=b Pm i¼1 eðqi þxwiÞ=b If x contracts are filled, then the premium is LðxÞ ¼ PRICE OFFERED MARKET MAKER QUOTE L x ð Þ ¼ xR b log X m i¼1 eð qiþxwiÞ=b ! b log X m i¼1 eqi =b ! ( ) The maximum obtainable premium was determined by solving dL dx ¼ R P x ð Þ ¼ 0 which shows that the order that maximizes the premium is the one that raises the price of the contract to the bid price. When P(0)�R then the premium was negative. Such orders were not filled. When P(xmax)�R then the maximum premium corresponded to the full order of xmax. When P(0)<R<P(xmax) then the maximum premium was for a partial fulfillment of the order, 0<x<xmax. The value of x was determined with a line search. Once all submitted orders had been ranked by the maximum obtainable premium, the one with the highest premium (if it was non-negative) was filled. Premiums were then recalculated and the remaining orders reranked. This process was repeated until there were no more unfilled orders with a non-negative premium. Teams were recruited from British universities. There were 28 teams, drawn from depart- ments with expertise in meteorology and climate science, as well as statistics, machine learning and economics. The invited teams were each endowed with 1000 credits with which to trade. The ten teams with the most credits after the September market had been settled received

awards of £10,000 for first place, £9,000 for second, £8,000 for third, and so on down to £1,000 for tenth place. It should be acknowledged that, under these pay offs, the utility of participants is not linear in the number of credits they accumulate, undermining the properness of the scoring rule [27]. The gradual decline in rewards with placing was to mitigate the potential dis- tortion introduced by the tournament element. Results All six markets were opened on 12th March 2018 with auctions to set the initial prices. 23 orders from five teams were filled during the auction clearing process. Most teams did not trade until the markets opened for real-time trading a week later. Between then and 30th Sep- tember 23,284 orders were filled across the six markets. Fig 1 shows the prices in the joint-out- come space for the July market on 15th May. The joint distribution captures the negative relationship between temperature and rainfall—hot summers tend to be dry—that is seen in the distribution of historic Julys. Early summer 2018 turned out to be very warm, with the warmest May on record and the second warmest June and July. Fig 2 shows the daily number of trades and the daily trade volume (in credits) for each of the markets. Most trading in a market occurred during the month that the market was PLOS ONE Joint-outcome prediction markets for climate risks PLOS ONE | https://doi.org/10.1371/journal.pone.0309164 August 30, 2024 8 / 14