1 Introduction In this paper, we design a new platform for trading contingent claims, the Knightian Pari-mutuel Mechanism. The term ”pari-mutuel” originates from the automated horse race betting system invented in the 19th century. The pari-mutuel betting system automatically calculates payoff odds for each horse based on the amount of money bet on each horse. It also completely shields the market organizer from financial loss. To illustrate, suppose that people wager their money on the outcome of a race between two horses: A and B. People wager a total of $50 on Horse A and $100 on Horse B. The total premium of $150 is paid to those who correctly predicted the outcome. Thus, if Horse A wins, those who wagered money on Horse A receive $3 for each dollar they wagered. If Horse B wins, the winners make $1.5 for each dollar they wagered. Because the payment to the winners is financed exclusively by the fees collected from both winners and losers, the market maker does not need to worry about his/her loss. This is called the self-financing property of the market. The rate of return from wagering on a particular horse conveys information on the collective perception of that horse’s chances of winning. Consider the example above. Wagering on Horse B yields a lower rate of return than wagering on Horse A because people wagered more money on Horse B than on Horse A. The more money people wager on a particular horse the lower the rate of return becomes. People bet money on a horse if they believe that horse is likely to win the race. Thus, the rate of return from wagering money on a horse is low if many people believe that the horse will win the race. The pari-mutuel system maps the popularity of horses to the rates of return from wagering money on those horses. This simple pari-mutuel system subsequently evolved into more sophisticated prediction mar- kets. For example, more recently developed markets (Peters et al., 2005; Peters et al., 2007) trade securities with fixed final payoffs. The prices of those securities fluctuate in a way that reflects their popularity in the market. Despite considerable heterogeneity across various prediction markets, they typically exhibit three defining characteristics. First, the popularity of a particular security is mapped to a higher price of that security through an automated market-clearing algorithm. Second, the market maker’s maximum possible loss at maturity is bounded. Irrespective of the outcome at the time when contingent claims mature, the market maker is not expected to lose more than a certain pre- specified amount. In this paper, when we say that the market is completely pari-mutuel, we mean 1