in such a way that the transaction leaves the market maker’s expected utility over the future mon- etary payoff unaffected. Agrawal et al. (2011) suggests an improvement of Chen and Pennock’s (2007) market. The market maker may find it difficult to propose a unique probability distribu- tion to describe the event for which the claims are written. The KPM addresses Agrawal et al. (2011)’s suggestion: It allows the market maker to indicate a set of multiple reasonable probability distributions instead of a single distribution. The KPM acknowledges that the market maker often cannot pin down a single subjective probability distribution. Our paper is related to the recent literature that explains a wide variety of prediction markets from a unified theoretical perspective. The most notable work in this respect is Agrawal et al. (2011). They show that the four most well-known prediction markets in the literature can be unified under one theoretical framework. In a similar vein, we reconcile pari-mutuel mechanisms from the prediction market literature with the model from the economics literature. My paper is related to a growing body of literature that focuses on the role of Knightian uncertainty in decision making. In the past decade, Knightian uncertainty has received a significant amount of attention in areas ranging from macroeconomic modeling (Hansen and Sargent, 2008) to market microstructure theory (Easley and O’Hara, 2009; Easley and O’Hara, 2010). We present a brief overview of the theory of decision making under ambiguity. First, it is necessary to distinguish between risk and ambiguity. Risk applies to situations in which it is possible to attach a probability distribution to an unknown prospect. By contrast, ambiguity refers to situations in which it is impossible to do so. For example, consider a situation in which a person receives a dollar if and only if he/she draws a red ball from a box. The box contains both red balls and blue balls. If the person knows the fraction of balls that are red, he/she knows the probability of receiving a dollar. In this case, the person is said to be facing risk. On the other hand, suppose that the person does not know the fraction of balls in the box that are red. Then, the person cannot assign a number to the probability of winning a dollar. This person is said to be facing ambiguity. In the 1920s, Knight was the first to note the difference between these two concepts (Knight, 1936). An ambiguous prospect requires a different analysis from that of a risky prospect. To this end, Theorem 1 reproduces the main finding of Gilboa and Schmeidler (1989) in the language of Ghirardato et al. (2004). Let S denote the set of all possible states (e.g., the person chooses a red 4 2 The Theory of Decision Making under Ambiguity