world cup, stock prices). Suppose that there are N possible outcomes of the uncertain event, each of which is indexed by i ∈ { 1 , 2 , ..., N } . The CPCAM is a call auction. For simplicity, only buy orders are accepted. Suppose that the market participants as a whole submit J orders to the market maker. Let the matrix A ∈ R N × J denote the payoff structure of J orders. The ( i, j ) element of A denotes the per-share payoff of the j th order, where j ∈ { 1 , 2 , ..., J } if the i th outcome is realized. Define the vector b ∈ R J such that the j th element of this vector is the limit price associated with the j th order. Define the vector Q ∈ R J such that its j th element is the limit quantity for the j th order. δ ∈ R N denotes the starting order. The starting order is a unique feature of pari-mutuel auctions (Lange and Economide, 2005; Peters et al., 2005). Before regular traders submit their orders, the market organizer seeds the market with the starting order δ . For each i , the organizer purchases δ$_{i}$ dollars’ worth of the Arrow-Debreu security that pays $1 per share if and only if the i th outcome is realized. Arrow-Debreu securities are introduced only for the starting order and thus are not traded in the regular trading session. Let ”the i th Arrow-Debreu security” refer to the one that pays $1 per share if and only if the i th event is realized. At this point, the organizer does not know the number of shares of Arrow-Debreu securities he/she owns because those securities are not yet priced. The prices of Arrow-Debreu securities are determined only when the markets are cleared at the end of the regular trading session. The number of the i th Arrow-Debreu security the organizer holds is determined by dividing δ$_{i}$ by the price of that security. Then, the auctioneer pays the market organizer just like any other trader. The starting orders are included in the model to ensure that the market clearing optimization problem yields a unique set of prices for contingent claims (Lange and Economide, 2005; Peters et al., 2005). Equation (3) is the CPCAM. Let ε ∈ R N denote the vector of state prices: The i th element of ε is the state price for the i th outcome. ε$_{i}$ is the Lagrange multiplier associated with the constraint ∑ J j $_{=1}$A$_{i,j}$ x$_{j}$ + s$_{i}$ = M . The state prices are the building blocks on the basis of which all contingent claims traded on this market are priced. For example, the market-clearing price for the contingent claim with the payoff structure A$_{·}$$_{j}$ is A T · $_{j}$ε . s ∈ R N and M are dummy variables. x ∈ R J is the vector of order fills. For example, the j th element of x is the number of shares of the claim that the submitter of the j th order is allowed to purchase. 7