Abstract: A computer system includes a server computer that handles transactions with user devices to create and manage events, create and manage user accounts and process wagers. Transactions regarding wagers in connection with events can be processed in real-time. The wagers are processed using a payoff function that rewards participation and accurate information, yet does not permit arbitrage or otherwise reward splitting a wager by participating under multiple identities. To compute a payoff, a first score is computed based on the probability estimate by a participant and the outcome. A second score is computed based on an aggregate of wagers of all other participants for each participant, where the first score for the participant is no more than the second score for at least one outcome. The payoff for the participant is then computed as a function of the first score and the second score.

Abstract: A computer system includes a server computer that handles transactions with user devices to create and manage events, create and manage user accounts and process wagers. Transactions regarding wagers in connection with events can be processed in real-time. The wagers are processed using a payoff function that rewards participation and accurate information, yet does not permit arbitrage or otherwise reward splitting a wager by participating under multiple identities. To compute a payoff, a first score is computed based on the probability estimate by a participant and the outcome. A second score is computed based on an aggregate of wagers of all other participants for each participant, where the first score for the participant is no more than the second score for at least one outcome. The payoff for the participant is then computed as a function of the first score and the second score.

Abstract: A computer system implements an automated multi-user, multi-event real-time online prediction market, thus providing a more efficient and accurate mechanism to collect opinion information in digital form. The amount of liquidity in the market can be changed as a function of time to reflect how valuable information is at any given time. A computer that implements a prediction market, which offers securities for a plurality of events, is programmed to allocate a data structure for storing a transaction history, access current time information and define a cost function for the market. In one implementation, the cost function switches from a first function to a second function at a point in time prior to occurrence of an event. In another implementation, the cost function can be time dependent so as to gradually change over time.

Abstract: A computer system includes a server computer that handles transactions with user devices to create and manage events, create and manage user accounts and process wagers. Transactions regarding wagers in connection with events can be processed in real-time. The wagers are processed using a payoff function that rewards participation and accurate information, yet does not permit arbitrage or otherwise reward splitting a wager by participating under multiple identities. To compute a payoff, a first score is computed based on the probability estimate by a participant and the outcome. A second score is computed based on an aggregate of wagers of all other participants for each participant, where the first score for the participant is no more than the second score for at least one outcome. The payoff for the participant is then computed as a function of the first score and the second score.

Abstract: Method and systems for design and operation of a prediction market. A plurality of security bundles and a plurality of payoff vectors may be defined, such that each payoff vector in the plurality of payoff vectors is associated with at least one outcome in a plurality of outcomes. A prediction market engine may be provided for determining a price for each security bundle in the plurality of security bundles by using at least one processor to minimize a convex function over a convex set comprising a convex hull of the plurality of payoff vectors.