Formulations
A smart market formulation may be written as a net pool, in which the decision variables explicitly calculate buys and sells, and the market model clears only those quantities. The net pool market can be mathematically infeasible if participants are unwilling to trade sufficient quantities to allow feasibility. Alternatively, the formulation may be a gross pool, in which the decision variables determine total quantities that each participant receives; the market manager calculates net sales after the model's solution, based on participants' initial holdings. The gross pool market will tend to be mathematically feasible, but could have an unacceptably high cost in the optimal objective value, should (buy) bids be too low compared to (sell) offers. The difference between these two formulations is only technical, as the market designs are economically equivalent by the Coase theorem.
See also mechanism design.
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