Abstract
We consider an auction design problem under network flow constraints. We focus on pricing mechanisms that provide fair solutions, where fairness is defined in absolute and relative terms. The absolute fairness is equivalent to “no individual losses” assumption. The relative fairness can be verbalized as follows: no agent can be treated worse than any other in similar circumstances. Ensuring the fairness conditions makes only part of the social welfare available in the auction to be distributed on pure market rules. The rest of welfare must be distributed without market rules and constitutes the so-calledprice of fairness. We prove that there exists the minimum ofprice of fairnessand that it is achieved when uniform unconstrained market price is used as the base price. Theprice of fairnesstakes into account costs of forced offers and compensations for lost profits. The final payments can be different than locational marginal pricing. That means that the widely applied locational marginal pricing mechanism does not in general minimize theprice of fairness.
Highlights
Classical auction mechanisms are based on the supply/demand curves intersection which sets accepted and rejected offers and determines the uniform market price
In this paper we introduce the price of fairness (PoF) for networked auctions
Our main theorem proves that the minimal PoF can be achieved if the unconstrained market price is used for settlements and some additional nodal components are paid at each node
Summary
Classical auction (through the whole paper by “auction” we mean closed double sealed exchange-like mechanism; in other words an “auction” is a set of trading rules for an exchange) mechanisms are based on the supply/demand curves intersection which sets accepted and rejected offers and determines the uniform market price. One of the main shortcomings is only partial distribution of social welfare between market participants This means that there is some price that is paid to restore the fairness conditions. In this paper we introduce the price of fairness (PoF) for networked auctions. Our main theorem proves that the minimal PoF can be achieved if the unconstrained market price is used for settlements and some additional nodal components are paid at each node. This means that widely used locational marginal pricing approach does not minimize the PoF.
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