Payment stability under a uniform market-clearing price in two-sided multi-unit auctions

Abstract

The applications of two-sided multiunit auctions include multiple important examples, including day-ahead electricity markets. While several market-clearing methods are applicable for such auctions, the uniform price-based approach is the most widespread in practice. It is possible to analyze the properties of the payoff vector induced by the uniform price clearing in the context of cooperative game theory. In the current work, we show that as long as only convex orders are present in the market, the payoff vector induced by the market-clearing price is in the core. We show furthermore that if nonconvex orders are also present, together with the possibility of paradox rejection, as in the case of several practical applications, it is possible that the induced payoff vector falls outside of the core, or the core may be empty as well.