Title: Robust Strategic Bidding in Auction-Based Markets. [link]

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Abstract: We propose an alternative methodology to devise profit-maximizing strategic bids under uncertainty in markets endowed with a sealed-bid uniform-price auction with multiple divisible products. The optimal strategic bid of a price maker agent largely depends on the knowledge (information) of the rivals' bidding strategy. By recognizing that the bid of rival competitors may deviate from the equilibrium and are of difficult probabilistic characterization, we proposed a two-stage robust optimization model with equilibrium constraints to devise a risk-averse strategic bid in the auction. The proposed model is a trilevel optimization problem that can be recast as a particular instance of a bilevel program with equilibrium constraints. Reformulation procedures are proposed to construct a single-level-equivalent formulation suitable for column and constraint generation (CCG) algorithm. Differently from previously reported works on two-stage robust optimization, our solution methodology does not employ the CCG algorithm to iteratively identify violated scenarios for the uncertain factors, which in this thesis are obtained through continuous variables. In the proposed solution methodology, the CCG is applied to identify a small subset of optimality conditions for the third-level model capable of representing the auction equilibrium constraints at the optimum solution of the master (bidding) problem. A numerical case study based on short-term electricity markets is presented to illustrate the applicability of the proposed robust model. Results show that even for the case where an impression of 1% on the rivals' offer at the Nash equilibrium is observed, the robust solution provides a non-negligible risk reduction in out-of-sample analysis.

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Keywords: Sealed-Bid Uniform-Price Auction; Strategic Bidding; Price-Maker Agents; MPEC; Robust Optimization; Column-and-Constraint Generation; Mixed-Integer Linear Programming; Disjunctive Constraints; Day-Ahead Electricity Markets.

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