Bid pooling in reverse multi-unit Dutch auctions: an experimental investigation

Abstract

In this article we experimentally investigate reverse multi-unit Dutch auctions in which bidders compete to sell their single unit to a buyer who wants to purchase several objects. Our study yields three insights: (i) bids are substantially higher than Nash equilibrium bids predicted by standard economic theory; (ii) these higher-than-predicted prices gradually decline in later periods; and (iii) bid pooling (or simultaneous bidding) is frequently observed-the majority of bidders submit their bids immediately after the first bidder has sold his unit. A model that distinguishes between myopic and sophisticated bidding strategies helps to organize these patterns both on the aggregate and on the individual level.

Optimization-based modelling and game-theoretic framework for techno-economic analysis of demand-side flexibility: a real case study

“…4 (c), the results are identical to the PAB mechanism: both mechanisms are price discriminatory and, under the assumption that all agents follow the same strategy, the result is the same. However, some experimental studies, for example, by Gillen et al [36] showed that due to the specific clearing procedure, the DRA market participants tend to follow the underbidding (UB) strategy, which in this case provides market equilibrium prices which deviate from the true market equilibrium by 1 £/MW/h for the three and six agents scenarios. The results for the Vickery-Clarke-Groves (VCG) auction, presented in Fig.…”

“…In the objective function (34), the first term constitutes the costs for accepted flexible capacity P A with offer price π O = {π O a ∈ R |G| ≥0 }, while the second term limits the acceptance of offers, excluding those whose price exceeds ceiling price π. The first constraint (35) limits accepted capacity P A to the offered capacity P O , while the second constraint (36) establishes that the demand capacity is equal to the accepted capacity plus the unmet demand.…”

“…For the discriminatory price markets, i.e., PAB and DRA, the output includes only accepted capacity P A a , which is rewarded by the offer price π O a , known privately to each agent. In case of the uniform price market, i.e., PAC, the price is uniform for all accepted offers, and in addition to the accepted capacity P A a the agents are informed of the Market Clearing Price (MCP), which is found as a dual variable λ of constraint (36).…”

“…In this section, only the equilibrium prices that correspond to the dominant strategies, i.e., upper bound of the results illustrated in Fig. 4, have been considered, with the additional study for DRA in which the agents tend to follow the UB strategy, as suggested by [36]. In both discriminatory pricing mechanisms (PAB and DRA) the OP and UB strategies led to the offer prices of the infra-marginal offers approaching market equilibrium price; hence, consideration of market equilibrium prices for the cost-benefit analysis is reasonable for both discriminatory and uniform pricing mechanism.…”

“…The highest average price (12.4 £/MW/h) and the highest price variability are expected for PAB and DRA mechanisms, assuming that the flexibility providers follow the overpricing strategy. If the underbidding strategy is chosen for DRA (as was shown in [36]), the expected average price decreases to 9.3 £/MW/h. The lowest price variability is expected for PAC mechanism under the assumption that the understatement strategy is dominant; the average expected price equals to 9.6 £/MW/h in this case.…”