Thesis submitted in partial fulfilment of the requirements for the degree of Master of Management in Finance and Investment in the faculty of Commerce, Law and Management, Wits Businesss School, University of the Witwatersrand, 2012. / Idiosyncratic considerations relevant to South Africa’s economic and legal framework, as well as determining factors taken from the financial markets and the asset being auctioned are used to critically review the current auction mechanism used by the South African government to borrow funds publicly. A logistic regression with panel data is used in the empirical analysis. The dependent variable has a dichotomous outcome of uniform-price and discriminatory auction mechanisms. Data from 43 different countries over the period 2005 to 2011 are used for the analysis. It was hypothesized that countries with higher uncertainty about the price of their public debt, should use the auction mechanism that reduces under-pricing. Results from the logit regression supported this view. Upon comparing South Africa’s profile with the logit regression results, alongside a review of the literature, it becomes apparent that the proposed model does not provide a definitive answer. However, the model does aid policymakers’ decision on which auction mechanism should be preferred over the other for South Africa.

We experimentally study the effects of allotment - the division of an item into homogeneous units - in independent private value auctions. We compare a single-item, first-price auction with two equivalent treatments with allotment: a two-unit discriminatory auction and two simultaneous single-unit first-price auctions. We find that allotment mitigates overbidding, with this effect being stronger in the discriminatory auction. In the allotment treatments, we observe large and persistent bid spreading. Across treatments, the discriminatory auction is the least efficient and generates the lowest revenue.

In a deregulated electricity market, auction serves as a primary pricing tool in various segments of the market including day-ahead, real time, ancillary services markets, and Financial Transmission Rights (FTRs) market. Deregulated power markets around the world use different auction strategies that exist in the literature, since very little comparative guidelines exist as to the relative merits of these strategies. In this thesis, a computational methodology and its solution framework are developed to evaluate the impact of an auction strategy on the equilibrium prices in a constrained network with multiple generators at nodes, and where transactions are settled using the optimal power flow (OPF) program. The methodology is tested on a power market represented by a sample 12-bus IEEE network available in the MATPOWER software, which is reconfigured to allow multiple generators to supply power at a bus. The network is used as a platform to comprehensively assess the performance of uniform price auction, discriminatory auction, and second-price uniform auction. Auction rules are used to update generator costs, which are then introduced into the OPF program for obtaining optimal price and quantity allocations. This Auction-OPF procedure is embedded within a game theoretic model that obtains the equilibrium bidding strategies and the corresponding prices and quantities for the network. A detailed comparison of the auction mechanisms is carried out using different measures of performance such as revenue, average prices, and quantity weighted average prices. The comparison shows that there is, perhaps, an appreciable difference among the auction mechanisms. However, to statistically confirm the impact of auction choices, a mixed level factorial experiment is designed with auction strategy, network load, and congestion as three different factors and a closeness measure (defined as the difference between average total revenue and the average total cost of generators in the network per hour) as the responsible variable. An analysis of variance conducted on the experimental outcomes indicates that the load level and the auction strategy significantly affect the network performance. The presence market power under the auction strategies is examined through two well known indices, Herfindahl-Hirschmann Index (HHI) and Lerners Index. It is concluded from the HHI values that all three auction strategies allow the market to be moderately competitive. The Lerners index values show that, while discriminatory auction results in highest bid markup, second price uniform auction induces bidding at or close to the marginal cost.

<p>In most electricity markets, producers submit supply functions to a procurement uniform-price auction under uncertainty before demand has been realized. In the Supply Function Equilibrium (SFE), every producer commits to the supply function that maximises his expected profit given the bids of competitors. </p><p>The presence of multiple equilibria is a basic weakness of the SFE framework. Essay I shows that with (i) symmetric producers, (ii) perfectly inelastic demand, (iii) a reservation price (price cap), and (iv) capacity constraints that bind with a positive probability, a unique symmetric SFE exists. The equilibrium price reaches the price cap exactly when capacity constraints bind.</p><p>Another weakness is difficulty finding a valid asymmetric SFE with non-decreasing supply functions. Essay II shows that for firms with asymmetric capacity constraints but identical constant marginal costs there exists a unique and valid SFE. Equilibrium supply functions exhibit kinks as well as vertical and horizontal segments. The price at which the capacity constraint of a firm binds is increasing in the firm’s share of market capacity. The capacity constraint of the second largest firm binds when the market price reaches the price cap. Thereafter, the largest firm supplies its remaining capacity with a perfectly elastic segment at the price cap. Essay III presents a numerical algorithm that calculates a similar SFE for asymmetric firms with increasing marginal costs. </p><p>Essay IV derives the SFE of a pay-as-bid auction such as the balancing market for electric power in Britain. A unique SFE always exists if the demand’s hazard rate is monotonically decreasing, as for a Pareto distribution of the second kind. Assuming this probability distribution, the pay-as-bid procurement auction is compared to the SFE of a uniform-price procurement auction. Two theorems in Essay V prove that the demand-weighted average price is (weakly) lower in the pay-as-bid procurement auction. </p>

In most electricity markets, producers submit supply functions to a procurement uniform-price auction under uncertainty before demand has been realized. In the Supply Function Equilibrium (SFE), every producer commits to the supply function that maximises his expected profit given the bids of competitors. The presence of multiple equilibria is a basic weakness of the SFE framework. Essay I shows that with (i) symmetric producers, (ii) perfectly inelastic demand, (iii) a reservation price (price cap), and (iv) capacity constraints that bind with a positive probability, a unique symmetric SFE exists. The equilibrium price reaches the price cap exactly when capacity constraints bind. Another weakness is difficulty finding a valid asymmetric SFE with non-decreasing supply functions. Essay II shows that for firms with asymmetric capacity constraints but identical constant marginal costs there exists a unique and valid SFE. Equilibrium supply functions exhibit kinks as well as vertical and horizontal segments. The price at which the capacity constraint of a firm binds is increasing in the firm’s share of market capacity. The capacity constraint of the second largest firm binds when the market price reaches the price cap. Thereafter, the largest firm supplies its remaining capacity with a perfectly elastic segment at the price cap. Essay III presents a numerical algorithm that calculates a similar SFE for asymmetric firms with increasing marginal costs. Essay IV derives the SFE of a pay-as-bid auction such as the balancing market for electric power in Britain. A unique SFE always exists if the demand’s hazard rate is monotonically decreasing, as for a Pareto distribution of the second kind. Assuming this probability distribution, the pay-as-bid procurement auction is compared to the SFE of a uniform-price procurement auction. Two theorems in Essay V prove that the demand-weighted average price is (weakly) lower in the pay-as-bid procurement auction.