Distributing Resources: An Exploration of Auctions and Other Allocation Mechanisms

This thesis consists of four largely independent essays on game theory and the allocation of resources. It applies both theoretical and empirical methods, covering both cooperative and non-cooperative game theoretical approaches. The thesis focuses on three different allocation mechanisms: auctions, grandfathering and the Shapley value. The first two mechanisms are applied directly within the fisheries context whilst the Shapley value is discussed in a general setting. Theoretical applications often employ a number of assumptions, which are rarely met in practice, and fail to take into account the contextual setting. This thesis empirically analyses real life examples in order to enhance our understanding of individual players and their interactions. The first chapter on the famous solution concept — the Shapley value — introduces a cooperative game in which some of the information may be missing from the characteristic function. We put forward two ways of extending the Shapley value to the missing information domain. Using our proposals, it is possible to find a ‘fair and efficient solution’ in situations where coalitions might not have formed or information is withheld. The second chapter presents a theoretical model for fisheries which is capable of exploring the effects of utilising different combinations of allocation mechanisms — grandfathering and auctions — for fishing quota. In the model, the government has applied an environmental tax, which can be reduced through investment, to limit the negative externalities of the fishing activity. This in turn affects the firms' valuations at the auctions, incorporating bidder valuations as an endogenous component within the model. The model demonstrates the effects of changing specific variables within the government's control on revenue, total welfare, level of investment and equilibrium prices at the auction. We conclude by stating that the model is applicable in the fisheries context, but further work is required to improve its relevance in the policy arena. The third chapter is an empirical essay on the ascending and uniform-price multiunit auctions of fishing rights in the Faroe Islands from 2016 to 2018. In the essay, we identify problems with signalling, bidding rings and low-price equilibria. We believe this is the first case of all three phenomena happening in the same bidding environment. We conclude that the underperformance of ascending and uniform-price auctions are not just theoretical curiosities, but rather a pervasive phenomenon in practical auction design. We continue in the empirical domain in the fourth chapter, where we use several methods to analyse price patterns in the auctions at the Faroe Fish Market in 2017. We apply the method employed by Ashenfelter (1989) in his work on the declining price anomaly. We also run regressions to establish how the auction round affects absolute and relative price changes and explore the impact of the number of bids, quantity sold and the price of the first round. Finally, we analyse the average price of cod in every round across the whole period. We find that declining prices are a strong feature of the Faroese fish market, but after considering contributing factors, we conclude that perhaps declining prices should not come as such a surprise after all