Multi-Unit Auctions to Allocate Water Scarcity Simulating Bidding Behaviour with Agent Based Models

Multi-unit auctions are promising mechanisms for the reallocation of water. The main advantage of such auctions is to avoid the lumpy bid issue. However, there is great uncertainty about the best auction formats when multi-unit auctions are used. The theory can only supply the structural properties of equilibrium strategies and the multiplicity of equilibria makes comparisons across auction formats difficult. Empirical studies and experiments have improved our knowledge of multi- unit auctions but they remain scarce and most experiments are restricted to two bidders and two units. Moreover, they demonstrate that bidders have limited rationality and learn through experience. This paper constructs an agent-based model of bidders to compare the performance of alternative auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids to improve their net incomes. We demonstrate that under the generalized Vickrey, simulated bids converge towards truthful bids as predicted by the theory and that bid shading is the rule for the uniform and discriminatory auctions. Our study allows us to assess the potential gains from agent-based modelling approaches in the assessment of the dynamic performance of multi-unit procurement auctions. Some recommendations on the desirable format of water auctions are provided.