Designing Non-Convex Markets (DNCM)

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Multi-object markets have been at the centre stage of the economic sciences since the early days. General equilibrium theory and auction theory have developed general models showing assumptions when multi-object market mechanisms are in a competitive equilibrium or when they are incentive-compatible and efficient. Real markets often do not satisfy the assumptions of generic models. Market design describes a recent stream in the literature aiming to design specific types of markets and reflect important features of the respective allocation problems. These features can typically be described as constraints in the allocation and pricing problems. Examples include constraints that are used to model complex preferences of market participants (e.g. complements and substitutes), constraints restricting the set of possible outcomes of a market, or also budget constraints. These constraints turn the allocation problem into a non-convex optimisation problem. Examples of such non-convex markets are widespread and include spectrum auction markets, markets for airport time-slots, logistics services, pollution rights, port capacities, or day-ahead electricity markets. While respective allocation problems were considered intractable only a few years ago for realistic problem sizes, the advances in mathematical optimisation are staggering. Advanced mathematical optimisation has recently been used in high-stakes markets worldwide. However, the theory of these markets is in its infancy. DNCM aims at new types of market models, open source software, and experimental results.