Combinatorial markets in theory and practice: mitigating incentives and facilitating elicitation

Strategyproof mechanisms provide robust equilibria with minimal assumptions about knowledge and rationality, but can be unachievable in combination with other desirable properties, such as budget-balance, stability against deviations by coalitions, and computational tractability. We thus seek a relaxation of this solution concept, and propose several definitions for general settings with private and quasi-linear utility. We are then able to describe the ideal mechanism according to these definitions by formulating the design problem as a constrained optimization problem. Discretization and statistical sampling allow us to reify this problem as a linear program to find ideal mechanisms in simple settings. However, this constructive approach is not scalable. We thus advocate for using the quantiles of the ex post unilateral gain from deviation as a method for capturing useful information about the incentives in a mechanism. Where this also is too expensive, we propose using the KL-Divergence between the payoff distribution at truthful reports and the distribution under a strategyproof "reference" mechanism that solves a problem relaxation. We prove bounds that relate such quasimetrics to our definitions of approximate incentive compatibility; we demonstrate empirically in combinatorial market settings that they are informative about the eventual equilibrium, where simple regret-based metrics are not. We then design, implement, and analyze a mechanism for just such an overconstrained setting: the first fully expressive, iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language (TBBL) that is concise and expressive for CEs. Bidders specify lower and upper bounds in TBBL on their value for different, trades and refine these bounds across rounds. A proxied interpretation of a revealed-preference activity rule, coupled with simple linear prices, ensures progress across rounds. We are able to prove efficiency under truthful bidding despite using linear pricing that can only approximate competitive equilibrium. Finally, we apply several key concepts from this general mechanism in a combinatorial market for finding the right balance between power and performance in allocating computational resources in a data center.