Strategyproof mechanisms provide robust equilibrium 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. In the search for maximally-strategyproof mechanisms that simultaneously satisfy other desirable properties, we introduce a new metric to quantify the strategyproofness of a mechanism, based on comparing the payoff distribution, given truthful reports, against that of a strategyproof “reference” mechanism that solves a problem relaxation. Focusing on combinatorial exchanges, we demonstrate that the metric is informative about the eventual equilibrium, where simple regretbased metrics are not, and can be used for online selection of an effective mechanism. 1

IIS-0905390. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We also acknowledge Intel Corporation and IBM for their machine gifts. Keywords: Game theory, continuous games, games of imperfect information, equilibrium We present a new approach for solving large (even infinite) multiplayer games of imperfect information. The key idea behind our approach is that we include additional inputs in the form of qualitative models of equilibrium strategies (how the signal space should be qualitatively partitioned into action regions). In addition, we show that our approach can lead to strong strategies in large finite games that we approximate with infinite games. We prove that our main algorithm is correct even if given a set of qualitative models (satisfying a technical property) of which only some are accurate. We also show how to check the output in settings where all of the models might be wrong (under a weak assumption). Our algorithms can compute equilibria in several classes of games for which no prior algorithms have been developed, and we demonstrate that they run efficiently in practice. In the course of our analysis, we also develop the first mixed-integer programming formulations for computing an epsilon-equilibrium in general multiplayer normal and extensive-form

Experimental analysis of agent strategies in multiagent systems presents a tradeoff between granularity and statistical confidence. Collecting a large amount of data about each strategy profile improves confidence, but restricts the range of strategies and profiles that can be explored. We propose a flexible approach, where multiple game-theoretic formulations can be constructed to model the same underlying scenario (observation dataset). The prospect of incorrectly selecting an empirical model is termed generalization risk, and the generalization risk framework we describe provides a general criterion for empirical modeling choices, such as adoption of factored strategies or other structured representations of a game model. We propose a principled method of managing generalization risk to derive the optimal game-theoretic model for the observed data in a restricted class of models. Application to a large dataset generated from a trading agent scenario validates the method.

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 thusseekarelaxationofthissolutionconcept, 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 formulatingthedesignproblemasaconstrained optimizationproblem. Discretization andstatistical sampling allowus to reify thisproblem asalinear programto findideal 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