Equilibrium computation in markets usually considers settings where player valuation functions are known. We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of common valuation functions, and provide algorithms which output direct PAC equilibrium allocations, not estimates based on attempting to learn valuation functions. Since there exist trivial PAC market outcomes with an unbounded worst-case efficiency loss, we lower-bound the efficiency of our algorithms. While the efficiency loss under general distributions is rather high, we show that in some cases (e.g., unit-demand valuations), it is possible to find a PAC market equilibrium with significantly better utility.

The Price is (Probably) Right: Learning Market Equilibria from Samples

We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent’s bundle, and weak, where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent’s bundle in the envying agent’s bundle. We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists; however, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1 but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work exhibits several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.


Weighted Envy-Freeness in Indivisible Item Allocation

Threshold task games (TTGs) are a class of cooperative games in which participants form coalitions to complete tasks associated with different rewards and thresholds for success. We provide efficient algorithms for computing approximately optimal coalition structures in TTGs. We also present non-trivial bounds on the cost of stability for this class. We put our theoretical results to practice; we design a web-based framework which allows human players to interact in a collaborative task-based model. Our analysis of human play in two different countries shows that players succeed in general to form optimal coalition structures, and converge to approximately stable payoff divisions.


Threshold Task Games: Theory, Platform and Experiments

Complex machine learning models are regularly used in critical decision-making domains, as black-box algorithms. This has given rise to several calls for algorithmic explainability. Many explanation algorithms proposed in literature assign importance to each feature individually. However, such explanations fail to capture the joint effects of sets of features. Indeed, few works so far formally analyze high dimensional model explanations. In this paper, we propose a novel high dimension model explanation method that captures the joint effect of feature subsets. We propose a new axiomatization for a generalization of the Banzhaf Index; our method can also be thought of as an approximation of a black-box model by a higher-order polynomial. In other words, this work justifies the use of the generalized Banzhaf index as a model explanation by showing that it uniquely satisfies a set of natural desiderata and that it is the optimal local approximation of a black-box model.

High Dimensional Model Explanations: an Axiomatic Approach

S2: Game Theory 2

technical paper

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AAMAS 2021

GAIW

AAMAS is the leading scientific conference for research in autonomous agents and multi-agent systems. The AAMAS conference series was initiated in 2002 as the merging of three respected scientific meetings: the International Conference on Multi-Agent Systems (ICMAS), the International Workshop on Agent Theories, Architectures, and Languages (ATAL), and the International Conference on Autonomous Agents (AA). The aim of the joint conference is to provide a single, high-profile, internationally-respected archival forum for scientific research in the theory and practice of autonomous agents and multi-agent systems.

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AAMAS 2020

AAMAS is the leading scientific conference for research in autonomous agents and multi-agent systems. The AAMAS conference series was initiated in 2002 as the merging of three respected scientific meetings: the International Conference on Multi-Agent Systems (ICMAS), the International Workshop on Agent Theories, Architectures, and Languages (ATAL), and the International Conference on Autonomous Agents (AA). 

Yair Zick

4

5

Presentations

The Price is (Probably) Right: Learning Market Equilibria from Samples

Weighted Envy-Freeness in Indivisible Item Allocation

Threshold Task Games: Theory, Platform and Experiments

High Dimensional Model Explanations: an Axiomatic Approach

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