This paper explores equilibrium concepts for Bayesian games, which are fundamental models of games with incomplete information. We aim at three desirable properties of equilibria. First, equilibria can be naturally realized by introducing a mediator into games. Second, an equilibrium can be computed efficiently in a distributed fashion. Third, any equilibrium in that class approximately maximizes social welfare, as measured by the price of anarchy, for a broad class of games. These three properties allow players to compute an equilibrium and realize it via a mediator, thereby settling into a stable state with approximately optimal social welfare. Our main result is the existence of an equilibrium concept that satisfies these three properties. Toward this goal, we characterize various (non-equivalent) extensions of correlated equilibria, collectively known as Bayes correlated equilibria. In particular, we focus on communication equilibria (also known as coordination mechanisms), which can be realized by a mediator who gathers each player's private information and then sends correlated recommendations to the players. We show that if each player minimizes a variant of regret called untruthful swap regret in repeated play of Bayesian games, the empirical distribution of these dynamics converges to a communication equilibrium. We present an efficient algorithm for minimizing untruthful swap regret with a sublinear upper bound, which we prove to be tight up to a multiplicative constant. As a result, by simulating the dynamics with our algorithm, we can efficiently compute an approximate communication equilibrium. Furthermore, we extend existing lower bounds on the price of anarchy based on the smoothness arguments from Bayes Nash equilibria to equilibria obtained by the proposed dynamics.
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The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not computational intractability can be circumvented if one focuses on specific classes of Markov games. One such example is two-player zero-sum Markov games, in which efficient ways to compute a Nash equilibrium are known. Inspired by zero-sum polymatrix normal-form games (Cai et al., 2016), we define a class of zero-sum multi-agent Markov games in which there are only pairwise interactions described by a graph that changes per state. For this class of Markov games, we show that an $\epsilon$-approximate Nash equilibrium can be found efficiently. To do so, we generalize the techniques of (Cai et al., 2016), by showing that the set of coarse-correlated equilibria collapses to the set of Nash equilibria. Afterwards, it is possible to use any algorithm in the literature that computes approximate coarse-correlated equilibria Markovian policies to get an approximate Nash equilibrium.
This article describes an R package bqror that estimates Bayesian quantile regression for ordinal models introduced in Rahman (2016). The paper classifies ordinal models into two types and offers computationally efficient, yet simple, Markov chain Monte Carlo (MCMC) algorithms for estimating ordinal quantile regression. The generic ordinal model with 3 or more outcomes (labeled ORI model) is estimated by a combination of Gibbs sampling and Metropolis-Hastings algorithm. Whereas an ordinal model with exactly 3 outcomes (labeled ORII model) is estimated using Gibbs sampling only. In line with the Bayesian literature, we suggest using marginal likelihood for comparing alternative quantile regression models and explain how to compute the same. The models and their estimation procedures are illustrated via multiple simulation studies and implemented in two applications. The article also describes several other functions contained within the bqror package, which are necessary for estimation, inference, and assessing model fit.
Optimization is offered as an objective approach to resolving complex, real-world decisions involving uncertainty and conflicting interests. It drives business strategies as well as public policies and, increasingly, lies at the heart of sophisticated machine learning systems. A paradigm used to approach potentially high-stakes decisions, optimization relies on abstracting the real world to a set of decision(s), objective(s) and constraint(s). Drawing from the modeling process and a range of actual cases, this paper describes the normative choices and assumptions that are necessarily part of using optimization. It then identifies six emergent problems that may be neglected: 1) Misspecified values can yield optimizations that omit certain imperatives altogether or incorporate them incorrectly as a constraint or as part of the objective, 2) Problematic decision boundaries can lead to faulty modularity assumptions and feedback loops, 3) Failing to account for multiple agents' divergent goals and decisions can lead to policies that serve only certain narrow interests, 4) Mislabeling and mismeasurement can introduce bias and imprecision, 5) Faulty use of relaxation and approximation methods, unaccompanied by formal characterizations and guarantees, can severely impede applicability, and 6) Treating optimization as a justification for action, without specifying the necessary contextual information, can lead to ethically dubious or faulty decisions. Suggestions are given to further understand and curb the harms that can arise when optimization is used wrongfully.
In the modeling of parasite transmission dynamics, understanding the reproductive characteristics of these parasites is crucial. This paper presents a mathematical model that explores the reproductive behavior of dioecious parasites and its impact on transmission dynamics. Specifically, the study focuses on the investigation of various reproductive variables such as the mating probability and the fertilized egg production in the case of helminth parasites. While previous studies have commonly assumed Poisson and negative binomial distributions to describe the distribution of parasites among hosts, this study adopts an arbitrary distribution model and examines its consequences on some reproductive variables. These variables include mean number of fertile females, mean egg production, mating probability and mean fertilized egg production. In addition, the study of these variables takes into account the sex distribution of the parasites and whether male and female parasites are considered to be distributed together or separately. We show that the models obtained for the case of male and female parasites distributed separately in the hosts are ecologically unrealistic. We present the results obtained for some specific models and we tested the models obtained in this work using Monte Carlo simulations.
Minimum variance controllers have been employed in a wide-range of industrial applications. A key challenge experienced by many adaptive controllers is their poor empirical performance in the initial stages of learning. In this paper, we address the problem of initializing them so that they provide acceptable transients, and also provide an accompanying finite-time regret analysis, for adaptive minimum variance control of an auto-regressive system with exogenous inputs (ARX). Following [3], we consider a modified version of the Certainty Equivalence (CE) adaptive controller, which we call PIECE, that utilizes probing inputs for exploration. We show that it has a $C \log T$ bound on the regret after $T$ time-steps for bounded noise, and $C\log^2 T$ in the case of sub-Gaussian noise. The simulation results demonstrate the advantage of PIECE over the algorithm proposed in [3] as well as the standard Certainty Equivalence controller especially in the initial learning phase. To the best of our knowledge, this is the first work that provides finite-time regret bounds for an adaptive minimum variance controller.
The complex interactions between algorithmic trading agents can have a severe influence on the functioning of our economy, as witnessed by recent banking crises and trading anomalies. A common phenomenon in these situations are fire sales, a contagious process of asset sales that trigger further sales. We study the existence and structure of equilibria in a game-theoretic model of fire sales. We prove that for a wide parameter range (e.g., convex price impact functions), equilibria exist and form a complete lattice. This is contrasted with a non-existence result for concave price impact functions. Moreover, we study the convergence of best-response dynamics towards equilibria when they exist. In general, best-response dynamics may cycle. However, in many settings they are guaranteed to converge to the socially optimal equilibrium when starting from a natural initial state. Moreover, we discuss a simplified variant of the dynamics that is less informationally demanding and converges to the same equilibria. We compare the dynamics in terms of convergence speed.
Influence operations are large-scale efforts to manipulate public opinion. The rapid detection and disruption of these operations is critical for healthy public discourse. Emergent AI technologies may enable novel operations which evade current detection methods and influence public discourse on social media with greater scale, reach, and specificity. New methods with inductive learning capacity will be needed to identify these novel operations before they indelibly alter public opinion and events. We develop an inductive learning framework which: 1) determines content- and graph-based indicators that are not specific to any operation; 2) uses graph learning to encode abstract signatures of coordinated manipulation; and 3) evaluates generalization capacity by training and testing models across operations originating from Russia, China, and Iran. We find that this framework enables strong cross-operation generalization while also revealing salient indicators$\unicode{x2013}$illustrating a generic approach which directly complements transductive methodologies, thereby enhancing detection coverage.
We discuss a federated learned compression problem, where the goal is to learn a compressor from real-world data which is scattered across clients and may be statistically heterogeneous, yet share a common underlying representation. We propose a distributed source model that encompasses both characteristics, and naturally suggests a compressor architecture that uses analysis and synthesis transforms shared by clients. Inspired by personalized federated learning methods, we employ an entropy model that is personalized to each client. This allows for a global latent space to be learned across clients, and personalized entropy models that adapt to the clients' latent distributions. We show empirically that this strategy outperforms solely local methods, which indicates that learned compression also benefits from a shared global representation in statistically heterogeneous federated settings.
In high-dimensional Bayesian statistics, several methods have been developed, including many prior distributions that lead to the sparsity of estimated parameters. However, such priors have limitations in handling the spectral eigenvector structure of data, and as a result, they are ill-suited for analyzing over-parameterized models (high-dimensional linear models that do not assume sparsity) that have been developed in recent years. This paper introduces a Bayesian approach that uses a prior dependent on the eigenvectors of data covariance matrices, but does not induce the sparsity of parameters. We also provide contraction rates of derived posterior distributions and develop a truncated Gaussian approximation of the posterior distribution. The former demonstrates the efficiency of posterior estimation, while the latter enables quantification of parameter uncertainty using a Bernstein-von Mises-type approach. These results indicate that any Bayesian method that can handle the spectrum of data and estimate non-sparse high dimensions would be possible.
With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifically, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we first filter out the undesirable high-frequency noise while preserving the graph geometric features via graph filtering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss. Results on several benchmark datasets show the superiority of our method with respect to state-of-the-art approaches. In particular, our simple approach outperforms existing deep learning-based methods.
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