arXiv subjects

Tristan Tomala

Publications and source records attributed to Tristan Tomala.

11 recordsLinked to original sources

arXiv2026

Information Design and Full Implementation in Nonatomic Games

This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian games with nonatomic players, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with negative payoff externalities, such as congestion and Cournot games. Specifically, if the game admits a strictly concave potential in every state, then for every Bayes correlated equilibrium outcome with finite support and rational action distributions, there exists a direct information structure that implements this outcome under all equilibria. When the potential is weakly concave, we show that all equilibria implement the same expected total payoff. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented.

econ.TH↗

arXiv2025

Single-Letter Characterization of the Mismatched Distortion-Rate Function

The mismatched distortion-rate problem has remained open since its formulation by Lapidoth in 1997. In this paper, we characterize the mismatched distortion-rate function. Our single-letter solution highlights the adequate conditional distributions for the encoder and the decoder. The achievability result relies on a time-sharing argument that allows to convexify the upper bound of Lapidoth. We show that it is sufficient to consider two regimes, one with a large rate and another one with a small rate. Our main contribution is the converse proof. Suppose that the encoder selects a single-letter conditional distribution distinct from the one in the solution, we construct an encoding strategy that leads to the same expected cost for both encoder and decoder. This ensures that the encoder cannot gain by changing the single-letter conditional distribution. This argument relies on a careful identification of the sequence of auxiliary random variables. By building on Caratheodory's Theorem we show that the cardinality of the auxiliary random variables is equal to the one of the source alphabet plus three.

cs.IT↗

arXiv2023

Correlated Equilibria in Large Anonymous Bayesian Games

We consider multi-population Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on this player's own action, the distribution of players' actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games and introduce the concept of Bayes correlated Wardrop equilibrium, which extends the concept of Bayes correlated equilibrium to nonatomic games. We prove that Bayes correlated Wardrop equilibria are limits of action flows induced by Bayes correlated equilibria of the game with a large finite set of small players. For nonatomic games with complete information admitting a convex potential, we prove that the set of correlated and of coarse correlated Wardrop equilibria coincide with the set of probability distributions over Wardrop equilibria, and that all equilibrium outcomes have the same costs. We get the following consequences. First, all flow distributions of (coarse) correlated equilibria in convex potential games with finitely many players converge to Wardrop equilibria when the weight of each player tends to zero. Second, for any sequence of flows satisfying a no-regret property, its empirical distribution converges to the set of distributions over Wardrop equilibria and the average cost converges to the unique Wardrop cost.

cs.GT↗

arXiv2021

Social Learning in Nonatomic Routing Games

We consider a discrete-time nonatomic routing game with variable demand and uncertain costs. Given a routing network with single origin and destination, the cost function of each edge depends on some uncertain persistent state parameter. At every period, a random traffic demand is routed through the network according to a Wardrop equilibrium. The realized costs are publicly observed and the public Bayesian belief about the state parameter is updated. We say that there is strong learning when beliefs converge to the truth and weak learning when the equilibrium flow converges to the complete-information flow. We characterize the networks for which learning occurs. We prove that these networks have a series-parallel structure and provide a counterexample to show that learning may fail in non-series-parallel networks.

econ.TH↗

arXiv2021

Contracting over persistent information

We consider a dynamic moral hazard problem between a principal and an agent, where the sole instrument the principal has to incentivize the agent is the disclosure of information. The principal aims at maximizing the (discounted) number of times the agent chooses a particular action, e.g., to work hard. We show that there exists an optimal contract, where the principal stops disclosing information as soon as its most preferred action is a static best reply for the agent or else continues disclosing information until the agent perfectly learns the principal's private information. If the agent perfectly learns the state, he learns it in finite time with probability one; the more patient the agent, the later he learns it.

econ.TH↗

arXiv2020

Point-to-Point Strategic Communication

We propose a strategic formulation for the joint source-channel coding problem in which the encoder and the decoder are endowed with distinct distortion functions. We provide the solutions in four different scenarios. First, we assume that the encoder and the decoder cooperate in order to achieve a certain pair of distortion values. Second, we suppose that the encoder commits to a strategy whereas the decoder implements a best response, as in the persuasion game where the encoder is the Stackelberg leader. Third, we consider that the decoder commits to a strategy, as in the mismatched rate-distortion problem or as in the mechanism design framework. Fourth, we investigate the cheap talk game in which the encoding and the decoding strategies form a Nash equilibrium.

cs.IT↗

arXiv2020

Strategic Communication with Side Information at the Decoder

We investigate the problem of strategic point-to-point communication with side information at the decoder, in which the encoder and the decoder have mismatched distortion functions. The decoding process is not supervised, it returns the output sequence that minimizes the decoder's distortion function. The encoding process is designed beforehand and takes into account the decoder's distortion mismatch. When the communication channel is perfect and no side information is available at the decoder, this problem is referred to as the Bayesian persuasion game of Kamenica-Gentzkow in the Economics literature. We formulate the strategic communication scenario as a joint source-channel coding problem with side information at the decoder. The informational content of the source influences the design of the encoding since it impacts differently the two distinct distortion functions. The side information complexifies the analysis since the encoder is uncertain about the decoder's belief on the source statistics. We characterize the single-letter optimal solution by controlling the posterior beliefs induced by the Wyner-Ziv's source encoding scheme. This confirms the benefit of sending encoded data bits even if the decoding process is not supervised.

cs.IT↗

arXiv2019

Persuasion with limited communication capacity

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight, i.e., if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies that tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel.

cs.IT↗

arXiv2018

Information-Theoretic Limits of Strategic Communication

In this article, we investigate strategic information transmission over a noisy channel. This problem has been widely investigated in Economics, when the communication channel is perfect. Unlike in Information Theory, both encoder and decoder have distinct objectives and choose their encoding and decoding strategies accordingly. This approach radically differs from the conventional Communication paradigm, which assumes transmitters are of two types: either they have a common goal, or they act as opponent, e.g. jammer, eavesdropper. We formulate a point-to-point source-channel coding problem with state information, in which the encoder and the decoder choose their respective encoding and decoding strategies in order to maximize their long-run utility functions. This strategic coding problem is at the interplay between Wyner-Ziv's scenario and the Bayesian persuasion game of Kamenica-Gentzkow. We characterize a single-letter solution and we relate it to the previous results by using the concavification method. This confirms the benefit of sending encoded data bits even if the decoding process is not supervised, e.g. when the decoder is an autonomous device. Our solution has two interesting features: it might be optimal not to use all channel resources; the informational content impacts the encoding process, since utility functions capture preferences on source symbols.

cs.IT↗

arXiv2017

Information Design for Strategic Coordination of Autonomous Devices with Non-Aligned Utilities

In this paper, we investigate the coordination of autonomous devices with non-aligned utility functions. Both encoder and decoder are considered as players, that choose the encoding and the decoding in order to maximize their long-run utility functions. The topology of the point-to-point network under investigation, suggests that the decoder implements a strategy, knowing in advance the strategy of the encoder. We characterize the encoding and decoding functions that form an equilibrium, by using empirical coordination. The equilibrium solution is related to an auxiliary game in which both players choose some conditional distributions in order to maximize their expected utilities. This problem is closely related to the literature on "Information Design" in Game Theory. We also characterize the set of posterior distributions that are compatible with a rate-limited channel between the encoder and the decoder. Finally, we provide an example of non-aligned utility functions corresponding to parallel fading multiple access channels.

cs.IT↗

arXiv2016

Dynamic Atomic Congestion Games with Seasonal Flows

We propose a model of discrete time dynamic congestion games with atomic players and a single source-destination pair. The latencies of edges are composed by free-flow transit times and possible queuing time due to capacity constraints. We give a precise description of the dynamics induced by the individual strategies of players and of the corresponding costs, either when the traffic is controlled by a planner, or when players act selfishly. In parallel networks, optimal and equilibrium behavior eventually coincides, but the selfish behavior of the first players has consequences that cannot be undone and are paid by all future generations. In more general topologies, our main contributions are three-fold. First, we show that equilibria are usually not unique. In particular, we prove that there exists a sequence of networks such that the price of anarchy is equal to $n-1$, where $n$ is the number of vertices, and the price of stability is equal to 1. Second, we illustrate a new dynamic version of Braess's paradox: the presence of initial queues in a network may decrease the long-run costs in equilibrium. This paradox may arise even in networks for which no Braess's paradox was previously known. Third, we propose an extension to model seasonalities by assuming that departure flows fluctuate periodically over time. We introduce a measure that captures the queues induced by periodicity of inflows. This measure is the increase in costs compared to uniform departures for optimal and equilibrium flows in parallel networks.

cs.GT↗