Bayes correlated equilibria and no-regret dynamics

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

High-Dimensional Prediction for Sequential Decision Making

We study the problem of making predictions of an adversarially chosen high-dimensional state that are unbiased subject to an arbitrary collection of conditioning events, with the goal of tailoring these events to downstream decision makers. We give efficient algorithms for solving this problem, as well as a number of applications that stem from choosing an appropriate set of conditioning events. For example, we can efficiently make predictions targeted at polynomially many decision makers, giving each of them optimal swap regret if they best-respond to our predictions. We generalize this to online combinatorial optimization, where the decision makers have a very large action space, to give the first algorithms offering polynomially many decision makers no regret on polynomially many subsequences that may depend on their actions and the context. We apply these results to get efficient no-subsequence-regret algorithms in extensive-form games (EFGs), yielding a new family of regret guarantees for EFGs that generalizes some existing EFG regret notions, e.g. regret to informed causal deviations, and is generally incomparable to other known such notions. Next, we develop a novel transparent alternative to conformal prediction for building valid online adversarial multiclass prediction sets. We produce class scores that downstream algorithms can use for producing valid-coverage prediction sets, as if these scores were the true conditional class probabilities. We show this implies strong conditional validity guarantees including set-size-conditional and multigroup-fair coverage for polynomially many downstream prediction sets. Moreover, our class scores can be guaranteed to have improved $L_2$ loss, cross-entropy loss, and generally any Bregman loss, compared to any collection of benchmark models, yielding a high-dimensional real-valued version of omniprediction.Comment: Added references, Arxiv abstract edite

Robust approachability and regret minimization in games with partial monitoring

Approachability has become a standard tool in analyzing earning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set, rather than being a single vector. Using this variant we tackle the problem of approachability in games with partial monitoring and develop simple and efficient algorithms (i.e., with constant per-step complexity) for this setup. We finally consider external regret and internal regret in repeated games with partial monitoring and derive regret-minimizing strategies based on approachability theory

Pricing and Hedging Illiquid Energy Derivatives:an Application to the JCC Index

In this paper we discuss a simple econometric strategy for pricing and hedging illiquid financial products, such as the Japanese crude oil cocktail (JCC) index, the most popular OTC energy derivative in Japan. First, we review the existing literature for computing optimal hedge ratios (OHR) and we propose a critical classification of the existing approaches. Second, we compare the empirical performance of different econometric models (namely, regression models in price-levels, price first differences, price returns, as well as error correction and autoregressive distributed lag models) in terms of their computed OHR using monthly data on the JCC over the period January 2000-January 2006. Third, we illustrate and implement a procedure to cross-hedge and price two different swaps on the JCC: a one-month swap and a three-month swap with a variable oil volume. We explain how to compute a bid/ask spread and to construct the hedging position for the JCC swap. Fourth, we evaluate our swap pricing scheme with backtesting and rolling regression techniques. Our empirical findings show that it is not necessary to use sophisticated econometric techniques, since the price level regression model permits to compute a more reliable optimal hedge ratio relative to its competing alternatives.Hedging Models, Cross-Hedging, Energy Derivatives, Illiquid Financial Products, Commodity Markets, JCC Price Index

Cooperative AI via Decentralized Commitment Devices

Credible commitment devices have been a popular approach for robust multi-agent coordination. However, existing commitment mechanisms face limitations like privacy, integrity, and susceptibility to mediator or user strategic behavior. It is unclear if the cooperative AI techniques we study are robust to real-world incentives and attack vectors. However, decentralized commitment devices that utilize cryptography have been deployed in the wild, and numerous studies have shown their ability to coordinate algorithmic agents facing adversarial opponents with significant economic incentives, currently in the order of several million to billions of dollars. In this paper, we use examples in the decentralization and, in particular, Maximal Extractable Value (MEV) (arXiv:1904.05234) literature to illustrate the potential security issues in cooperative AI. We call for expanded research into decentralized commitments to advance cooperative AI capabilities for secure coordination in open environments and empirical testing frameworks to evaluate multi-agent coordination ability given real-world commitment constraints.Comment: NeurIPS 2023- Multi-Agent Security Worksho

Fast swap regret minimization and applications to approximate correlated equilibria

We give a simple and computationally efficient algorithm that, for any constant $\varepsilon>0$, obtains $\varepsilon T$-swap regret within only $T = \mathsf{polylog}(n)$ rounds; this is an exponential improvement compared to the super-linear number of rounds required by the state-of-the-art algorithm, and resolves the main open problem of [Blum and Mansour 2007]. Our algorithm has an exponential dependence on $\varepsilon$, but we prove a new, matching lower bound. Our algorithm for swap regret implies faster convergence to $\varepsilon$-Correlated Equilibrium ($\varepsilon$-CE) in several regimes: For normal form two-player games with $n$ actions, it implies the first uncoupled dynamics that converges to the set of $\varepsilon$-CE in polylogarithmic rounds; a $\mathsf{polylog}(n)$-bit communication protocol for $\varepsilon$-CE in two-player games (resolving an open problem mentioned by [Babichenko-Rubinstein'2017, Goos-Rubinstein'2018, Ganor-CS'2018]); and an $\tilde{O}(n)$-query algorithm for $\varepsilon$-CE (resolving an open problem of [Babichenko'2020] and obtaining the first separation between $\varepsilon$-CE and $\varepsilon$-Nash equilibrium in the query complexity model). For extensive-form games, our algorithm implies a PTAS for $\mathit{normal}$ $\mathit{form}$ $\mathit{correlated}$ $\mathit{equilibria}$, a solution concept often conjectured to be computationally intractable (e.g. [Stengel-Forges'08, Fujii'23])