Georgios Piliouras

We investigate a family of one-dimensional maps for which the bifurcation diagrams look differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising from this family of maps.

Transaction fee mechanisms are pivotal elements of blockchain economies, as they resolve the inherent scarcity in the number of transactions that can be added to each block. First-price auction mechanisms implemented by early blockchain protocols, however, contributed to pronounced intra-block disparities, unpredictable waiting times, high congestion, and other inefficiencies. To mitigate these effects, alternative fee market mechanism has been proposed, e.g., Ethereum’s EIP-1559. In this article, we investigate the ramifications of EIP-1559 on system performance and user experience. Although we prove that EIP-1559 exhibits chaotic behavior even under optimal conditions, we demonstrate that the influence of this chaotic behavior on the primary design objective of the fee mechanism—blocks whose long-term average size equals the target—is limited. Our theoretical bound shows that block sizes in the EIP-1559 mechanism are lower bounded by target utilization—half-full blocks—and the upper bound is capped at 6% beyond the target. These findings are confirmed by an empirical evaluation that shows that the average discrepancy has been 2.9% under Proof-of-Work and decreases to around 1% or less following Ethereum’s transition to Proof-of-Stake. However, the chaotic oscillations in block sizes and the slow adjustments during periods of demand bursts (e.g., NFT drops) result in undesirable inter-block variations in mining rewards and compromise the overall user experience. To address these issues, we propose an alternative base fee adjustment rule, characterized by a learning rate that adapts according to an additive increase, multiplicative decrease (AIMD) update scheme. Our data-driven simulations show that the latter robustly outperforms the EIP-1559 protocol across various demand scenarios.

Inspired by the challenges at the intersection of Evolutionary Game Theory and Machine Learning, we investigate a class of discrete-time multiagent reinforcement learning (MARL) dynamics in population/nonatomic congestion games, where agents have diverse beliefs and learn at different rates. These congestion games, a well-studied class of potential games, are characterized by individual agents having negligible effects on system performance, strongly aligned incentives, and well-understood advantageous properties of Nash equilibria. Despite the presence of static Nash equilibria, we demonstrate that MARL dynamics with heterogeneous learning rates can deviate from these equilibria, exhibiting instability and even chaotic behavior and resulting in increased social costs. Remarkably, even within these chaotic regimes, we show that the time-averaged macroscopic behavior converges to exact Nash equilibria, thus linking the microscopic dynamic complexity with traditional equilibrium concepts. By employing dynamical systems techniques, we analyze the interaction between individual-level adaptation and population-level outcomes, paving the way for studying heterogeneous learning dynamics in discrete time across more complex game scenarios.

We investigate the interplay between passivity, no-regret, and convergence in contractive games for various learning dynamic models and their higher-order variants. Our setting is continuous time. Building on prior work for replicator dynamics, we show that if learning dynamics satisfy a passivity condition between the payoff vector and the difference between its evolving strategy and any fixed strategy, then it achieves finite regret. We then establish that the passivity condition holds for various learning dynamics and their higher-order variants. Consequentially, the higher-order variants can achieve convergence to Nash equilibrium in cases where their standard order counterparts cannot, while maintaining a finite regret property. We provide numerical examples to illustrate the lack of finite regret of different evolutionary dynamic models that violate the passivity property. We also examine the fragility of the finite regret property in the case of perturbed learning dynamics. Continuing with passivity, we establish another connection between finite regret and passivity, but with the related equilibrium-independent passivity property. Finally, we present a passivity-based classification of dynamic models according to the various passivity notions they satisfy, namely, incremental passivity, $δ$-passivity, and equilibrium-independent passivity. This passivity-based classification provides a framework to analyze the convergence of learning dynamic models in contractive games.

As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as solution concepts of strategic quantum interactions, but these approaches did not directly connect to decentralized adaptive setups where agents possess limited information. This paper delves into the dynamics of quantum-enabled agents within decentralized systems that employ no-regret algorithms to update their behaviors over time. Specifically, we investigate two-player quantum zero-sum games and polymatrix quantum zero-sum games, showing that no-regret algorithms converge to separable quantum Nash equilibria in time-average. In the case of general multi-player quantum games, our work leads to a novel solution concept, that of the separable quantum coarse correlated equilibria (QCCE), as the convergent outcome of the time-averaged behavior no-regret algorithms, offering a natural solution concept for decentralized quantum systems. Finally, we show that computing QCCEs can be formulated as a semidefinite program and establish the existence of entangled (i.e., non-separable) QCCEs, which are unlearnable via the current paradigm of no-regret learning.

Maximal Extractable Value (MEV) has emerged as a new frontier in the design of blockchain systems. In this paper, we propose making the MEV extraction rate as part of the protocol design space. Our aim is to leverage this parameter to maintain a healthy balance between block producers (who need to be compensated) and users (who need to feel encouraged to transact). We follow the approach introduced by EIP-1559 and design a similar mechanism to dynamically update the MEV extraction rate with the goal of stabilizing it at a target value. We study the properties of this dynamic mechanism and show that, while convergence to the target can be guaranteed for certain parameters, instability, and even chaos, can occur in other cases. Despite these complexities, under general conditions, the system concentrates in a neighborhood of the target equilibrium implying high long-term performance. Our work establishes, the first to our knowledge, dynamic framework for the integral problem of MEV sharing between extractors and users.

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a game adequately capture the limit behavior of natural game dynamics. These two results have created a need and opportunity to articulate a principled computational theory of the meaning of the game that is based on game dynamics. Given any game in normal form, and any prior distribution of play, we study the problem of computing the asymptotic behavior of a class of natural dynamics called the noisy replicator dynamics as a limit distribution over the sink equilibria of the game. When the prior distribution has pure strategy support, we prove this distribution can be computed efficiently, in near-linear time to the size of the best-response graph. When the distribution can be sampled -- for example, if it is the uniform distribution over all mixed strategy profiles -- we show through experiments that the limit distribution of reasonably large games can be estimated quite accurately through sampling and simulation.