Jason Milionis

Jason Milionis, Christos Papadimitriou, Georgios Piliouras et al.

Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile is mapped to the next, this becomes a problem in the theory of dynamical systems. We apply this theory, and in particular the concepts of chain recurrence, attractors, and Conley index, to prove a general impossibility result: there exist games for which any dynamics is bound to have starting points that do not end up at a Nash equilibrium. We also prove a stronger result for $ε$-approximate Nash equilibria: there are games such that no game dynamics can converge (in an appropriate sense) to $ε$-Nash equilibria, and in fact the set of such games has positive measure. Further numerical results demonstrate that this holds for any $ε$ between zero and $0.09$. Our results establish that, although the notions of Nash equilibria (and its computation-inspired approximations) are universally applicable in all games, they are also fundamentally incomplete as predictors of long term behavior, regardless of the choice of dynamics.

Rashida Hakim, Jason Milionis, Christos Papadimitriou et al.

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.

Lioba Heimbach, Kushal Babel, Jason Milionis

Gas metering on EVM-compatible blockchains assumes that execution conditions are stable: that the resource mix is constant enough to justify collapsing execution costs into a single scalar with fixed relative prices, and that state drift between submission and execution does not materially alter a transaction's outcome. We measure the extent to which this assumption fails. We present a trace-level measurement study of EVM workloads on Ethereum (L1) and Base (L2) throughout 2025, sampling 3,000 blocks per day per chain. We decompose each transaction into opcode-level execution gas, intrinsic gas, refunds, and persistent state deltas. To measure state sensitivity, we re-execute transactions from September 2025 on older states and record how gas usage and storage access patterns change. We find the resource mix to be far from stable: on Base, storage reads and compute account for 29.2% and 24.3% of execution gas, while Ethereum devotes 34.9% to storage writes. Ethereum's gas limit doubling during 2025 shifted its own profile toward compute-heavier, Base-like patterns. Base also exhibits a higher fraction of cold storage reads (49.7% versus 39.6% on Ethereum). Persistent state growth, a permanent cost priced as a transient one, reaches 456 GB on Base versus 38 GB on Ethereum. Execution outcomes are equally unstable: gas estimates vary across nearby historical states for 46.0% of transactions on Base, compared to 13.9% on Ethereum, with especially high sensitivity for MEV and DeFi activity. Storage access patterns also diverge across states, limiting the effectiveness of access lists and complicating parallel execution. Our work provides an empirical foundation for multi-dimensional gas metering and explicit pricing of state growth. They show that state-sensitive execution behavior complicates workload estimation, directly affecting transaction predictability and user experience.

Jason Milionis, Alkis Kalavasis, Dimitris Fotakis et al.

We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy constraints in such regression settings were studied under strong a priori bounds on covariates. We consider the case of Gaussian marginals and extend recent differentially private techniques on mean and covariance estimation (Kamath et al., 2019; Karwa and Vadhan, 2018) to the sub-gaussian regime. We provide a novel technical analysis yielding differentially private algorithms for the above classical regression settings. Through the case of Binary Regression, we capture the fundamental and widely-studied models of logistic regression and linearly-separable SVMs, learning an unbiased estimate of the true regression vector, up to a scaling factor.