Related papers: Analytical Approach to Parallel Repetition

As part of an effort to apply the rigorous guarantees of formal verification to multi-agent systems, the field of equilibrium analysis, also called rational verification, studies equilibria in multiplayer games to reason about system-level…

Large language models can score well on named game-theory benchmarks while failing on the same strategic computation once semantic cues are removed. We show this gap with procedurally generated zero-sum matrix games: a model that recognizes…

Consider a game where a refereed a referee chooses (x,y) according to a publicly known distribution P_XY, sends x to Alice, and y to Bob. Without communicating with each other, Alice responds with a value "a" and Bob responds with a value…

Non-local games (NLGs) provide a versatile framework for probing quantum correlations and for benchmarking the power of entanglement. In finite dimensions, the standard method for playing several games in parallel requires a tensor product…

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…

Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…

We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…

Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach has been less…

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…

Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient…

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was…

Earlier versions proposed Graded Projection Recursion (GPR) as a deterministic packed-recursion framework for model-honest near-quadratic dense matrix multiplication. This revised version withdraws the exact dense matrix multiplication…

Game theory provides the gold standard for analyzing adversarial engagements, offering strong optimality guarantees. However, these guarantees often become brittle when assumptions such as perfect information are violated. Reinforcement…

Characterizing the limit behavior -- that is, the attractors -- of learning dynamics is one of the most fundamental open questions in game theory. In recent work on this front, it was conjectured that the attractors of the replicator…

Infinitely repeated games support equilibrium concepts beyond those present in one-shot games (e.g., cooperation in the prisoner's dilemma). Nonetheless, repeated games fail to capture our real-world intuition for settings with many…

In complexity theory, gap-preserving reductions play a crucial role in studying hardness of approximation and in analyzing the relative complexity of multiprover interactive proof systems. In the quantum setting, multiprover interactive…

Hardness amplification is a central problem in the study of interactive protocols. While ``natural'' parallel repetition transformation is known to reduce the soundness error of some special cases of interactive arguments: three-message…

We look at substructural calculi from a game semantic point of view, guided by certain intuitions about resource conscious and, more specifically, cost conscious reasoning. To this aim, we start with a game, where player I defends a claim…

We study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems that show that when the signals observed by the players satisfy a condition known as $(\epsilon, \gamma)$-differential privacy, that…