Related papers: Strong Parallel Repetition for Unique Games on Sma…

Red-blue pebble games model the computation cost of a two-level memory hierarchy. We present various hardness results in different red-blue pebbling variants, with a focus on the oneshot model. We first study the relationship between…

In this paper, we address the problem of testing exchangeability of a sequence of random variables, $X_1, X_2,\cdots$. This problem has been studied under the recently popular framework of testing by betting. But the mapping of testing…

We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known…

We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…

Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly…

We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…

In this paper, the author defines Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative. Two special types of GUGP are illuminated, GUGP-NWA, where the weights of all edges are negative, and…

Reinforcement-based learning dynamics may exhibit several limitations when applied in a distributed setup. In (repeatedly-played) multi-player/action strategic-form games, and when each player applies an independent copy of the learning…

Partial order reductions have been successfully applied to model checking of concurrent systems and practical applications of the technique show nontrivial reduction in the size of the explored state space. We present a theory of partial…

Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with…

We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…

This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently…

Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (STOC 2017). The combinatorial object underlying these approaches is a universal tree, as identified by Czerwi\'nski et al.…

We investigate a phenomenon of "one-to-two-player lifting" in infinite-duration two-player games on graphs with zero-sum objectives. More specifically, let $C$ be a class of strategies. It turns out that in many cases, to show that all…

Uniform substitution of function, predicate, program or game symbols is the core operation in parsimonious provers for hybrid systems and hybrid games. By postponing soundness-critical admissibility checks, this paper introduces a uniform…

After the NP-hardness of computational problems such as 3SAT and MaxCut was established, a natural next step was to explore whether these problems remain hard to approximate. While the quantum extensions of some of these problems are known…

General game testing relies on the use of human play testers, play test scripting, and prior knowledge of areas of interest to produce relevant test data. Using deep reinforcement learning (DRL), we introduce a self-learning mechanism to…

Reinforcement learning has the potential to automate the acquisition of behavior in complex settings, but in order for it to be successfully deployed, a number of practical challenges must be addressed. First, in real world settings, when…

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble…

Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…