Related papers: Pure-Circuit: Tight Inapproximability for PPAD
We study the computational complexity of the problem of computing local min-max equilibria of games with a nonconvex-nonconcave utility function $f$. From the work of Daskalakis, Skoulakis, and Zampetakis [DSZ21], this problem was known to…
We investigate the computational complexity of min-max optimization under coupled constraints. The work of Daskalakis, Skoulakis, and Zampetakis [DSZ21] was the first to study min-max optimization through the lens of computational…
We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for…
While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query…
We investigate the complexity of bounding the uncertainty of graphical games, and we provide new insight into the intrinsic difficulty of computing Nash equilibria. In particular, we show that, if one adds very simple and natural additional…
We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…
Whether a PTAS (polynomial-time approximation scheme) exists for game equilibria has been an open question, and its absence has indications and consequences in three fields: the practicality of methods in algorithmic game theory,…
A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a…
We study the inapproximability of the induced disjoint paths problem on an arbitrary $n$-node $m$-edge undirected graph, which is to connect the maximum number of the $k$ source-sink pairs given in the graph via induced disjoint paths. It…
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…
Metric data plays an important role in various settings such as metric-based indexing, clustering, classification, and approximation algorithms in general. Due to measurement error, noise, or an inability to completely gather all the data,…
We present a new technique for efficiently removing almost all short cycles in a graph without unintentionally removing its triangles. Consequently, triangle finding problems do not become easy even in almost $k$-cycle free graphs, for any…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
We consider the problem of computing stationary points in min-max optimization, with a particular focus on the special case of computing Nash equilibria in (two-)team zero-sum games. We first show that computing $\epsilon$-Nash equilibria…
Optimizing parameters of Two-Prover-One-Round Game (2P1R) is an important task in PCPs literature as it would imply a smaller PCP with the same or stronger soundness. While this is a basic question in PCPs community, the connection between…
We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…