Related papers: Lower Bound for the Unique Games Problem
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…
We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…
For the set of graphs with a given degree sequence, consisting of any number of $2's$ and $1's$, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of $m$-matchings. We find the…
In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…
We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial…
We consider network games where a large number of agents interact according to a network sampled from a random network model, represented by a graphon. By exploiting previous results on convergence of such large network games to graphon…
We consider the problem of maximizing the minimum (weighted) value of all components of a vector over a polymatroid. This is a special case of the lexicographically optimal base problem introduced and solved by Fujishige. We give an…
We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same…
We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always…
In the classical online model, the maximum independent set problem admits an $\Omega(n)$ lower bound on the competitive ratio even for interval graphs, motivating the study of the problem under additional assumptions. We first study the…
We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…
We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…
This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant…