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Publication# Near-Optimal Communication Lower Bounds for Approximate Nash Equilibria

Abstract

We prove an N2-o(1) lower bound on the randomized communication complexity of finding an epsilon-approximate Nash equilibrium (for constant epsilon > 0) in a two-player N x N game.

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Related concepts (10)

Related publications (35)

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Communication complexity

In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. The problem is usually stated as follows: two parties (traditionally called Alice and Bob) each receive a (potentially different) -bit string and .

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Mika Tapani Göös, Siddhartha Jain

The Collision problem is to decide whether a given list of numbers (x_1,…,x_n) ∈ [n]ⁿ is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n^Ω(1) randomised communication lower bound for the natural two-party version of Collision where Ali ...

This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. ...

Rachid Guerraoui, Jovan Komatovic, Pierre Philippe Civit, Manuel José Ribeiro Vidigueira, Vincent Gramoli, Seth Gilbert

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with n processes and at most f < n/3 failures, any solution t ...

2023