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Linear complementarity programming is a generalization of linear programming which encompasses the computation of Nash equilibria for bimatrix games. While the latter problem is PPAD-complete, we show that the tropical analogue of the…

Optimization and Control · Mathematics 2022-11-07 Xavier Allamigeon , Stéphane Gaubert , Frédéric Meunier

Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…

Computer Science and Game Theory · Computer Science 2012-07-02 Michael L. Littman , Nishkam Ravi , Arjun Talwar , Martin Zinkevich

We present a partial operator-theoretic characterization of approachability principle and based on this characterization, we interpret a particular distributed payoff allocation algorithm to be a sequence of time-varying paracontractions.…

Systems and Control · Electrical Eng. & Systems 2019-12-02 Aitazaz Ali Raja , Sergio Grammatico

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…

Computer Science and Game Theory · Computer Science 2013-04-25 Yaron Velner

We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…

Computer Science and Game Theory · Computer Science 2012-06-18 Enrique Munoz de Cote , Michael L. Littman

This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…

Optimization and Control · Mathematics 2026-02-16 Kenshi Abe , Mitsuki Sakamoto , Kaito Ariu , Atsushi Iwasaki

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…

Optimization and Control · Mathematics 2022-07-11 Nikolai Krivulin , Sergei Sergeev

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these…

Computer Science and Game Theory · Computer Science 2025-02-21 Denizalp Goktas , Amy Greenwald , Sadie Zhao , Alec Koppel , Sumitra Ganesh

We develop a tropical analog of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m+n)) time, where m…

Combinatorics · Mathematics 2015-07-31 Xavier Allamigeon , Pascal Benchimol , Stéphane Gaubert , Michael Joswig

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…

Computational Complexity · Computer Science 2015-08-10 Rajeev Kohli , Ramesh Krishnamurti

In this paper, we present methods for solving a system of linear equations, $ AX=b $, over tropical semirings. To this end, if possible, we first reduce the order of the system through some row-column analysis, and obtain a new system with…

Commutative Algebra · Mathematics 2019-06-26 Sedighe Jamshidvand , Shaban Ghalandarzadeh , Amirhossein Amiraslani , Fateme Olia

Semidefinite programming can be considered over any real closed field, including fields of Puiseux series equipped with their nonarchimedean valuation. Nonarchimedean semidefinite programs encode parametric families of classical…

Optimization and Control · Mathematics 2018-02-22 Xavier Allamigeon , Stéphane Gaubert , Ricardo D. Katz , Mateusz Skomra

In this paper, we study the average case complexity of the Unique Games problem. We propose a natural semi-random model, in which a unique game instance is generated in several steps. First an adversary selects a completely satisfiable…

Data Structures and Algorithms · Computer Science 2011-04-20 Alexandra Kolla , Konstantin Makarychev , Yury Makarychev

This paper introduces a new method to achieve stable convergence to Nash equilibrium in duopoly noncooperative games. Inspired by the recent fixed-time Nash Equilibrium seeking (NES) as well as prescribed-time extremum seeking (ES) and…

Optimization and Control · Mathematics 2024-05-27 Victor Hugo Pereira Rodrigues , Tiago Roux Oliveira , Miroslav Krstić , Tamer Başar

We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such…

Optimization and Control · Mathematics 2012-08-03 Marianne Akian , Jean Cochet-Terrasson , Sylvie Detournay , Stéphane Gaubert

We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a…

Logic in Computer Science · Computer Science 2020-07-17 Richard Combes , Mikael Touati

The paper [Ras15a] introduced distribution-valued games. This game-theoretic model uses probability distributions as payoffs for games in order to express uncertainty about the payoffs. The player's preferences for different payoffs are…

Optimization and Control · Mathematics 2021-03-26 Vincent Bürgin

Game theoretic approaches have gained traction as robust methodologies for designing distributed local algorithms that induce a desired overall system configuration in multi-agent settings. However, much of the emphasis in these approaches…

Systems and Control · Electrical Eng. & Systems 2021-11-03 Rohit Konda , Rahul Chandan , David Grimsman , Jason R. Marden

We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…

Logic in Computer Science · Computer Science 2013-01-14 Patricia Bouyer , Nicolas Markey , Jörg Olschewski , Michael Ummels

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…

Populations and Evolution · Quantitative Biology 2016-09-08 Rui Dilao , Joao Graciano