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We study two-player zero-sum concurrent stochastic games with finite state and action space played for an infinite number of steps. In every step, the two players simultaneously and independently choose an action. Given the current state…
The extensive-form game has been studied considerably in recent years. It can represent games with multiple decision points and incomplete information, and hence it is helpful in formulating games with uncertain inputs, such as poker. We…
We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
Online bipartite matching is a fundamental problem in online algorithms. The goal is to match two sets of vertices to maximize the sum of the edge weights, where for one set of vertices, each vertex and its corresponding edge weights appear…
We conduct a comprehensive analysis of the discrete-time exponential-weights dynamic with a constant step size on all general-sum and symmetric $2 \times 2$ normal-form games, i.e. games with $2$ pure strategies per player, and where the…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…
Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…
The nucleolus is a central solution concept in cooperative game theory. While its computation is NP-hard in general, it can be computed in polynomial time for convex games; however, the only published polynomial-time algorithm relies on the…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
This paper studies the last-iterate convergence properties of the exponential weights algorithm with constant learning rates. We consider a repeated interaction in discrete time, where each player uses an exponential weights algorithm…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
We prove that the constructive weighted coalitional manipulation problem for the Schulze voting rule can be solved in polynomial time for an unbounded number of candidates and an unbounded number of manipulators.
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {\sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes…