Related papers: Faster and Simpler Algorithm for Optimal Strategie…

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…

Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…

We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm…

This paper studies two-player zero-sum stochastic Bayesian games where each player has its own dynamic state that is unknown to the other player. Using typical techniques, we provide the recursive formulas and sufficient statistics in both…

In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

Inspired by scenarios where the strategic network design and defense or immunisation are of the central importance, Goyal et al. [3] defined a new Network Formation Game with Attack and Immunisation. The authors showed that despite the…

We design algorithms for minimizing $\max_{i\in[n]} f_i(x)$ over a $d$-dimensional Euclidean or simplex domain. When each $f_i$ is $1$-Lipschitz and $1$-smooth, our method computes an $\epsilon$-approximate solution using $\widetilde{O}(n…

In competitive resource allocation environments, agents often choose to form alliances; however, for some agents, doing so may not always be beneficial. Is there a method of forming alliances that always reward each of their members? We…

Max-min bilinear optimization models, where one agent maximizes and an adversary minimizes a common bilinear objective, serve as canonical saddle-point formulations in optimization theory. They capture, among others, two-player zero-sum…

Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…

Various popular multiplayer battle royale games share a lot of common elements. Drawing from our observations, we summarized these shared characteristics and subsequently proposed a novel heuristic algorithm named multiplayer battle…

This paper proposes an optimization algorithm based on how human fight and learn from each duelist. Since this algorithm is based on population, the proposed algorithm starts with an initial set of duelists. The duel is to determine the…

We present a mathematical framework for modeling two-player noncooperative games in which one player is uncertain of the other player's costs but can preemptively allocate information-gathering resources to reduce this uncertainty. We refer…

This paper introduces Local Learner (2L), an algorithm for providing a set of reference strategies to guide the search for programmatic strategies in two-player zero-sum games. Previous learning algorithms, such as Iterated Best Response…

This paper employs a novel method for the empirical analysis of political discourse and develops a model that demonstrates dynamics comparable with the empirical data. Applying a set of binary text classifiers based on convolutional neural…

This paper studies how to efficiently update the saddle-point strategy, or security strategy of one player in a matrix game when the other player develops new actions in the game. It is well known that the saddle-point strategy of one…

LP-duality theory has played a central role in the study of cores of games, right from the early days of this notion to the present time. The classic paper of Shapley and Shubik \cite{Shapley1971assignment} introduced the "right" way of…

We explain a highly efficient algorithm for playing the simplest type of dots and boxes endgame optimally (by which we mean "in such a way so as to maximise the number of boxes that you take"). The algorithm is sufficiently simple that it…

Ye showed recently that the simplex method with Dantzig pivoting rule, as well as Howard's policy iteration algorithm, solve discounted Markov decision processes (MDPs), with a constant discount factor, in strongly polynomial time. More…