Related papers: Sprague-Grundy values and complexity for LCTR

In the cup game, an adversary distributes 1 unit of water among $n$ cups every time step. The player then selects a single cup from which to remove 1 unit of water. In the bamboo trimming problem, the adversary must choose fixed rates for…

In this article, we introduce certain kinds of computable reduction games with imperfect information. One can view such a game as an extension of the notion of Turing reduction, and generalized Weihrauch reduction as well. Based on the work…

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

We aim to solve the problem of temporal-constraint learning from demonstrations to reproduce demonstration-like logic-constrained behaviors. Learning logic constraints is challenging due to the combinatorially large space of possible…

This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…

We introduce LMLRSGA, a limited memory variant of Low Rank Symplectic Gradient Adjustment (LRSGA) for differentiable games. It is an iterative scheme for approximating Nash equilibria with first order like cost while retaining the…

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…

Strong placement games (SP-games) are a class of combinatorial games whose structure allows one to describe the game via simplicial complexes. A natural question is whether well-known invariants of combinatorial games, such as "game value",…

Autonomous vehicles must balance ranked objectives, such as minimizing travel time, ensuring safety, and coordinating with traffic. Games of ordered preference effectively model these interactions but become computationally intractable as…

The following optimal stopping problem is considered. The vertices of a graph $G$ are revealed one by one, in a random order, to a selector. He aims to stop this process at a time $t$ that maximizes the expected number of connected…

We investigate the combinatorial game Slime Trail.This game is played on a graph with a starting piece in a node. Each player's objective is to reach one of their own goal nodes. Every turn the current player moves the piece and deletes the…

Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic…

We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

We derive upper and lower bounds for the policy regret of $T$-round online learning problems with graph-structured feedback, where the adversary is nonoblivious but assumed to have a bounded memory. We obtain upper bounds of $\widetilde…

In reinforcement learning (RL), offline learning decoupled learning from data collection and is useful in dealing with exploration-exploitation tradeoff and enables data reuse in many applications. In this work, we study two offline…

We compare here the relative strength of four widely used procedures on finite strategic games: iterated elimination of weakly/strictly dominated strategies by a pure/mixed strategy. A complication is that none of these procedures is based…

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…

The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…