相关论文: Lattice games without rational strategies

We prove that the universal lattices -- the groups $G=\SL_d(R)$ where $R=\Z[x_1,...,x_k]$, have property $\tau$ for $d\geq 3$. This provides the first example of linear groups with $\tau$ which do not come from arithmetic groups. We also…

We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal…

We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal…

We prove game-theoretic generalizations of some well known zero-one laws. Our proofs make the martingales behind the laws explicit, and our results illustrate how martingale arguments can have implications going beyond measure-theoretic…

We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant…

Large language models (LLMs) have been extensively used as the backbones for general-purpose agents, and some economics literature suggest that LLMs are capable of playing various types of economics games. Following these works, to overcome…

The worldsheet formulation of lattice gauge theories has two appealing features: the gauge non-redundancy and the geometrical transparency. Both properties are profitable in order to perform numerical computations. In the case of dynamical…

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy…

This study investigates the influence of lattice structure in evolutionary games. The snowdrift games is considered in networks with high clustering coefficients, that use four different strategy-updating. Analytical conjectures using pair…

We investigate the impossibility of universally winning trading strategies -- those generating strict profit across all market trajectories -- through three distinct mathematical paradigms. Fundamentally, under standard admissibility…

A combinatorial game is a two-player game without hidden information or chance elements. The main object of combinatorial game theory is to obtain the outcome, which player has a winning strategy, of a given combinatorial game. Positions of…

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

We introduce language-based games, a generalization of psychological games [6] that can also capture reference-dependent preferences [7]. The idea is to extend the domain of the utility function to situations, maximal consistent sets in…

This paper investigates the long-term behavior of an interacting particle system of interest in the hot topic of evolutionary game theory. Each site of the $d$-dimensional integer lattice is occupied by a player who is characterized by one…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…

Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional…

Strategic reasoning enables agents to cooperate, communicate, and compete with other agents in diverse situations. Existing approaches to solving strategic games rely on extensive training, yielding strategies that do not generalize to new…