Related papers: Finding a Winning Strategy for Wordle is NP-comple…
"Solitaire Chess" is a logic puzzle published by Thinkfun, that can be seen as a single person version of traditional chess. Given a chess board with some chess pieces of the same color placed on it, the task is to capture all pieces but…
We develop a new approach that computes approximate equilibrium strategies in Jotto, a popular word game. Jotto is an extremely large two-player game of imperfect information; its game tree has many orders of magnitude more states than…
In this study, we delve into the dynamics of Wordle using data analysis and machine learning. Our analysis initially focused on the correlation between the date and the number of submitted results. Due to initial popularity bias, we modeled…
Wordle presents an algorithmically rich testbed for constraint satisfaction problem (CSP) solving. While existing solvers rely on information-theoretic entropy maximization or frequency-based heuristics without formal constraint treatment,…
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…
In 1975 the first author proved that every finite tight two-person game form $g$ is Nash-solvable, that is, for every payoffs $u$ and $w$ of two players the obtained game $(g;u,w)$, in normal form, has a Nash equilibrium (NE) in pure…
In the Binary Networked Public Goods game, every player needs to decide if she participates in a public project whose utility is shared equally by the community. We study the problem of deciding if there exists a pure strategy Nash…
We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is shelf-shuffled exactly one time. One after the other a single card is drawn from the shuffled deck. The guesser makes has guess…
In this work, we investigate the distributed generalized Nash equilibrium (GNE) seeking problems for $N$-coalition games with inequality constraints. First, we study the scenario where each agent in a coalition has full information of all…
A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an…
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
The most important factors which contribute to the efficiency of game-theoretical algorithms are time and game complexity. In this study, we have offered an elegant method to deal with high complexity of game theoretic multi-objective…
We propose a new General Game Playing (GGP) language called Regular Boardgames (RBG), which is based on the theory of regular languages. The objective of RBG is to join key properties as expressiveness, efficiency, and naturalness of the…
Consider an important meeting to be held in a team-based organization. Taking availability constraints into account, an online scheduling poll is being used in order to decide upon the exact time of the meeting. Decisions are to be taken…
Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions,…
Large Language Models (LLMs) are increasingly deployed in real-world scenarios where they may lack sufficient information to complete a given task. In such settings, the ability to actively seek out missing information becomes a critical…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…