Related papers: An estimation method for game complexity
The paper reviews two prominent approaches for the measurement of technological complexity: the method of reflection and the assessment of technologies' combinatorial difficulty. It discusses their central underlying assumptions and…
Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the…
We introduce a one-person game that we call Padlock Solitaire which resembles the well-known clock solitaire card game. Analyzing variants of this game we obtain simple proofs of some classical results of combinatorics including ballot…
Decades of research have been invested in making computer programs for playing games such as Chess and Go. This paper focuses on a new game, Tetris Link, a board game that is still lacking any scientific analysis. Tetris Link has a large…
In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify…
We consider approximating the minmax value of a multi-player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of epsilon log n digits (for any constant epsilon>0 is…
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…
We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game---a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically…
In recent years, there has been a growing interest in games on graphs within the research community, fueled by their relevance in applications such as economics, politics, and epidemiology. This paper aims to comprehensively detail the…
We present a general algorithm to order moves so as to speedup exact game solvers. It uses online learning of playout policies and Monte Carlo Tree Search. The learned policy and the information in the Monte Carlo tree are used to order…
We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
We show that the quantum query complexity of evaluating NAND-tree instances with average choice complexity at most $W$ is $O(W)$, where average choice complexity is a measure of the difficulty of winning the associated two-player game. This…
Pebble games were extensively studied in the 1970s and 1980s in a number of different contexts. The last decade has seen a revival of interest in pebble games coming from the field of proof complexity. Pebbling has proven to be a useful…
We consider a variation on Maker-Breaker games on graphs or digraphs where the edges have random costs. We assume that Maker wishes to choose the edges of a spanning tree, but wishes to minimise his cost. Meanwhile Breaker wants to make…
Recent advances in Large Language Models (LLMs) have demonstrated their potential as autonomous agents across various tasks. One emerging application is the use of LLMs in playing games. In this work, we explore a practical problem for the…
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…
We analyze the computational complexity of several popular video games released for the Nintendo Game Boy video game console. We analyze the complexity of generalized versions of four popular Game Boy games: Donkey Kong, Wario Land, Harvest…
Large language models (LLMs) have achieved striking successes on many benchmarks, yet recent studies continue to expose fundamental weaknesses. In this paper, we introduce Concept, a simple word-guessing board game, as a benchmark for…
Human computation games (HCGs) are a crowdsourcing approach to solving computationally-intractable tasks using games. In this paper, we describe the need for generalizable HCG design knowledge that accommodates the needs of both players and…