Related papers: Games for Succinctness of Regular Expressions

Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The…

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play…

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier)…

Game semantics has been used with considerable success in formulating fully abstract semantics for languages with higher-order procedures and a wide range of computational effects. Recently, nominal games have been proposed for modelling…

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in…

We investigate the following version of the well-known R\'enyi-Ulam game. Two players - the Questioner and the Responder - play against each other. The Responder thinks of a number from the set $\{1,\ldots,n\}$, and the Questioner has to…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

This paper presents a new model for word sense disambiguation formulated in terms of evolutionary game theory, where each word to be disambiguated is represented as a node on a graph whose edges represent word relations and senses are…

Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether agents have…

We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…

The Minority Game is a simple model for the collective behavior of agents in an idealized situation where they have to compete through adaptation for a finite resource. This review summarizes the statistical mechanics community efforts to…

This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…

Game theory, as an analytical tool, is frequently utilized to analyze human behavior in social science research. With the high alignment between the behavior of Large Language Models (LLMs) and humans, a promising research direction is to…

We investigate the proof theory of regular expressions with fixed points, construed as a notation for (omega-)context-free grammars. Starting with a hypersequential system for regular expressions due to Das and Pous, we define its extension…

Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in…

We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…

The remoteness from a simple game to a weighted game can be measured by the concept of the dimension or the more general Boolean dimension. It is known that both notions can be exponential in the number of voters. For complete simple games…

In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical…

Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of…

Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…