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In the realm of evolutionary game theory, standard frameworks typically presuppose that every player possesses comprehensive knowledge and unrestricted access to the entire strategy space. However, real-world human society inherently…
The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…
To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hope of successful reproduction. In structured populations the array of those that are eligible…
In games like chess, strategy evolves dramatically across distinct phases - the opening, middlegame, and endgame each demand different forms of reasoning and decision-making. Yet, many modern chess engines rely on a single neural network to…
Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently it has been introduced into evolutionary game theory. In evolutionary game dynamics, the…
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…
We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We…
Cooperation or defection and participation or withdrawal are well-known options of behavior in game-like activities in free societies, yet the co-evolutionary dynamics of these behavioral traits in the individual level are not well…
The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…
Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…
We consider models of growing multi-level systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy…
How cooperation emerges in human societies is still a puzzle. Evolutionary game theory has been the standard framework to address this issue. In most models, every individual plays with all others, and then reproduce and die according to…
We examine the impact of a change in diversity introduced by a new product on the evolution of an economic system. Modeling Schumpeterian competition as a population game with a unique, attracting, evolutionarily stable state (the…
We study the evolution of cooperation in structured populations within popular models of social dilemmas, whereby simple coevolutionary rules are introduced that may enhance players abilities to enforce their strategy on the opponent.…
Prioritized experience replay is a reinforcement learning technique whereby agents speed up learning by replaying useful past experiences. This usefulness is quantified as the expected gain from replaying the experience, a quantity often…
We define a novel quantitative strategy inspired by the ecological notion of nestedness to single out the scale at which innovation complexity emerges from the aggregation of specialized building blocks. Our analysis not only suggests that…
Large Language Models (LLMs) exhibit remarkable capabilities, yet it remains unclear to what extent these reflect sophisticated recall or genuine reasoning ability. We introduce chess as a controlled testbed aimed at disentangling these…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
We propose a new framework for imitation learning -- treating imitation as a two-player ranking-based game between a policy and a reward. In this game, the reward agent learns to satisfy pairwise performance rankings between behaviors,…