Related papers: A Discrete Evolutionary Model for Chess Players' R…
Various social contexts ranging from public goods provision to information collection can be depicted as games of strategic interactions, where a player's well-being depends on her own action as well as on the actions taken by her…
Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Game-theoretic solution concepts, such as the Nash equilibrium, have been key to finding stable joint actions in multi-player games. However, it has been shown that the dynamics of agents' interactions, even in simple two-player games with…
The environment undergoes perpetual changes that are influenced by a combination of endogenous and exogenous factors. Consequently, it exerts a substantial influence on an individual's physical and psychological state, directly or…
The Elo rating system has been recognised as an effective method for modelling students and items within adaptive educational systems. The existing Elo-based models have the limiting assumption that items are only tagged with a single…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…
The voter model on networks is crucial to understand opinion formation. Uni-directional social interactions are ubiquitous in real social networks whereas undirected interactions are intensively studied. We establish a voter model on a…
We investigate the effects of update rules on the dynamics of an evolutionary game-theoretic model - the N-player evolutionary trust game - consisting of three types of players: investors, trustworthy trustees, and untrustworthy trustees.…
In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new…
People make strategic decisions many times a day - during negotiations, when coordinating actions with others, or when choosing partners for cooperation. The resulting dynamics can be studied with learning theory and evolutionary game…
We study how reasoning evolves in a language model -- from supervised fine-tuning (SFT) to reinforcement learning (RL) -- by analyzing how a set of theoretically-inspired datasets influences language model performance in chess. We find that…
In this paper we present results from recent experiments that suggest that chess players associate emotions to game situations and reactively use these associations to guide search for planning and problem solving. We describe the design of…
We present a stochastic model for a social network, where new actors may join the network, existing actors may become inactive and, at a later stage, reactivate themselves. Our model captures the evolution of the network, assuming that…
An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (``mutant'') strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the…
This paper investigates the evaluation of learned multiagent strategies in the incomplete information setting, which plays a critical role in ranking and training of agents. Traditionally, researchers have relied on Elo ratings for this…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Learning in games refers to scenarios where multiple players interact in a shared environment, each aiming to minimize their regret. An equilibrium can be computed at a fast rate of $O(1/T)$ when all players follow the optimistic…