Related papers: Achieving the Highest Possible Elo Rating
In two-player zero-sum games, the learning dynamic based on optimistic Hedge achieves one of the best-known regret upper bounds among strongly-uncoupled learning dynamics. With an appropriately chosen learning rate, the social and…
In competitive games, it is common to assign each player a real number rating signifying their skill level. A rating system is a procedure by which player ratings are adjusted upwards each time they win, or downwards each time they lose.…
We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the…
The Shapley value is arguably the most central normative solution concept in cooperative game theory. It specifies a unique way in which the reward from cooperation can be "fairly" divided among players. While it has a wide range of real…
When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive…
Multi-turn, multi-agent LLM game evaluations often exhibit substantial run-to-run variance. In long-horizon interactions, small early deviations compound across turns and are amplified by multi-agent coupling. This biases win rate estimates…
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…
Large language models (LLM) have shown remarkable abilities in text generation, question answering, language translation, reasoning and many other tasks. It continues to advance rapidly and is becoming increasingly influential in various…
People, robots, and companies mostly divide time and effort among projects, and \defined{shared effort games} model people investing resources in public endeavors and sharing the generated values. In linear $\theta$ sharing (effort) games,…
Consider a game consisting of independent turns with even money payoffs in which the player wins with a fixed probability $p \geq 1/3$ and loses with probability $1 - p$. The Labouchere system is a betting strategy which entails keeping a…
In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from…
The following game was introduced in a list of open problems from 1983 attributed to Erd\H{o}s: two players take turns claiming edges of a $K_n$ until all edges are exhausted. Player 1 wins the game if the largest clique that they claim at…
Offline learning has become widely used due to its ability to derive effective policies from offline datasets gathered by expert demonstrators without interacting with the environment directly. Recent research has explored various ways to…
Traditional tennis rating systems (e.g., Elo) summarize overall player strength but do not isolate the independent value of serving. Using point-by-point data from Wimbledon and the U.S.\ Open, we develop serve-specific player metrics that…
Machine intelligence marks the ultimate dream of making machines' intelligence comparable to human beings. While recent progress in Large Language Models (LLMs) show substantial specific skills for a wide array of downstream tasks, they…
Many crucial problems in deep learning and statistical inference are caused by a variational gap, i.e., a difference between model evidence (log-likelihood) and evidence lower bound (ELBO). In particular, in a classical VAE setting that…
In various game scenarios, selecting a fixed number of targets from multiple enemy units is an extremely challenging task. This difficulty stems from the complex relationship between the threat levels of enemy units and their feature…
League of Legends (LoL) is the most widely played multiplayer online battle arena (MOBA) game in the world. An important aspect of LoL is competitive ranked play, which utilizes a skill-based matchmaking system to form fair teams. However,…
We consider the following game. A deck with $m$ copies of each of $n$ distinct cards is shuffled in a perfectly random way. The Guesser sequentially guesses the card from top to bottom. After each guess, the Guesser is informed whether the…
Assessing and comparing player skill in online multiplayer gaming environments is essential for fair matchmaking and player engagement. Traditional ranking models like Elo and Glicko-2, designed for two-player games, are insufficient for…