Related papers: Depth, balancing, and limits of the Elo model
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
Rating systems play a crucial role in evaluating player skill across competitive environments. The Elo rating system, originally designed for deterministic and information-complete games such as chess, has been widely adopted and modified…
Elo rating systems measure the approximate skill of each competitor in a game or sport. A competitor's rating increases when they win and decreases when they lose. Increasing one's rating can be difficult work; one must hone their skills…
ELO rating system is proposed by Arpad Elo, a Hungarian-American physics professor. Originally, it was proposed for the ranking system of chess players, but it was soon adapted to many other zero-sum sports fields like football, baseball,…
The Elo rating system, which was originally proposed by Arpad Elo for chess, has become one of the most important rating systems in sports, economics and gaming nowadays. Its original formulation is based on two-player zero-sum games, but…
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
Reasoning is not just about solving problems -- it is also about evaluating which problems are worth solving at all. Evaluations of artificial intelligence (AI) systems primarily focused on problem solving, historically by studying how…
Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…
We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…
Evaluation has traditionally focused on ranking candidates for a specific skill. Modern generalist models, such as Large Language Models (LLMs), decidedly outpace this paradigm. Open-ended evaluation systems, where candidate models are…
In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…
Scalable oversight, the process by which weaker AI systems supervise stronger ones, has been proposed as a key strategy to control future superintelligent systems. However, it is still unclear how scalable oversight itself scales. To…
When mathematical modelling is applied to capture a complex system, multiple models are often created that characterize different aspects of that system. Often, a model at one level will produce a prediction which is contradictory at…
It was recently observed that Elo ratings fail at preserving transitive relations among strategies and therefore cannot correctly extract the transitive component of a game. We provide a characterization of transitive games as a weak…
We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the…
Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an…
Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…
The Elo rating system is a simple and widely used method for calculating players' skills from paired comparisons data. Many have extended it in various ways. Yet the question of updating players' variances remains to be further explored. In…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…