Related papers: Probabilistic model for Padel games dynamics
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Tennis is one of the world's biggest and most popular sports. Multiple researchers have, with limited success, modeled the outcome of matches using probability modelling or machine learning approaches. The approach presented here predicts…
In the run-up to any major sports tournament, winning probabilities of participants are publicized for engagement and betting purposes. These are generally based on simulating the tournament tens of thousands of times by sampling from…
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…
We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any action profile, player B's payoff coincides with player A's payoff with probability p…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
Stochastic games are fundamental in various applications, including the control of cyber-physical systems (CPS), where both controller and environment are modeled as players. Traditional algorithms typically aim to determine a single…
Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of…
Passing during power plays in hockey is a crucial component to move one's team closer to scoring a goal. With the use of women's ice hockey event and tracking data from the elimination round games during the 2022 Winter Olympics, we…
Forecasting sporting events encapsulate a compelling intellectual endeavor, underscored by the substantial financial activity of an estimated $80 billion wagered in global sports betting during 2022, a trend that grows yearly. Motivated by…
The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in many settings of interest, agent utility functions themselves vary as a…
This article presents a holistic compound Poisson regression model framework to forecast number of corner kicks taken in association football. Corner kick taken events are often decisive in the match outcome and inherently arrive in batch…
We investigate how to efficiently predict play personas based on playtraces. Play personas can be computed by calculating the action agreement ratio between a player and a generative model of playing behavior, a so-called procedural…
There have been several popular reports of various groups exploiting the deterministic nature of the game of roulette for profit. Moreover, through its history the inherent determinism in the game of roulette has attracted the attention of…