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Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the Bradley-Terry model, which incorporates the…

In recent years, analytics has started to revolutionize the game of basketball: quantitative analyses of the game inform team strategy, management of player health and fitness, and how teams draft, sign, and trade players. In this review,…

We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…

We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic…

In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's…

Partially observable stochastic games provide a rich mathematical paradigm for modeling multi-agent dynamic decision making under uncertainty and partial information. However, they generally do not admit closed-form solutions and are…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…

This paper studies the optimization of strategies in the context of possibly randomized two players zero-sum games with incomplete information. We compare 5 algorithms for tuning the parameters of strategies over a benchmark of 12 games. A…

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…

As the technology advances, an ample amount of data is collected in sports with the help of advanced sensors. Sports Analytics is the study of this data to provide a constructive advantage to the team and its players. The game of…

We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two…

This paper tackles the problem of adversarial examples from a game theoretic point of view. We study the open question of the existence of mixed Nash equilibria in the zero-sum game formed by the attacker and the classifier. While previous…

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…

We address the value of a baserunner at first base waiting to see if a ball in play falls in for a hit, before running. When a ball is hit in the air, the baserunner will usually wait, to gather additional information as to whether a ball…

The application of Data Science and Analytics to optimize or predict outcomes is Ubiquitous in the Modern World. Data Science and Analytics have optimized almost every domain that exists in the market. In our survey, we focus on how the…

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

We investigate zero-sum turn-based two-player stochastic games in which the objective of one player is to maximize the amount of rewards obtained during a play, while the other aims at minimizing it. We focus on games in which the minimizer…

Many security and other real-world situations are dynamic in nature and can be modelled as strictly competitive (or zero-sum) dynamic games. In these domains, agents perform actions to affect the environment and receive observations --…