Related papers: Lead distance under a pickoff limit in Major Leagu…

Stochastic two-player games model systems with an environment that is both adversarial and stochastic. The adversarial part of the environment is modeled by a player (Player 2) who tries to prevent the system (Player 1) from achieving its…

We formulate the head-to-head matchups between Major League Baseball pitchers and batters from 1954 to 2008 as a bipartite network of mutually-antagonistic interactions. We consider both the full network and single-season networks, which…

We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…

We study discounted infinitely repeated games in which players agree on a cooperative mixed action profile but, at each step, observe only the realized pure actions. This form of imperfect monitoring breaks classical trigger strategies,…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

In an introductory paper on dollar game played on a graph, Matt Baker wrote the following: ``The total number of borrowing moves required to win the game when playing the 'borrowing binge strategy' is independent of which borrowing moves…

We propose a decentralized solution for a pursuit-evasion game involving a heterogeneous group of rational (selfish) pursuers and a single evader based on the framework of potential games. In the proposed game, the evader aims to delay (or,…

Repeated games are useful models to analyze long term interactions of living species and complex social phenomena. Zero-determinant (ZD) strategies in repeated games discovered by Press and Dyson in 2012 enforce a linear payoff relationship…

We consider concurrent games played on graphs. At every round of the game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…

Two-vehicle racing is natural example of a competitive dynamic game. As with most dynamic games, there are many ways in which the underlying solution concept can be structured, resulting in different equilibrium concepts. The assumed…

We consider autonomous racing of two cars and present an approach to formulate racing decisions as a non-cooperative non-zero-sum game. We design three different games where the players aim to fulfill static track constraints as well as…

We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…

We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…

We present a tractable framework for detecting changes in performance metrics and apply these methods to Major League Baseball (MLB) batting and pitching data from the 2023 and 2024 seasons. We propose a changepoint detection algorithm that…

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…

We investigate the time evolution of lead changes within individual games of competitive team sports. Exploiting ideas from the theory of random walks, the number of lead changes within a single game follows a Gaussian distribution. We show…

In limited overs cricket, the team batting first posts a target score for the team batting second to achieve in order to win the match. The team batting second is constrained by decreasing resources in terms of number of balls left and…

We study countably infinite Markov decision processes (MDPs) with real-valued transition rewards. Every infinite run induces the following sequences of payoffs: 1. Point payoff (the sequence of directly seen transition rewards), 2. Mean…

The infield shift has been increasingly used as a defensive strategy in baseball in recent years. Along with the upward trend in its usage, the notoriety of the shift has grown, as it is believed to be responsible for the recent decline in…

Recent measurement technologies enable us to analyze baseball at higher levels. There are, however, still many unclear points around the pitching strategy. The two elements make it difficult to measure the effect of pitching strategy.…