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In many real-world settings agents engage in strategic interactions with multiple opposing agents who can employ a wide variety of strategies. The standard approach for designing agents for such settings is to compute or approximate a…
At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff…
We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry…
Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…
Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial profits. Despite the strong connection existing between football models and the bookmakers' betting odds, no authors have…
This paper employs a Bayesian methodology to predict the results of soccer matches in real-time. Using sequential data of various events throughout the match, we utilize a multinomial probit regression in a novel framework to estimate the…
The goal of agents in multi-agent environments is to maximize total reward against the opposing agents that are encountered. Following a game-theoretic solution concept, such as Nash equilibrium, may obtain a strong performance in some…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
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.…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
Game-theoretic concepts have been extensively studied in economics to provide insight into competitive behaviour and strategic decision making. As computing systems increasingly involve concurrently acting autonomous agents, game-theoretic…
Dynamically planning in complex systems has been explored to improve decision-making in various domains. Professional basketball serves as a compelling example of a dynamic spatio-temporal game, encompassing context-dependent…
Classical results of Decision Theory, and its extension to a multi-agent setting: Game Theory, operate only at the associative level of information; this is, classical decision makers only take into account probabilities of events; we go…
Major League Baseball (MLB) has a storied history of using statistics to better understand and discuss the game of baseball, with an entire discipline of statistics dedicated to the craft, known as sabermetrics. At their core, all…
This paper explores multi-entry strategies for betting pools related to single-elimination tournaments. In such betting pools, participants select winners of games, and their respective score is a weighted sum of the number of correct…
When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
It is common to be interested in rankings or order relationships among entities. In complex settings where one does not directly measure a univariate statistic upon which to base ranks, such inferences typically rely on statistical models…
Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in…