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The forecasting of sports events is of broad interest from the applied but also from the theoretical perspective. In this work the question is addressed for the example of the German soccer Bundesliga how a theoretically optimum forecast of…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
Bipartite matching problem is to study two disjoint groups of agents who need to be matched pairwise. It can be applied to many real-world scenarios and explain many social phenomena. In this article, we study the effect of competition on…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
Much of modern society is founded on orchestrating institutions that produce social goods by fostering motivated teams, pitting them against each other, and distributing the fruits of the arms races that ensue. However, even when the…
Organizations learn from the market, political, and societal responses to their actions. While in some cases both the actions and responses take place in an open manner, in many others, some aspects may be hidden from external observers.…
Structural change consists of industrial diversification towards more productive, knowledge intensive activities. However, changes in the productive structure bear inherent links with job creation and income distribution. In this paper, we…
Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…
In soccer, game context can result in skewing offensive statistics in ways that might misrepresent how well a team has played. For instance, in England's 1-2 loss to France in the 2022 FIFA World Cup quarterfinal, England attempted…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
RoboCup soccer competitions are considered among the most challenging multi-robot adversarial environments, due to their high dynamism and the partial observability of the environment. In this paper we introduce a method based on a…
Recent advances in reinforcement learning with social agents have allowed us to achieve human-level performance on some interaction tasks. However, most interactive scenarios do not have as end-goal performance alone; instead, the social…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…
Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M. If M is an orthogonal matrix, then a digraph which supports M…
In simple games, larger coalitions typically wield more power, but do all players align their efforts effectively? Consider a voting scenario where a coalition forms, but needs more voters to pass a bill. The cohesion of the new group of…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
The development of cooperative relations within and between firms plays an important role in the successful implementation of business strategy. How to produce such relations is less well understood. We build on work in relational contract…
The demand for global university league tables has been high over the past two decades. However, significant criticism of their methodologies is accumulating without being addressed. I revisit global university league tables by normalizing…
Challenge the Champ is a simple tournament format, where an ordering of the players -- called a seeding -- is decided. The first player in this order is the initial champ, and faces the next player. The outcome of each match decides the…