Related papers: Maximizing Value in Challenge the Champ Tournament…
We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…
In knockout tournaments, players compete in successive rounds, with losers eliminated and winners advancing until a single champion remains. Given a tournament digraph $D$, which encodes the outcomes of all possible matches, and a…
A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd\H{o}s and J. W. Moon. By probabilistic methods, the existence of "unrankable" tournaments was proved. On the other hand, they…
In the light of the need to achieve a ranking which is understood by all tennis supporters, the ATP ranking is exposed to constant complaints from players and at the same time exposes new players to be benefited with a good tournament to be…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…
Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
The organizer of a machine learning competition faces the problem of maintaining an accurate leaderboard that faithfully represents the quality of the best submission of each competing team. What makes this estimation problem particularly…
We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…
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 multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies…
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…
Scheduling a sports tournament is a complex optimization problem, which requires a large number of hard constraints to satisfy. Despite the availability of several such constraints in the literature, there remains a gap since most of the…
A tournament is a complete directed graph. A king in a tournament is a vertex v such that every other vertex is reachable from v via a path of length at most 2. It is well known that every tournament has at least one king, one of which is a…
Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered…
We introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2.…
A king in a directed graph is a vertex $v$ such that every other vertex is reachable from $v$ via a path of length at most $2$. It is well known that every tournament (a complete graph where each edge has a direction) has at least one king.…
We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the…
We characterize robust tournament design -- the prize scheme that maximizes the lowest effort in a rank-order tournament where the distribution of noise is unknown, except for an upper bound, $\bar{H}$, on its Shannon entropy. The robust…