Related papers: How to Design a Stable Serial Knockout Competition
Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…
We propose a new single-winner voting system using ranked ballots: Stable Voting. The motivating principle of Stable Voting is that if a candidate A would win without another candidate B in the election, and A beats B in a head-to-head…
We are concerned with the stability of a coalitional game, i.e., a transferable-utility (TU) cooperative game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings.…
We carry out a game-theoretic analysis of the recursive game "Guts," a variant of poker featuring repeated play with possibly growing stakes. An interesting aspect of such games is the need to account for funds lost to all players if…
We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously;…
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…
Online games are the most popular form of entertainment among youngsters as well as elders. Recognized as e-Sports, they may become an official part of the Olympic Games by 2020. However, a long waiting time for matchmaking will largely…
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…
In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…
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 unimodular if the determinant of its skew-adjacency matrix is $1$. In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament $T$ with skew-adjacency matrix $S$ is invertible…
The group stage of a sports tournament is often made more appealing by introducing additional constraints in the group draw that promote an attractive and balanced group composition. For example, the number of intra-regional group matches…
Incentivizing the existing participants to invite new participants to join an auction, matching or cooperative game have been extensively studied recently. One common challenge to design such incentive in these games is that the invitees…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable…
Many sports tournaments are organised in a hybrid design consisting of a round-robin group stage followed by a knock-out phase. The traditional seeding regime aims to create balanced groups roughly at the same competition level but may…
We use replicator dynamics to study an iterated prisoners' dilemma game with memory. In this study, we investigate the characteristics of all 32 possible strategies with a single-step memory by observing the results when each strategy…
A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…
A new formalism for analyzing the progression of cricket game using Stochastic differential equation (SDE) is introduced. This theory enables a quantitative way of representing every team using three key variables which have physical…
In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct…