Steven J. Brams
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View article: Making tennis fairer: The grand tiebreak <sup/>
Making tennis fairer: The grand tiebreak <sup/> Open
Tennis, like other games and sports, is governed by rules, including the rules that determine the winner of points, games, sets, and matches. If the two players are equally skilled, each has an equal chance of winning matches. However, the…
View article: Revisiting the Secretary Problem
Revisiting the Secretary Problem Open
The venerable Secretary Problem asks how a decision maker (DM) should select one of n candidates, who come up randomly, when the only information available is each candidate’s strict rank within the set of previous applicants. Moreover, DM…
View article: Multi-Tier Tournaments: Matching and Scoring Players
Multi-Tier Tournaments: Matching and Scoring Players Open
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.…
View article: A game that poses a challenge to artificial intelligence
A game that poses a challenge to artificial intelligence Open
A game that poses a challenge to artificial intelligence Steven J. Brams, hailing from New York University, unveils a game that poses a challenge to artificial intelligence. Artificial intelligence (AI) has enormous promise and huge risk. …
View article: Fairer Shootouts in Soccer: The ( <i>m, n</i> ) Rule
Fairer Shootouts in Soccer: The ( <i>m, n</i> ) Rule Open
Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidenc…
View article: Multi-Tier Tournaments: Matching and Scoring Players
Multi-Tier Tournaments: Matching and Scoring Players Open
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.…
View article: Fairer Shootouts in Soccer: The $m-n$ Rule
Fairer Shootouts in Soccer: The $m-n$ Rule Open
Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidenc…
View article: On Maxsum Fair Cake Divisions
On Maxsum Fair Cake Divisions Open
We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations …
View article: Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black
Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black Open
Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move foll…
View article: Two-Person Fair Division of Indivisible Items: Compatible and Incompatible Properties
Two-Person Fair Division of Indivisible Items: Compatible and Incompatible Properties Open
Suppose two players wish to divide a finite set of indivisible items, over which each distributes a specified number of points. Assuming the utility of a player’s bundle is the sum of the points it assigns to the items it contains, we anal…
View article: A Note on Stabilizing Cooperation in the Centipede Game
A Note on Stabilizing Cooperation in the Centipede Game Open
In the much-studied Centipede Game, which resembles the Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium i…
View article: Books By Our Readers
Books By Our Readers Open
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View article: Divine Games: Game Theory and the Undecidability of a Superior Being
Divine Games: Game Theory and the Undecidability of a Superior Being Open
A game-theoretical analysis of interactions between a human being and an omnipotent and omniscient godlike being highlights the inherent unknowability of the latter's superiority. In Divine Games, Steven Brams analyzes games that a human b…
View article: Making the Rules of Sports Fairer
Making the Rules of Sports Fairer Open
The rules of many sports are not fair — they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all f…
View article: Making the Rules of Sports Fairer
Making the Rules of Sports Fairer Open
The rules of many sports are not fair—they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all fiv…