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Bret Benesh

Publications and source records attributed to Bret Benesh.

4 recordsLinked to original sources

Reducing the Incentive to Tank: The Ex Post Gold Plan

Many recent proposals for reducing tanking in draft lotteries share a common structure: losses improve draft position early in the season while wins improve draft position later. While such systems improve late-season incentives, they retain a predictable pivot point that tanking teams can exploit strategically. This paper proposes a simple modification that introduces uncertainty into the timing of the incentive switch. The proposed metric, the \emph{Realized Elimination Wins Determinant} (REWIND), ranks teams according to the number of wins obtained after their ex post elimination date, which makes this a variation of the Gold Plan. Because the ex post elimination date cannot be known with certainty during the season, the mechanism weakens incentives for strategic losing while preserving incentives for competitive effort after elimination. Moreover, the ex post elimination date is typically earlier than other proposed pivot points, so there is a longer period where a tanking team's best strategy is to win. The Ex Post Gold plan uses the REWIND metric to create a simple system where every team will be incentivized to win at least half of their games in most seasons.

math.OC

Group bases for some solvable groups and semidirect products

A set $B$ is a basis for a vector space $V$ if every element of $V$ can be uniquely written as a linear combination of the elements of $B$. There is a similar definition of a basis for a finite group. We show that certain semidirect products of finite groups---including all semidirect products of finite abelian groups---have bases; any group of order $m$ or $2m$ for odd, cube-free $m$ has a basis; and the quaternions do not have a basis.

math.GR

Three-person impartial avoidance games for generating finite cyclic, dihedral, and nilpotent groups

We study a three-player variation of the impartial avoidance game introduced by Anderson and Harary. Three players take turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element that causes the set of jointly-selected elements to be a generating set for the group, with the previous player winning and the remaining player coming in second place. We describe the winning strategy for these games on cyclic, dihedral, and nilpotent groups.

math.GR