Silverman's game
Encyclopedia
In game theory
, Silverman's game is a zero sum game played on the unit square
. It is named for David Silverman.
It is played by two players on a given set S of positive real numbers. Before play starts, a threshold
and penalty 
are chosen with 
and 1 < T < ∞
Each player chooses an element of S. Without loss of generality
, suppose player A plays x and player B plays y, with x > y. Then the payoff to A is 1 if 1 < x/y < T and
if x/y > T; equal numbers involve zero payoff. Thus each player seeks to choose the larger number but, provided 
, there is a penalty of 
for choosing too large a number.
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, Silverman's game is a zero sum game played on the unit square
Unit square
In mathematics, a unit square is a square whose sides have length 1. Often, "the" unit square refers specifically to the square in the Cartesian plane with corners at , , , and .-In the real plane:...
. It is named for David Silverman.
It is played by two players on a given set S of positive real numbers. Before play starts, a threshold
and penalty are chosen with and 1 < T < ∞Each player chooses an element of S. Without loss of generality
Without loss of generality
Without loss of generality is a frequently used expression in mathematics...
, suppose player A plays x and player B plays y, with x > y. Then the payoff to A is 1 if 1 < x/y < T and
if x/y > T; equal numbers involve zero payoff. Thus each player seeks to choose the larger number but, provided , there is a penalty of for choosing too large a number.