Codex Nitriensis: Difference between revisions

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In [[game theory]], '''Silverman's game''' is a [[zero sum game]] played on the [[unit square]].  It is named for [[David Silverman (mathematician)|David Silverman]].
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It is played by two players on a given set ''S'' of [[positive number|positive real numbers]].  Before play starts, a threshold <math>T</math> and penalty <math>\nu</math> are chosen with <math>0<\nu<\infty</math> and 1&nbsp;<&nbsp;''T''&nbsp;<&nbsp;&infin;
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Each player chooses an element of ''S''.  [[Without loss of generality]], suppose player A plays ''x'' and player B plays ''y'', with ''x''&nbsp;>&nbsp;''y''.  Then the payoff to A is 1 if 1&nbsp;<&nbsp;''x''/''y''&nbsp;<&nbsp;''T'' and <math>-\nu</math> if ''x''/''y''&nbsp;>&nbsp;''T''; equal numbers involve zero payoff. Thus each player seeks to choose the larger number, but there is a penalty of <math>\nu</math> for choosing too large a number.
 
==References==
 
* R. J. Evans 1979.  ''Silverman's game on intervals''.  [[American Mathematical Monthly]], volume 86, number 4, pp. 277&ndash;281.
 
 
{{gametheory-stub}}
[[Category:Game theory]]

Latest revision as of 20:31, 3 September 2014

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