Silverman's game

Silverman's game

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 threshhold T and penalty u are chosen with 0< u and 1 < "T" < &infin;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 - u if "x"/"y" > "T"; equal numbers involve zero payoff. Thus each player seeks to choose the larger number but, provided u>1, there is a penalty of u for choosing too large a number.

References

* R. J. Evans 1979. "Silverman's game on intervals". American Mathematical Monthly, volume 86, number 5, pp. 277&ndash;281.


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