Philipp. Sci. Lett. 2013 6 (1) 016-020

available online: January 31, 2013

*Corresponding author

Email Address: gdavid@science.upd.edu.ph

Received: October 28, 2012

Revised: December 9, 2012

Accepted: December 10, 2012

A Variation of Discrete Silverman'sGame with Varying Payoffs

by Guido David* and Richele S. De AsisInstitute of Mathematics, and

Computational Science Research Center

University of the Philippines

Diliman, Quezon City

A discrete form of Silverman's game, a two-playerzero sum game, is played with each playerchoosing a number from 1 to n. Each player's goalis to choose the larger number as long as it is lessthan three times the opponent's chosen number.Here we consider a variation of Silverman's game, wherein thepayoff to the player choosing the larger number is the differencebetween the two numbers, but if the larger number is at leastthree times the smaller number, the payoff to the player choosingthe smaller number is twice the difference between the twonumbers. Analysis of payoff matrices and the Minimax Theoremare used to solve the game. In both versions of the game, resultsshow that when n = 3 the unique optimal strategy reduces eachplayer's choices to just three numbers. The difference betweenthe two solutions is in the probabilities each player must selectthe three choices.