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Searching for a fracture as a two-person zero-sum game

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  • Braester, Carol
  • Barak, Liana

Abstract

Searching for a fracture of a given hydraulic conductivity in a fractured rock, by means of observation bodies such as bore holes, is similar to a decision problem in a two-person zero-sum game with incomplete information. The searcher and the hidden fracture are considered the two players of the game. There is a finite number of moves or pure strategies in the hands of each player, that is, the former may drill a finite number of bore holes and the latter may be located or not in a certain hydraulic conductivity range of interest. A game model corresponding to this situation, taking into consideration the log-normal fracture hydraulic conductivity distribution, consistent with the occurrence in nature, is presented. The probability of finding a fracture in the jth interval of the hydraulic conductivity probability density function (PDF) graph after i drillings is taken as the payoff matrix of the game. The presented game model provides a solution for finding the number of bore holes to be drilled for intersecting a fracture within a prescribed hydraulic conductivity range. The method is exemplified for a particular data set.

Suggested Citation

  • Braester, Carol & Barak, Liana, 1991. "Searching for a fracture as a two-person zero-sum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 1-8.
    • Handle: RePEc:eee:phsmap:v:175:y:1991:i:1:p:1-8
    DOI: 10.1016/0378-4371(91)90265-E
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    Cited by:

    1. Barak, Liana & Braester, Carol, 1991. "Searching for fractures in a fracture network - a game theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(3), pages 311-318.

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