### Abstract

The conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. In the real world, sometimes the payoffs are not known and have to be estimated, and sometimes the payoffs are only approximately known. This paper develops a solution method for the two-person zero-sum game where the payoffs are imprecise and are represented by interval data. Since the payoffs are imprecise, the value of the game should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game. Based on the duality theorem and by applying a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs. Solving the pair of linear programs produces the interval of the value of the game. It is shown that the two players in the game have the same upper bound and lower bound for the value of the imprecise game. An example illustrates the whole idea and sheds some light on imprecise game.

Original language | English |
---|---|

Pages (from-to) | 1697-1700 |

Number of pages | 4 |

Journal | Computers and Industrial Engineering |

Volume | 56 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 May 1 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Engineering(all)

### Cite this

*Computers and Industrial Engineering*,

*56*(4), 1697-1700. https://doi.org/10.1016/j.cie.2008.06.002

}

*Computers and Industrial Engineering*, vol. 56, no. 4, pp. 1697-1700. https://doi.org/10.1016/j.cie.2008.06.002

**Matrix games with interval data.** / Liu, Shiang Tai; Kao, Chiang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Matrix games with interval data

AU - Liu, Shiang Tai

AU - Kao, Chiang

PY - 2009/5/1

Y1 - 2009/5/1

N2 - The conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. In the real world, sometimes the payoffs are not known and have to be estimated, and sometimes the payoffs are only approximately known. This paper develops a solution method for the two-person zero-sum game where the payoffs are imprecise and are represented by interval data. Since the payoffs are imprecise, the value of the game should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game. Based on the duality theorem and by applying a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs. Solving the pair of linear programs produces the interval of the value of the game. It is shown that the two players in the game have the same upper bound and lower bound for the value of the imprecise game. An example illustrates the whole idea and sheds some light on imprecise game.

AB - The conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. In the real world, sometimes the payoffs are not known and have to be estimated, and sometimes the payoffs are only approximately known. This paper develops a solution method for the two-person zero-sum game where the payoffs are imprecise and are represented by interval data. Since the payoffs are imprecise, the value of the game should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game. Based on the duality theorem and by applying a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs. Solving the pair of linear programs produces the interval of the value of the game. It is shown that the two players in the game have the same upper bound and lower bound for the value of the imprecise game. An example illustrates the whole idea and sheds some light on imprecise game.

UR - http://www.scopus.com/inward/record.url?scp=67349185615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349185615&partnerID=8YFLogxK

U2 - 10.1016/j.cie.2008.06.002

DO - 10.1016/j.cie.2008.06.002

M3 - Article

AN - SCOPUS:67349185615

VL - 56

SP - 1697

EP - 1700

JO - Computers and Industrial Engineering

JF - Computers and Industrial Engineering

SN - 0360-8352

IS - 4

ER -