Game Theory problem using Saddle point Method & Example-1

1. Find out the elements that is same in rectangle [ ] and circle ( ). 2. If Column MiniMax = Row MaxiMin then the game has saddle ... Weusecookiestoimproveyourexperienceonoursiteandtoshowyourelevantadvertising. Bybrowsingthiswebsite,youagreetoouruseofcookies.Learn more   Supportus (New)Allproblemcanbesolvedusingsearchbox Iwanttosellmywebsitewww.AtoZmath.comwithcompletecode Home What'snew CollegeAlgebra Games Feedback Aboutus Algebra Matrix&Vector NumericalMethods StatisticalMethods OperationResearch WordProblems Calculus Geometry Pre-Algebra Home>OperationResearchcalculators>GameTheory>>SaddlePointexample 1.Saddlepointexample (Enteryourproblem) (Enteryourproblem) Method&Example-1Example-2 Otherrelatedmethods SaddlepointDominancemethodAlgebraicmethodCalculusmethodArithmeticmethodMatrixmethod2XnGamesGraphicalmethodLinearprogrammingmethodBimatrixmethod 2.Example-2(Nextexample)1.Method&Example-1 Method saddlepointSteps(Rule) Step-1: 1.SelecttheminimumelementfromeachrowandwritetheminRowMinimumcolumn. 2.SelectthemaximumelementfromRowMinimumcolumnandencloseitin[].ItiscalledRowMaxiMin. Step-2: 1.SelectthemaximumelementfromeachcolumnandwritetheminColumnMaximumrow. 2.SelecttheminimumelementfromColumnMaximumrowandencloseitin().ItiscalledColumnMiniMax. Step-3: 1.Findouttheelementsthatissameinrectangle[]andcircle(). 2.IfColumnMiniMax=RowMaxiMinthenthegamehassaddlepointanditisthevalueofthegame. Example-1 FindSolutionofgametheoryproblemusingsaddlepointPlayerA\PlayerBB1B2B3B4A120151235A22514810A3402105A4-54110Solution:1.SaddlepointtestingPlayersPlayer`B``B_1``B_2``B_3``B_4`Player`A``A_1` 20  15  12  35 `A_2` 25  14  8  10 `A_3` 40  2  10  5 `A_4` -5  4  11  0 Weapplythemaximin(minimax)principletoanalyzethegame.Player`B``B_1``B_2``B_3``B_4`RowMinimumPlayer`A``A_1` 20  15  [(12)]  35 `[12]``A_2` 25  14  8  10 `8``A_3` 40  2  10  5 `2``A_4` -5  4  11  0 `-5`ColumnMaximum`40``15``(12)``35`SelectminimumfromthemaximumofcolumnsColumnMiniMax=(12)SelectmaximumfromtheminimumofrowsRowMaxiMin=[12]Here,ColumnMiniMax=RowMaxiMin=12`:.`Thisgamehasasaddlepointandvalueofthegameis12TheoptimalstrategiesforbothplayersareTheplayerAwillalwaysadoptstrategy1TheplayerBwillalwaysadoptstrategy3 Thismaterialisintendedasasummary.Useyourtextbookfordetailexplanation.Anybug,improvement,feedbackthenSubmitHere 2.Example-2(Nextexample) Sharethissolutionorpagewithyourfriends. Home What'snew CollegeAlgebra Games Feedback Aboutus   Copyright©2022.Allrightsreserved. Terms, Privacy      .