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...Introduction game theory was developed for the purpose of analyzing competitive situations involving conflicting interests in other words is used decision making under where there are one or more opponents i e players example chess poker etc games which have characteristics a competition and played according to definite rules provides solutions such assuming that each wants maximize his profits minimize losses what underlying assumptions finite numbers competitors act reasonably every player strives gains has number possible courses action choices assumed be made simultaneously so no knows opponent s choice until he decided own course pay off fixed predetermined offs must represent utilities function let any matrix order m x n then mathematical expectation denoted by p q defined as aij piqj j mixed strategies b respectively value it refers expected outcome per play when follow their optimal strategy generally v byv subsequent sections this chapter we provide several trivial illustratio...