| The existing researches on online rent problem always study the issue assuming astationary rental and purchasing price. Otherwise, we in this article apply a new modeldiscrete online rent model involves variable rental and purchasing price; therefore enlarge themathematic theory meaning of online rent problem. Such studies on online rent problemunder multi-factor affections may make good samples for virtual rent problems.Firstly, we study on the on online rent problem involves variable rental and purchasingprice under both online and offline expense models; secondly, via the study on equilibriumstrategy research, we analyze the worst case of such strategy and we give out the mathematicmodel on the equilibrium strategy of online rent problem, under both the interest-bearing andinterest-free circumstances, we also analyze and demonstrate the equilibrium strategiccompetitive ratio upper and lower boundaries, as well as the random equilibrium strategiccompetitive ratio based on which we develop the online algorithm on rental problemsinvolving variable rental and purchasing price; thirdly, We give out the equilibrium strategicmathematic model involving variable rental and purchasing price under the effect of discountand exchange rate, in which we analyze the competitive features of both the stationary andrandom equilibrium strategies under multi-factor affections. Meanwhile, we work out thecertain competitive ratio upper and lower bound and the random competitive ratio; ultimatelywe engage the numeric experiments to do the analyzing and comparison on the online rentalproblem involving variable fees, we analyze the certain and random equilibrium strategicresults in three different angels: involving or not involving interest, interest differences anddiscount differences. We discover that the higher the interest and the discount is, the lower thecost and the competitive ratio of the strategy will be, the risk of the online costumers iscommensurate to the competitive ratio and thusly shall the investors get certain and stableincome. |
