There are many applications available on AppStore that require firmware 3.1.3 installed on your iPhone. However if you don’t want to upgrade the iphone firmware, here is a simple solution for this problem.
On Cydia a tweaking app is released for jailbroken iPhones that will allow iPhone users to install the apps which are specifically released for iPhone OS 3.1.3. The purpose of this app is very simple as it replaces the information contained in a variable that shows the firmware version of iPhone/iPod.
You can find the “Firmware 3.1.3” in cydia via the BigBoss respository. I remember that another app, Fake 3.1.3, is also available for the same purpose but I don’t know what is the difference between the functioning method of these two apps.