Combine multiple games into one program

I am trying to make an arduino gaming system with a 16x2 lcd screen. I have managed to find around 4 games that I would like to use on it, but I can't find a way to combine them into one program; I don't want to have to upload a new program every time I want to switch game. I would like to know if anyone has any suggestions, or would be willing to help me to do this. Moreover, they all need to use the same button pins and potentiometer pins:
-Main button pin 6
-potentiometer pin A0
-piezo (if needed) pin A1

Games:
-Truck lane
-Ariadne
-Dotship
-Zombie showdown

Any help or directions would be helpful.
Thanks

Edit:
LCD pins are as found on tutorial
Game links are as follows:
-Zombie Showdown: http://forum.arduino.cc/index.php/topic,7808.0.html (there is a version in the comments with graphics)
-Ariadne: http://forum.arduino.cc/index.php/topic,7808.0.html
-Truck lane: http://www.instructables.com/id/Truck-Lane-a-16x2-LCD-Arduino-game/
-Dotship: Dotship, an Arduino Game (LCD, Pot and Pushbutton) ยท GitHub
Thanks again

You can have only one loop() and only one setup() so the first step is to re-name the loop() and setup() functions in each sketch. Make a new loop() that calls the loop() function of the currently selected game. Make a new setup() function that calls the setup() functions of each of the games. Move any code common to more than one game to the one setup() so the LCD, for example, only gets initialized once. The code to switch games will probably need to call the setup() for the newly selected game.

Good luck.

Thanks, but I'm still a little lost as to where all the start up code will go. And should i use a case statement and a menu to choose which game to use? Any code for a menu would be gratefully received, and I would welcome any advice about all the custom characters needed. Thanks in advance.