Core Mechanics
Collecting
Points
collecting
score
feedback
exchange
customization
Customisation
Exchange
There are not a lot of games that do an exchange that I know of but one game that I do know that does is Pokemon. In Pokemon, you can exchange Pokemon with other players either for Pokemon you don't have or better Pokemon.
In most games, it is required to collect. Ether its collecting Easter egg or collecting little things which may be used as points to buy upgrades, weapons or if you reach a 100 points you get a life.
points can be used as a see which player is better than the other with a scoring system. points can also be used as money in the game to unlock unlockables.
Not a lot of games have customization this is because its easier to program a single character that will not change throw out the game then make multiple which the code has to change every time the person changes there character or the made weapon.