A simple idea towards competition is to judge who is the winner, which called direct competition. In this situation, players in a game compete with each other in certain resources. I can get more from yours loss. In early farm simulation F2P games, such as Happy Farm (2008), the stealing crops mechanic makes players get the exact number of crops from the others’ loss. So there is a problem, if the competition is about 2 players and players who lose will not be happy with that, only half of the players can get fun from it. Clash of Clans make a improvement on it, when you defeating the opponents, you get exact what you should get, but the opponents do not lose as much as your rewards. Instead, they just lose half or even one fourth of your rewards. It makes everyone feels better but still keeps the competitive feature.
There is another kind of competition where everyone is the winner but someone more outstanding will win more. (It is so ironic and reminds me of “All animals are equal, but some animals are more equal than others”). In a lot of F2P card games, they use this mechanic. For example, in Million Arthur, every week there will be events hosted by the publisher. Everyone takes part in the event can get reward. But if you want the awesome reward, you need to be better than others. In other words, you need more investments, including money and time.
The classical cooperation in online games is synchronous (direct) cooperation, such as World of Warcraft. Players need to get online at the same time and play together to get extra bonus. It elicits more investments to the game because every companion’s engagement facilitate your engagement. However, for this kind of cooperation, pressures come with encouragement from your companions. You are not only encourage to play with friends at the same time, but also you are required to play with friends at the same time to ensure your and their bonus. That is why I stopped playing WoW.
Of course, the other kind of cooperation is asynchronous (indirect) cooperation, which means players can give others hand without being same time in the game. For example, I can help my friends by helping gardening their farm in Hayday. Players are not required to playing at the same totally. But players can still feel that other players exist and matter in the game.
In summary, most free-to-play games have these two kind of interactions between players because they are so fundamental. The level of these interactions really matters the target customers of the game. Direct means more focused and heavy players. Otherwise, the counterpart is relaxed and light players. Competition indicates male and strategy players. Cooperation indicates female and simulation players.