Network effect can most definitely exist in games. I can personally think of some clear examples, and they all have one thing in common: Networking.
MMORPGS have become a lot more common, of late. It seems like everyone is trying to jump on the bandwagon. If you are unfamiliar with the acronym, it stands for Massive Multiplayer Online Role Playing Games. The thing is, while a game can boast being massive multiplayer, it needs people to make this claim a reality. These games also commonly have a greater focus on the role part of the RPG genre; While most general RPG titles have some allowance for the user to play the game 'solo', many MMORPG titles restrict the player in such ways that many activities simply can not be engage successfully without the cooperation of a group of players.
World of Warcraft is always a good case example for MMORPGs. In the earlier days of "WoW", you would sit around the nearest main towns, and yell out to the many other users playing that you were "LF2M HEALZ DPS DM" (or "Looking for two more, one healer and one damage dealer, to run Dead Mines). Veterans will snicker at the trivial nature of running the Dead Mines in early WoW (given that at the time it was a very low level dungeon), but the point remains; Core damage dealers were generally not very good at absorbing damage, and relied on "tank" characters who were better at distracting enemys and absorbing damage than actually dealing damage. Tanks would not last indefinitely, and relied on a healer to keep them alive, to in turn keep the heat off the damage dealers.
Given that the cooperation of multiple users was required to engage many of the activities, it is not surprising that the reliability of being able to quickly get a group together and run a dungeon was somewhat based off how many users were actively playing on that server at the same time. The amount of users become a point of advertisement.
The above picture is my old box from roughly 2006. You would be naive to think the big gold "Over 5 million online!" was not placed with extreme deliberation; In reality, it is clear that someone has stuck this sticker on after the original box was printed. Almost as if they wanted to make sure the players new that even more people were playing World of Warcraft.
Online Competitive Games
The thing about any game that basis most of its game-play off online competition is that much of the game becomes unplayable if there isn't actually anyone to compete against. Games like League of Legends are only playable in online competition - without other users playing the game, online, you would not be able to play it. These games rely on networking, in that sense. Nobody wants to look at menu screen all day.
Other games may provide a single player experience, but are arguably much more substantial due to their online counterpart. Star Wars Battlefront, Call of Duty and Battlefield come to mind. While these games offer varying degrees of single player campaigns, it is the online multiplayer that has players racking up hours on hours. These days, such games matchmaking the player into giant battles featuring dozens of other players, a system that basis its productivity off of how many users are currently online.
These games become more valuable as more people play them, because it provides greater reliability of being able to find a game. Likewise, as a games user-base dwindles, the hardcore fans that stuck around start to worry that the dwindling number of users might lead to server closures, as the game company behind the IP move their investments towards more popular titles.
Augmented Reality games
Yes, I'm talking about Pokemon Go. Games like this may increase in value as you notice more people playing, as it simply becomes more socially acceptable.
In the early days, I personally gave a couple of AR games a go. Along with killing my battery, I often stopped playing because they made me feel weird. The people around me would be oblivious to the type of game I was playing, and it would not be uncommon to get curious stares, as onlookers tried to work out why I was waving my phone around like mad.
These days, I go to my local park, and there's always a group of people walking around playing Pokemon Go. Seeing so many other people play it, its value increases, for me. I see that it is socially more acceptable, and am less concerned about pulling out my own phone and trying to catch a Pikachu.
It is worth addressing that while I do not have any social phobias, I do know people that do. This sort of "oh hey, other people are doing it, too! I'm allowed to" feeling goes a long way for someone who feels social anxiety, or otherwise doesn't want to 'stand out'.
Any game you want support for after 10+ years
Ultimately, I personally see increased value in any game I enjoy, as more user take it on - even if I never engage with any of these users whatsoever. Ultimately, I know that if many other users are playing the game, the developer is more likely to support the game for longer, and release more content for it.
A good example is Diablo 2. One of my all time personal favorites, and made that much more valuable to me by the consistency in others playing it. In part due to the fact that 16 years down the track the game is still very popular, Blizzard have recently released a new patch for it. As a result, I can now replay my old favorite on my brand new Windows 10 laptop. It's value absolutely skyrockets, in part due to personal opinion and nostalgia.
There's always a downside
There is always a downside to increased 'traffic', if you will. In my personal experience, these downsides take a while longer to reveal themselves, and are far rarer.
- Congestion: If too many people play a game, it can mean longer waiting times. I use to leave my game queued for half an hour or so to log in to World of Warcraft, because too many players played on the same server, and it was always full. Too long experiencing such wait could easily devalue the experience, and in turn, the game. Blizzard quickly countered these issues with new servers, and free character transfers to pull your high-level characters off the highly-congested server.
- Law of Averages: If you put too many people in a room together, your pretty much guaranteed to not like a group of them. It is not uncommon for me to hear that particular users have stopped playing a game, because the community was off-putting. A good example might be Battlefield, where it is not uncommon for users to be hesitant to join team chat. Another good example that springs to mind is the early days of RuneScape 2. RuneScape is the first MMORPG I was ever able to play, due to having incredibly low system requirements, and offering a freemium model to play. Unfortunately, the users that made up the free-access servers were often very immature, especially as more mature users jumped to the subscription model and could access members-only servers. Ultimately, too many users can kill the mood of a game, if their all a bunch of 15 year olds fighting over one block of iron.