Player Interaction
I'm now of the opinion that interaction is unequivocally good, and important. Some of the most memorable moments are borne of competition or teamwork.
Other factors aside, more interaction is better.
Negotiation, trading & auctions
These highly interactive social mechanics provide more than enough interaction, but they have a huge impact on the play and feel of a game. They make a game very political, and less strategic. Do not include them in your game, unless that's what the game is supposed to be about.
I design games with lower interaction, but that's only because that type of game is about building or exploring something. The lower interaction is a downside, compensated for by the fact that the activity is very interesting. I look for every opportunity to inject interactivity into those games' systems.
In my adventure game, the players would go around exploring. The interaction was a bit low, so I added stealable items. Now, the players chase each other around the map. The emergent fun I've created between the players is far more enjoyable than the interaction between the players and the game. The exploration is still important, but it exists as a backdrop for a giant game of chasey/tag.
Wingspan is fundamentally a solitaire game, but they added competitive goals each round, and a central tray that all players can draw bird cards from. There are also bird cards that give resources to other players, or gain resources when another player does something. All this adds up to Wingspan having a decent amount of interaction.
Resource competition
Games about war, negotiation, trading, voting, etc have more than enough interaction.
For many other games, interaction isn't so direct. Instead, the players compete for resources. This is sufficient. Less interaction, in my opinion, is not.
Try to make resource competition as fierce as possible.
Have as few actions as possible, while still enabling reasonable choice. It's usually better to just have more options, but, with resource competition, the interactivity factor pulls in the other direction. The more likely it is that the players want the same things, the more the interactivity and tension.
Also, force the players to sift through dregs. Just getting what you need, is boring. Taking the least-bad option, from what's left, and constantly having to reevaluate your plan, is far more varied and interesting.
In the two-player version of my farming game, each player takes four actions per round. I put in a lot of work to reduce the number of choices, and now there are only eleven. So, eight of the eleven choices are being taken each round. Each round is a shoving match, to get what you need.
In one of my prototypes, players draw most of their cards from a central pool, but also discard to this pool.
How much interaction?
If you're unsure about how strong to make your interaction, err on the side of cutthroatness. It's better to have a game be brutal than boring.
When an opponent thwarts your plans, you should not be unaffected, but nor should you be doomed. You should be forced to pivot to a new plan.
Safe zones
Even in highly-aggressive games, some things should be off-limits for interaction. I need some kind of area where I can plan things, and not have them destroyed.
Radlands is very confrontational. You're constantly blowing up each other's stuff, in all kinds of ways. I was asked why I didn't put cards into the game that make the opponent discard cards from their hand. I decided that the player's hand would be untouchable, so that the player could properly plan things there, without interference. These plans could then be put to the test on the table, where the real battle occurs. This also stopped the game snowballing. Your opponent always has a way out, because they've got cards in their hand, that you can't touch.
In general, restrict conflict to one part of the game.
In one of my prototypes, players build a village. I wanted to make the game more interactive, so I added warriors. However, these warriors are only useful in competing for a set of prize cards. These cards are very significant and useful, however. An enemy with lots of warriors can monopolise these prizes, but they can never go beyond that, and come and burn down your village. This gives this game a good amount of interaction, but lets you largely do your own thing, without interference.
Incidental interaction
Players must interact with each other in ways they can understand — competing for opportunities, attacking each other, or benefiting each other.
In Sagrada, each player builds a pattern out of dice. The player wants to organise the colours and numbers of the dice in certain ways, to get more points. It's very thinky. Each player takes their dice from a central pool, but players have no idea what the other players will take, or why. You just hope no one takes your dice. I like the puzzle, but this level of interaction is too low for me.
In Azul, each player builds a tiled floor out of coloured tiles. These tiles are taken from a central pool. Players need to think about what tiles other players will take, and take those tiles before anyone else gets them. The players can also easily see what they'll be giving to their opponents, if they make a certain move, and will need to factor it into their moves.