Player Interaction

Other factors aside, more interaction is better.

Some of the most memorable moments are borne of competition or teamwork.

Your game should either be a very interesting puzzle, or a fierce competition with the other players. Either works.

For games that are inherently solitaire, have a highly-competitive area (usually some kind of resource pool) where there's brutal competition. Don't add this later. Make it part of the core of the game, at its inception.

My farm game is fairly puzzly and solitaire. However, the central board, where you choose your actions, has very few copies of each action, and the players will have to compete fiercely for them.
Wingspan is fundamentally a solitaire game, but they added competitive goals each round, and a central tray that all players draw bird cards from. There are also bird cards that give resources to other players, or gain resources when another player does something. These little bits all adds up to sufficient interaction.
In Radlands, you do build up a kind of an engine, but the opponent will smash down half of it on their turn. Your job is to decide what the important half is.
In my castaway game, there were natural disasters controlled by the game. There was also a central pool of cards. I wanted to make the game more interactive, so I made the natural disasters into cards that the players could play against each other.

Adding interaction

Move the objective of the game as close to the other players as possible. Ideally, the other players are the objective.

In my pirate game, the players could go around picking up tokens with treasure on them. They could also attack each other, and steal treasure. The players really liked these treasure tokens, but they actually made the game worse. The players would just go around picking up treasure, and generally not attack each other. Now, there's far less treasure on the map, so the players will go chasing each other around, trying to steal each other's treasure. It's vastly more interactive, and a better game.

Resource competition

Games about war, negotiation, trading, voting, etc have more than enough interaction.

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.

For many other games, interaction isn't so direct. Instead, the players compete for resources. This is sufficient. Less interaction than that, in my opinion, is not sufficient.

Have as few options 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 re-evaluate 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. The choices of the opponent have a huge impact on what you do.
In one of my prototypes, players draw most of their cards from a central pool, but also discard to this pool.

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 built a village. I wanted to make the game more interactive, so I added warriors. However, these warriors were 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.

A shared central resource pool is just enough, but players should be able to understand and affect the other players, through this pool. Otherwise, this interaction just randomly affects the other players. I call this "resource pool solitaire". It's like a group of people playing basketball in the same area as people are playing chasey/tag. They bump into each other, and affect each other's games, but not in any intentional way.

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.