Games are less interactive than they used to be. This is a good thing. Grinding the other players into dust is not what most players want.
However, some recent games have too little interaction, and each player is really just doing their own little puzzle.
Don't think "I'll add the interaction later." Interaction is a core part of your game, and has to be added in (or at least thought about) with the rest of the core. I've got a few dead prototypes, where I didn't do this. If you can't think of an appropriate way for the players to interact, you can't make the game.
Some of my game ideas really are just single-player games. There's really no market for those, though. I need to make them competitive, in the most logical way possible.
As far as I'm concerned, there's a minimum level of interaction a game needs. Things like competitive "objectives" are not sufficient, because they don't actually affect the players.
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 circular "display" boards in the middle of the table. Players need to think about what tiles other players will take, and take those tiles before anyone else gets them. Also, players won't want to let a big pile of the same-coloured tile build up, because an opponent will likely snaffle them up.
In Agricola, untaken resource tokens simply keep piling up. In general, I'll just focus on my own thing. However, if there's a pile of ten wood tokens on a space, I'll really start thinking about how long I can let it build up, before someone takes it.
Resource pools are acceptable, but they're an easy and overused form of interaction. Try to do something better, or create an interesting resource pool.
I'm increasingly fond of what I call "tight card pools". This is a very easy way to add high interaction to a card game. If cards are central to a game, I like to have players both draw from, and discard all cards to, a central pool. (Cards may also enter the game from the deck.) This means players have to think about what cards other players will also want, and also think about which cards they discard and hence make available to the other players.
In one of my prototypes, I have a very tight pool. Most cards are drawn from the central pool. This creates a lot of interaction, and also long-term planning, because players need to find a strategy amongst the cards in the pool.
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 the interaction 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.
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.