Attempting a taxonomy of player interaction along a scale of increasingly personal relations:
The simplest form: there is simply nothing the players can do to affect each other and thus no form of profitable reaction to another player’s choice or inversely, prompt a player to change course in reaction to your choice. Games absent interaction are the poster children for Multi-Player Solitaire.
There’s no requirement for understanding or predicting the other players, merely recognition that they exist and have potentials that may affect the results of your game. qDominion (usually) falls in this camp (there are small exceptions). Knowledge of the specifics of the other players is rarely if ever useful, but an overview of the gestalt of all the other players en masse is useful. Do any of them have any of XYZ cards? What is the rate of consumption of the QRS card stack across all players? The answers to such questions can profitably inform play choices.
Ahh, the first tremblings of mutual-perception! The question isn’t what effects a player may enforce on another, but rather how correct choice-prediction (and thus correct counter-counter-counter-counter–ad-infinitum-choice-prediction) may be translated into an advantage. The classic recent case is Race for the Galaxy; a game in which there are significant efficiency gains for drafting on other player’s choices. Predictive interaction is a slippery beast as it has a strong harmonic in Personal Interaction and a weaker harmonic in Personal Direct Interaction.(see below).
Players intimately affect each other, contructively, obstructively and destructively. They may help each other’s success, obstruct success, or directly destroy or foul each other’s success. I sank your battleship! The effects can range from the relatively subtle taking of a limited resource another had planned on taking themselves (eg roles in Puerto Rico, actions in Age of Steam, station markers or track tiles in the 18XX) to the very direct destruction or removal of player value (eg stock trashing and loot’n’dump in the 18XX, conquest and possible elimination in Risk, dumping a high point pain card on an opponent in Sticheln, or almost any player-interaction in Diplomacy).
Direct interaction can be sub-divided into Impersonal and Personal types
Personal Direct Interaction is the targeted subset of Direct Interaction and a weak harmonic of Predictive Interaction (due to the requirement of accurate player incentive/value prediction in foiling player’s personal success). The qualifier is that the subject is explicitly and deliberately targeted. Something isn’t done to all players or to any random player, but specifically to specific player with deliberate (ill) intent for that specific player’s success. Settlers of Catan‘s monopoly card card (all other players give the player all their resources of a given type) and calling time in Galaxy Trucker are usually Impersonal Direct Interaction as they are indiscriminate effects. In contrast encouraging a large bribe in Intrigue and then reneging on the implied or promised deal, building walls in another player’s presumed territory, using “their” resources” to cut them off from “their” buildings, or simply conquering a player’s temples and territory and annihilating their military and conquering their territory in Antike is Personal Direct Interaction.
The return of subtlety. Here the ticket isn’t to recognise or even so much to predict, but to comprehend the player(s) intimately. The challenge is to not only predict their immediate choices, but their patterns, their strengths and weaknesses as players, their intersection of character and individuality with the game and by the advantage of exploiting that intimate and intensely subjective comprehension, to beat them. Personal Interaction is a strong harmonic of both Predictive Interaction and Personal Direct Interaction (see above).
It is worth noting that the above divisions aren’t quite linear or evenly spaced along the not-quite-a-scale. That’s a problem with the soft-sciences: straight lines aren’t. Most noticeably Personal Interaction is variously orthogonal to both forms of Direct Interaction and the line between Subjective Interaction and Direct Interaction isn’t quite straight through Predictive Interaction.
Apocryphally, women as a gender are commonly said to dislike the destructive sides of Direct Interaction. I’ve not noticed that gender bias but several of the players I commonly play with (mostly male FWVLIW) share that trait: they are only interested in constructive positive-sum games. Additionally different players have various detection and preference ranges for the interaction levels they prefer. While I can detect the inter-player interaction among players of Race for the Galaxy it is too diffuse and impersonal to appeal to me. Similarly Impersonal Direct Interaction has little appeal for me. In contrast one of the chaps I play with simply isn’t comfortable with any form of Personal Direct Interaction where-as another chap pooh-poohs and avoids anything which doesn’t operate at the deepest level of Personal Interaction.