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Notes -
I do not consider repeated game strategy to be "out of game". It's a basic element of game theory - ever heard of repeated prisoner's dilemma?
I agree that kingmaking for someone just because they're your friend is not fun for anyone else at the table. Kingmaking for game theory purposes, especially if warned beforehand, is valid strategy. Introducing strategic spite into the game makes the table rethink how they build alliances and gives players more agency.
In which case the "Game" your are trying to optimize for is the sum payoff over the entire repeated scenario. That is, you have one main game, which is composed of many subgames, and acting rationally within the larger game may involve local "irrationalities" in the subgames which are only rational within the larger structure. Importantly, this is explicitly declared in the game formalism. Individual board games do not mention each other, so unless you're at like a board game tournament or doing a best 2 out of 3 or something, each game is being considered independently. Maybe you as a human being want to maximize the number of board games you want to win or something, but actually you also want to optimize for things like money and friendships and comfort and happiness and eventually we've gone full meta. My claim isn't that it's impossible to treat board games as repeated games or that you won't improve your winrate, my claim is that it's inappropriate and unfun. It's effectively a defection in the board game playing experience, something which increases your own enjoyment (assuming you like winning) at the expense of everyone else, and if everyone does it then everyone ends up having less fun.
Conditional on you being able to keep the spite entirely within the game, and credibly signal that to other players so they're not worried about making you upset in real life, I would again consider this to be a defection in the board game playing experience. It will make you more likely to win, and make the game less fun for everyone else because now you're restricting which actions they can do. If you unilaterally declare an ultimatum "nobody can do any harmful actions against me or I will sacrifice all chances of winning to destroy you" then you'll have a massive advantage as no player wants to incur your wrath (unless they're so far ahead they can afford it, or so far behind they are going to lose anyway and want to reverse-kingmaker you). But if everyone player does this then you have a big mutually assured destruction scenario and, unless the game was specifically designed around that scenario, is likely to be less fun than playing the way the game was intended.
Note that spite being a defection, a form of unsportsmanlike conduct, does not mean you should literally never do it. I would consider it appropriate in a meta tit-for-tat scenario, where you threaten players who behave unsportsmanly against you with unsportsmanly spite. If a player seems to be picking on you unfairly and spitefully, or doing some other action that is legal within the rules but the entire group agrees is bad behavior, then you can spite them back to punish their behavior. But in general the best outcome is one in which everyone cooperates, which means voluntarily forgoing a small set of behaviors that are technically legal but unfun, which varies from game to game but generally includes most meta concerns and kingmaking. You should generally seek to increase your chances of winning, but not goodheart it at the expense of having fun.
If I want to win each game (more or less - I don't tryhard all the time), by induction I want to win every game. I really do not see how that's worse than trying to win individual games. By that logic you shouldn't try to win a match and instead should just make whatever move is best in the shortest term every time.
Maybe it's just a badly balanced game if one player can be that fearsome while facing off against the entire table. Anyway, I didn't advocate for spitefully destroying the first player who attacked you at any cost. I'm advocating for reserving the right to do so if you have no chance of winning.
If it's not fun in that particular game then I won't do it or encourage it.
As long as there's an element of diplomacy in the game, some players will be inevitably spurned in some way in favor of others. Attacking everyone equally just means you're spreading yourself thin, it's generally a losing strategy. The possibility of revenge for breaking promises or ganging up keeps the diplomacy somewhat balanced.
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It's "out of game" in that it is strategizing one level up. It's not playing the current instance as the game, but instead the full set. If that's the level you want to analyze, fine, but I think it's fair to say it is tainting single-game strategy with meta strategy.
I also sign on to @MathWizard's game ethics here and have always had the feeling that caching chess opening strategy is distasteful - sort of against the spirit of the game - yes.. even in the face of hundreds of years of the top players doing just that.
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