I DON'T know much about game theory, but I've been thinking lately about strategy in a modified version of chess. In this version, not only does white go first, but only white gets a queen; the black queen is removed. However, to compensate, black gets a new power: every three moves, rather than moving itself, it can pick one of white's pieces to "block", sending it back to its original position on the board. Which side has more power here? Formally, probably black, since it can blow apart any strategy white tries to pursue by picking apart the structures of pieces white builds up. But there may be ways for white to counter black's power. What if white pursues multiple loose strategies at the same time, so that whichever setup of pieces black tries to dismantle, white can shift to another offensive, taking advantage of black's missed turn? The key here for white might be to entice black to commit to blocking one piece, wasting its own move, and then go ahead with whichever strategy black had chosen not to interfere with. This is analogous to a lot of real-life situations. Usually, we're faced with a number of options we might pursue, and we may be more or less indifferent to which of them we end up with. If we are making the choice within a group (a company, a set of friends, a family), we may find that others have the power to block whatever option we select. Indeed, we may find that other group members tend, in a dialogic reflex, to react to our preference for one option by vocally supporting a different one. Someone who recognises this tendency may react by making sure they keep several viable choices open, so that they will still be satisfied with whichever option the opponent decides not to block. Or they may delay statements of preference until the opponent has committed to blocking one option. Fortunately, once an opponent has blocked an option, they tend to be stuck with their block; it is usually hard for an opponent who has just resolutely committed to striking down option A to turn around and blast option B a moment later.

Indeed, the most effective tactic of all may be to ensure one has several equally good (or bad) options and to tentatively hint at a preference without formally committing to it, and then to let it dangle for some time, hoping that the opponent decides to use up their "block" and leave the other options freely available. It may even be a good idea to provoke the opponent's antagonism, making it appear that a block on this choice would be a severe defeat. The objective is to get the opponent to limit their freedom of movement by committing to a block, while maintaining one's own freedom of manoeuvre by refraining from commitment.

Of course, this type of approach risks the appearance of indecisiveness and ineffectuality. If you are acting with a group of colleagues or teammates, your failure to choose decisively between options may be demoralising, even if you are genuinely indifferent to which option is chosen. When hinting at a preference purely in order to lure the opponent into committing their block, you run the risk of inaccurately signaling to teammates that you really do prefer that option. This will make the opponent's block appear to your teammates as a serious defeat, which may be demoralising. And changing course frequently may be seen by allies as a sign of confusion and lack of vision, even though it in fact reflects tactical decisions. Such tactics may, in fact, be the only way of achieving any of your goals, if you are faced with an opponent who has the power to block any of your moves, and whose attitude is so relentlessly oppositional that they instinctively block any initiative they think you are really committed to.

These are just a couple of things I've been thinking about today. I'm not saying these thoughts explain anything about how powerful people in such situations actually are behaving. But I think the dynamic exists.

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