Your analysis is correct if we optimize our algorithm to maximize the profit from its most recent trade. But, as with the iterated prisoner's dilemma, what mak

Your analysis is correct if we optimize our algorithm to maximize the profit from its most recent trade. But, as with the iterated prisoner's dilemma, what makes a successful strategy can change when a game is played repeatedly. Imagine a genetic algorithm that comes up with a tit-for-tat strategy when playing the iterated prisoner's dilemma. Now imagine a similar genetic algorithm applied to automated trading. Imagine a market in which a large fraction of the trading is done by such algorithms. I think it is quite plausible that a cartel could form more or less spontaneously, without any conscious encouragement in that direction from human programmers. (But hey, maybe you have a good argument that I'm wrong.)