Applying game theory to arbitrage

amado

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Here's a challenge for the best of the best:

Let's say you have an arbitrage opportunity, appearing about 5-10 times an hour. From it's normal state of an arbitrage free equilibrium, the potential profit opportunity slowly starts becoming bigger and bigger. First, it moves beyond transaction costs, operations etc. It then, somewhat slowly continues expanding (albeit not in a linear fashion, as the market's jump around). Imagine that the time is not high-frequency, but that there's ample time to discover it - let's even say minutes. And that the potential profit could give you something insane, like a net 2% on your margin requirement for the trades every single time.

Now, as the latent profit potential grows - if you choose to do nothing, sooner or later someone is going to pick this off. It can take a minute, or it can take five seconds (but not milliseconds). If someone is actively monitoring this arbitrage opportunity they are not seizing it at a predetermined profit target (or letting it run for a fixed period of time). And each and every time you could easily intervene and grab it before the market eventually erodes it away.

Now, how to handle such a situation. You don't know if someone is actively working this arbitrage or not. Is someone doing it, but in a chaos-like manner? What were to happen if you started exploiting it? Would someone be pissed as you were stealing their bread and butter trade, and start undercutting you? Would it end up in an war down towards who has the cheapest transaction cost or lowest latency? Would you be better off trading it in a chaotic-like way yourself, as to not tip off suspicion that you're an organized player that's entered into the arb opportunity? A silent, mutual agreement with one or many faceless market players to "share" the money that's freely available to anyone?

So, forget about the full, first paragraph of the arbitrage opportunity - just accept the fact/theoretical situation - and focus on the question of how to maximize the potential profit, competing or collaborating with one or many (possibly fictitous) arbitrageurs. I think this could be a very interesting topic for discussion, and hope many of the brighter minds of T2W would chime in with some thoughts or self-experienced stories.
 
Thanks for that link, arabianights! Axelrod's work seems very interesting! My instincts are also leaning to a tit-for-tat solution as the most effective (profitable) one.
 
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