Tit-for-Tat, Bit Torrent and War Strategy

Game theory and strategic talk has always sounded like black humor to me. Here, I demonstrate this by example.

Tit-for-tat is reputed, in game-theoretic analysis, as an optimal strategy for repeated, zero-sum games. (See, for example, the analysis in Avinash Dixit's Thinking Strategically.)

There are many uses of tit-for-tat strategy.

For example, BitTorrent protocol uses a tit-for-tat strategy to create balanced up-loads and down-loads. Presumably, the P2P file sharing contains aspects similar to repeated, zero-sum games.

Tit-for-tat is also used by some of the authors and strategists of wars, which can also be considered as repeated, zero-sum games, with each day of the war, or each battle, representing one of the "games". (We see this in the war that has recently started and promises to continue.)

However, some strategists of war have replaced proper tit-for-tat with the concept of infinite escalation, or something akin to "TIT-for-tat," i.e. a vastly disproportinate response as a way to punish. (Here, I'm using capital letters to note the disproportionality of the "TIT" part to the "tat" part.)

However, not only is this strategy less optimal from the game-theoretic perspective and given infinitely-repeating zero-sum games, there is also a real-world catch to this more aggresive strategy that makes it less and less attractive as the games continue to repeat, i.e. as the war continues to go on.

For example, after a country's infrastructure has been destroyed there is not much else to do in terms of escalation other than massacring civilians. However, this is not a real strategy with a real pay-off. A TIT-for-tat (i.e. escalation) war strategist has already failed because he can rarely afford a long conflict. In fact, that is exactly the reason the escalation strategist chooses to escalate, hoping the other side to accept defeat as early as possible. In other words, the strategy itself speaks for its own weakness, i.e. its lack of tolerance for a long conflict.

Another problem with unmeasured escalation and "unproportional use of force" is that eventually the opponent may have the equipment to respond to the escalation, returning the game from TIT-for-tat to a more balanced TIT-for-TAT, which is another version of tit-for-tat.

Related links:

• BitTorrent protocl in the Opera browser.
• Brian's BitTorrent FAQ and Guide.
• Wired article on BitTorrent.
• Avinash Dixit.
• Thinking Strategically.