PolySciFi Blog

Wednesday, October 12, 2005


On game theory, magic gnomes, and cognitive radios

In this post, Tyler quotes Michael Mandel as writing:
Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes -- from full cooperation to near-disastrous conflict -- are consistent with the game-theory version of rationality.

To put it a different way: If the world had been blown up during the Cuban Missile Crisis of 1962, game theorists could have explained that as an unfortunate outcome -- but one that was just as rational as what actually happened. Similarly, an industry that collapses into run-amok competition, like the airlines, can be explained rationally by game theorists as easily as one where cooperation is the norm.
To present the criticism in a more direct manner, game theory actually makes many predictions on the outcomes of human interactions. However these predictions are not really testable with respect to the usefulness of game theory because any failed prediction can just be explained away as an improper modeling of the situation.

Which sounds just as useful as a "magic gnome" theory. Why did X happen? The magic gnomes caused it to happen. Why did Y happen when X was predicted? Because you failed to account for this previously undiscovered aspect of magic gnomes. Since we don't find magic gnomes to be a credible explanation of the real world, why should game theory be considered a credible explanation?

This failing of game theory is entirely due to our imperfect modeling of humans, something no field or theory has done well (unless you live in Hari Selden's universe). Tyler proceeds to list five ways in which game theory could become useful in the future - all of which revolve around science overcoming the imperfect modeling of humans.

However, I would point out that game theory is a very useful tool when the model correctly captures the actors' utility functions and decision rules. (Here "actors" is not used in the Hollywood sense, but in the sense of a thing under study that is performing some action.)

Daily, I use game theory to make accurate predictions about the adaptations of cognitive radios without any after-the-fact magic gnome theorizing. To fill everyone else in, according to VT's cognitive radio study group, a cognitive radio is
"an adaptive radio that is capable of the following:
  1. awareness of its environment and its own capabilities,
  2. goal driven autonomous operation,
  3. understanding or learning how its actions impact its goal,
  4. recalling and correlating past actions, environments, and performance."
The key for my work is that I am not concerned if science is up to the job of correctly modeling the "goal" or utility functions of cognitive radios because I probably programmed the goal into the radio. For my work, I can perfectly predict the steady-state power levels (which correspond to a Nash equilibrium in economics-speak) of a distributed power control algorithm. Or the set of operating frequencies for a distributed frequency selection algorithm. Or the countless other applications that we're developing every day.

So for engineers, game theory is clearly not a dead end, but that's because the abstract equations of game theory correctly model our real world problems.

Post Script
To the extent that machines and deterministic algorithms are being incorporated into activities typically studied by economics - e.g., bots buying/selling stocks, automatic sell/buy provisions, automatic restocking - game theory should be able to perfectly model those situations as well. So this a sixth response that Tyler could use to justify continuing down the game theory path a little longer is
"6. Technological approaches will result in programmable and precisely modelable machines that make economic decisions. Game theory will have clear predictions for these scenarios, just give technology time."


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