Monday, May 25, 2015

John Nash RIP

Obituary from The Guardian
From another obituary Economics in one lesson: Nash:
"he concept that makes an economist a true economist is instead Nash equilibrium. That is, it is the marginal contribution of an economist to any situation. The idea is simple: if you are trying to assess the impact of your actions, you need to consider the equilibrium. That is, you need to work out whether, if you did something, holding the actions of others fixed today, that others will likely keep their actions fixed tomorrow. If not, you need to alter your decision calculus markedly. For instance, it makes no sense to say that a new innovation (e.g., Bitcoin) will win in the market unless you can also assess that it will win in a market that understands the new innovation (e.g., one where many actors have adopted crypocurrencies or some other variant) as well as in a market still centred around traditional banking.
Indeed, even opportunity cost can be rarely computed without working out the full equilibrium of a path not taken. This is why, if I were to re-write Economics in One Lesson, it is Nash equilibrium that would be the lesson and not opportunity cost."
From a post Steven Hsu in 2011 What use is game theory?:
"I agree with Rubinstein that game theory has little predictive power in the real world, despite the pretty mathematics. Experiments at RAND (see, e.g., Mirowski's Machine Dreams) showed early game theorists, including Nash, that people don't conform to the idealizations in their models. But this wasn't emphasized (Mirowski would claim it was deliberately hushed up) until more and more experiments showed similar results. (Who woulda thought -- people are "irrational"! :-)

Perhaps the most useful thing about game theory is that it requires you to think carefully about decision problems. The discipline of this kind of analysis is valuable, even if the models have limited applicability to real situations."
Steven Hsu's obituary talks of one of Nash's profound contributions to mathematics.
One of the comments "I use game theory (potential games, specifically) to design distributed algorithms where multiple AIs interact with one another. It allows me to bound convergence time, guarantee stability, and predict operating points.
That it is applied to machine intelligence instead of human intelligence is critical as I'm assured that the utility functions that I'm modeling are exactly the utility functions being used to guide the decisions."

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