From the MIT article, "What computer science can teach economics" by Larry Hardesty, MIT News Office.
...Nash was the first to prove that every game must have a Nash equilibrium. Many economists assume that, while the Nash equilibrium for a particular market may be hard to find, once found, it will accurately describe the market’s behavior.In a market where prices must be recomputed due to extreme changes in circumstances, such as during the recent CDO, mortgage, credit, Bear Stearns, Lehman, liquidity, housing devaluation crises, the new environment creates uncertainties as to asset outcomes and prices. Market participants realize previous asset valuations and methodologies lost their validity and that they need to revalue.
Daskalakis’s doctoral thesis — which won the Association for Computing Machinery’s 2008 dissertation prize — casts doubts on that assumption. Daskalakis, working with Christos Papadimitriou of the University of California, Berkeley, and the University of Liverpool’s Paul Goldberg, has shown that for some games, the Nash equilibrium is so hard to calculate that all the computers in the world couldn’t find it in the lifetime of the universe. And in those cases, Daskalakis believes, human beings playing the game probably haven’t found it either.
In the real world, competitors in a market or drivers on a highway don’t (usually) calculate the Nash equilibria for their particular games and then adopt the resulting strategies. Rather, they tend to calculate the strategies that will maximize their own outcomes given the current state of play. But if one player shifts strategies, the other players will shift strategies in response, which will drive the first player to shift strategies again, and so on. This kind of feedback will eventually converge toward equilibrium: in the penalty-kick game, for example, if the goalie tries going in one direction more than half the time, the kicker can punish her by always going the opposite direction. But, Daskalakis argues, feedback won’t find the equilibrium more rapidly than computers could calculate it.
As market participants searched for new asset values, the complexity and uncertainty of the economic situation left buyers, sellers, traders, and investors without any available easy computational methods or strategies to reprice assets. In that situation, markets will rely on observable pricing by counter-parties and others for information and strategies to find new asset values. The market went into a feedback loop with all the associated up and down gyrations until it settled on a new equilibrium price.
The wild price swings in tradable assets created a general financial market panic and increased volatility. As the markets reached their new equilibrium price points, the volatility declined to previous lower levels, and calm returned to the financial markets. Although, at a significantly lower than before the crisis price based on new economic circumstances.
According to the implications of Daskalakis's paper, the market gyrations during the crisis were a search for new equilibrium price points using feedback loops because the new prices were too difficult to compute directly and efficiently in a reasonable amount of time. Extreme asset price changes are the result of the need to use trades and feedback loops to set prices. Direct, mathematical computations of the values are too slow and are not any faster than letting the market gyrate to an equilibrium price point.
Furthermore, the slowness to reach a new price equilibrium point will allow many market observers who use simple rules of thumb to price believing that interim prices are irrational. In fact, the market was in the process of determining new prices based on the new economic information.
All 201 pages of Constantinos Daskalakis' dissertation paper in PDF, "The Complexity of Nash Equilibria" is available here.
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