Clark uses scaffolding to refer to the external structures and processes that humans use to offload substantial amounts of problem-solving work in order to reduce the loads on their individual brains. He concludes that "...it is the human brain plus these chunks of external scaffolding that finally constitutes the smart, rational inference engine we call mind."
Standard (neoclassical) economic theory presumes that economic agents everywhere and always attempt to make choices that maximize their expected returns (utility) subject to budget constraints, taking as given preferences, technology, endowments, and correct information about the structure of their choice problems. The economic agent is thus viewed as a logically consistent, unhurried, and well-informed reasoner. Some economists (e.g., A. Denzau and Doug North in unpublished 1995 work) refer to this view as a paradigm of substantive rationality.
Herbert Simon (1982) coined the expression bounded rationality to refer to the observed tendency of people to satisfice rather than optimize. That is, when faced with a problem, people tend to rely on rules of thumb to find approximate workable solutions that require relatively small expenditures of time and processing power rather than exact solutions requiring relatively large expenditures of time and processing power.
Double auctions are markets in which buyers submit bids (offers to buy) and sellers submit asks (offers to sell) for standardized units of a real or financial asset.
A double auction is continuous if bids and asks can be posted and matched on a continuous basis during the hours the auction is open. Examples of continuous double auctions include the Chicago Board of Trade and the New York Stock Exchange.
In contrast, a double auction is discrete if bid and ask posting and matching are carried out at discrete time points in accordance with a prespecified schedule. A prime example of a discrete double auction is a clearinghouse double auction in which bids and asks are collected and submitted in batched form to a centralized agency at the beginning of a trading period and then matched by this agency in accordance with specified protocols at the end of the trading period. Examples of discrete double auctions include various electricity markets and Internet auctions.
Consider a collection of buyers and sellers participating in a market for a good Q during a particular trading period. A buyer's reservation bid price for a unit of Q is the maximum amount he would be willing to pay for the unit, and a seller's reservation ask price for a unit of Q is the minimum price he would be willing to accept in payment for the unit.
Given any unit of Q actually sold in the market, the buyer's net gains to trade are measured by the difference between his reservation bid price for the unit and his actual payment, and the seller's net gains to trade are measured by the difference between his actual payment for the unit and his reservation ask price.
It can be shown that the total net gains to trade (or "surplus value") generated through trades in the market for Q are maximized under competitive conditions in which all traders take prices as given and the unit price P of Q is set at a level P=P* that ensures demand equals supply. Market efficiency measures the actual total surplus value generated through market trades in comparison to the maximum total surplus value that would be attained under competitive conditions, and market advantage measures the actual distribution of total surplus value across the market traders in comparison to the distribution that would be attained under competitive conditions.
The following discussion explains the construction of market efficiency and market advantage measures in greater detail.
Idealized Benchmark: The Competitive Market Outcome
The buyers' aggregate demand curve for Q is a schedule giving the maximum amount of Q that buyers' would be willing to buy at each different unit price P. [Conversely, for each level of Q, the aggregate demand curve indicates the maximum unit price P for Q that buyers are willing to pay.] In general, this aggregate demand curve will be a downward sloping curve when plotted in the Q-P plane.
The sellers' aggregate supply curve for Q is a schedule giving the maximum amount of Q that sellers would be willing to sell at each different unit price P. [Conversely, for each level of Q, the aggregate supply curve indicates the minimum unit price P for Q that sellers are willing to accept.] In general, this supply curve will be an upward sloping curve when plotted in the Q-P plane.
These aggregate demand and supply curves are schematically depicted below.
Price P D | D S SUPPLY CURVE | D S | D S | D S | D S | BuyVal D S P* |.............D S | S D | SellVal S D | S D | S D | S D | S D | S D DEMAND CURVE S____________________________________________ Quantity Q 0 Q*
If every unit of Q were priced at P=P*, and buyers and sellers were price takers, then buyers would demand Q* and sellers would supply Q*. Hence, the market would clear at (Q*,P*).
Given these competitive conditions, buyer total surplus value would be measured by the area BuyVal lying between the demand curve (giving maximum willingness to pay) and the price line P=P* (giving actual payment). Moreover, seller total surplus value would be measured by the area SellVal lying between the price line P=P* (giving actual payment) and the supply curve (giving minimum acceptable payment). It can be shown that the total surplus value MaxVal = BuyVal+SellVal is the maximum possible total surplus value that can be generated in this market.
Actual Market Surplus Outcomes:
The surplus measures MaxVal, BuyVal, and SellVal are idealized concepts describing total surplus and surplus distributions under competitive conditions conditional on known reservation prices. Now consider, instead, the market as it actually proceeds during the course of the trading period when reservation prices are private trader information.
Define actual buyer total surplus value (ActualBuyVal) to be the difference between what the buyers would have been maximally willing to pay for their purchases and the amount they actually ended up paying for these purchases. Define actual seller total surplus value (ActualSellVal) to be the difference between what the sellers were actually paid for the items they sold and the minimal amount they would have been willing to accept in payment for these same items. Actual total surplus value (ActualVal) is then the sum of actual buyer total surplus value ActualBuyVal and actual seller total surplus value ActualSellVal.
By construction, actual total surplus value ActualVal cannot exceed maximum possible total surplus value MaxVal, but ActualVal can be strictly less than MaxVal. For example, due to incomplete information about available trading opportunities, a buyer B and a seller S might fail to trade during a trading period even though B's reservation bid price is strictly higher than S's reservation ask price. The difference between their reservation bid and ask prices then represents wasted (unextracted) surplus value.
The market efficiency of the market for Q in the given trading period is defined to be the ratio of actual total surplus value ActualVal to maximum possible total surplus value MaxVal, multipled by 100 to give a percentage measure.
Actual Total Surplus Value Market Efficiency = 100 * ---------------------------- Maximum Possible Total Surplus Value ActualVal = 100 * ----------- . MaxVal
A trader is said to engage in opportunistic pricing if he makes a bid or ask price offer that deviates from his reservation price. Define the market advantage of a trader to be extent to which the trader is able to gain surplus value (relative to competitive conditions) by engaging in opportunistic pricing.
More precisely, define buyer market advantage to be the difference between the actual total surplus value ActualBuyVal accruing to buyers and the total surplus value BuyVal that buyers would attain under competitive conditions, reported as a percentage of BuyVal. Similiarly, define seller market advantage to be the difference between the actual total surplus value ActualSellVal accruing to sellers and the total surplus value SellVal that sellers would attain under competitive conditions, reported as a percentage of SellVal.
ActualBuyVal - BuyVal BuyerMarketAdvant = ---------------------- ; BuyVal ActualSellVal - SellVal SellerMarketAdvant = ------------------------ . SellVal
At the end of Chapter 4 (p. 82), Clark lists a number of major conceptual and methodological challenges posed by the embodied cognition approach:
Clark subsequently concludes (p. 83):
In Chapter 9, Clark returns to this theme.
Clark (p.179-180) argues that the extension of the embodied cognition framework to encompass more advanced cognition involves three aspects:
Clark continues (p. 180):
Clark (citing other researchers as well) points out that standard economic theory, with its substantive rationality postulates, seems to work best for highly scaffolded choice problems and to falter or fail as the degree of scaffolding declines.
More precisely, standard economic theory works best in the presence of constraining policies and institutional practices. According to Clark (p. 182):
Clark continues (p. 182):
Clark ends Section 9.2 (pp. 183-184) with a discussion of a well-known agent-based computational study by Gode and Sunder (1993). These authors show that high market efficiency is consistently obtained for a class of continuous double-auction experiments conducted with "zero intelligence" computational traders who make random bids and asks constrained only by budget constraints. Thus, the high market efficiency appears to be attributable to the special institutional form of the continuous double auction independent of the learning behavior of the individual auction participants.
As indicated above, an affirmative answer to this question is suggested by Gode and Sunder (1993) for continuous double auctions. However, subsequent findings strongly caution against over-generalizing the Gode and Sunder findings.
For example, Dave Cliff and Janet Bruton (1997) demonstrate that the high market efficiency observed by Gode and Sunder (1993) requires that the "true" aggregate demand and supply curves for buyers and sellers constructed on the basis of their reservation bid and ask prices be symmetric. More precisely, the slopes of these curves, although opposite in sign, must be of approximately equal magnitudes. In general, the mean transaction price resulting from the trading by Gode and Sunder's zero-intelligence traders can be reliably predicted from the particular probability density functions used by buyers and sellers to generate their bids and asks. In the absence of symmetry, this mean transaction price can differ significantly from the demand=supply "competitive equilibrium" price P* required for market efficiency.
Deddy Koesrindartoto (2001) shows that market efficiency can be seriously degraded in a discrete double auction with midpoint pricing (i.e., prices set at the midpoints of bid-ask spreads) if traders learn via a well-known individual reinforcement learning algorithm due to Alvin Roth and Ido Erev. The reason is that the latter algorithm fails to update choice probabilities in response to zero-profit outcomes. This can substantially degrade market efficiency in the context of a double auction because zero-profit outcomes are prevalent in the early stages of the auction when traders are undertaking price discovery and failure to match due to ask prices exceeding bid prices is common.
Nicolaisen, Petrov, and Tesfatsion (2001) show that high-market efficiency is obtained in the auction experiments run by Koesrindartoto (2001) if buyers and sellers instead learn via a modified version of the Roth-Erev individual reinforcement learning algorithm that corrects for the zero-profit updating problem. On the other hand, the authors show that market efficiency is seriously degraded if, despite the presence of revenue, cost, and capacity differences among buyers and among sellers, the buyer population and the seller population each attempt to learn "optimal" bid and ask prices by social mimicry using population-level genetic algorithms. The authors caution (p. 522): "While the discriminatory double auction may reliably deliver high market efficiency when buyers and sellers refrain from inappropriate learning behavior, it may not be robust against the active exercise of bad judgement."
Finally, Chen, Tai, and Chie (2002a,b) show that too much "smartness" can degrade market efficiency in a discriminatory double auction with discriminatory midpoint pricing. (See the basic references listed above for pointers to zip and postcript versions of these papers). Under this pricing protocol, a different price is set for each matched buyer and seller at the midpoint of their bid-ask spread. The authors show that it can be rational for buyers to bid higher then their reservation bid prices and sellers to ask lower than their reservation ask prices if they expect that this risky price offer behavior will increase their chances of having their offers accepted while still resulting in a midpoint price that ensures them a profitable trade. The authors permit their traders to evolve these types of high-risk but potentially higher-return pricing stategies via genetic programming. Their experimental findings show that this results in a relatively unstable price and lower market efficiency than when budget constraints are tightly imposed on traders as in Gode and Sunder (1993).
Bottom Line: Studies subsequent to Gode and Sunder (1993) have shown that learning can matter substantially for market efficiency even in the presence of strong scaffolding such as double-auction protocols.
Clark asks (p. 184): "What kind of individual mind needs an external scaffold?
Clark notes that a vital role for external scaffolding is strongly predicted by research on individual cognition, beginning with the work of Herbert Simon (1982) on satisficing, proceeding through connectionist ideas (artificial neural networks and parallel processing, cf. Section 3), and down to present day work on embodied cognition.
He concludes (p. 186):
Clark notes (p. 186-187):
Clark sites seminal work by Hutchins and Hazelhurst (1991), who attempt to model the interplay of individual learning, cultural and artifactual evolution, and patterns of inter-group communication. The authors considers successive generations of agents modelled as artificial neural networks with simple fixed architectures (a few linked processing units).
Despite the absence of any change in their neural architectures, the agents gradually evolve better external cultural artifacts in the form of symbolic structures representing moon and tide states. These cultural artifacts increase the collective ability of the agents to predict an environmental regularity - the relation of moon phase to tide state - important for the acquisition of shellfish and other important food resources.
It is interesting to consider the relation of this work on the evolution of "cultural predictors" to the co-evolution of "individual predictors" by traders in the Santa Fe Artificial Stock Market Model studied in Section II of the course.
Indeed, although a number of ACE researchers are now studying the evolution of forecasting rules - in particular for financial markets - typically these rules take the form of privately owned tools applied by individual agents for individual advantage, not cultural artifacts for the collective benefit of society as a whole. To date, very few ACE researchers have attempted to incorporate cultural evolution considerations in their models. One interesting exception is Gintis (2000).
For further discussion related to this issue, see Tesfatsion (2002).
Clark asks (p. 191): Without central control, what stops agent behaviors from becoming chaotic and self-defeating?
Brooks (1994) considers three sources of constraint: