• Less than fully rational agents are hard

• Start from the opposite direction

• Use simple trial and error

• Modeling Contribution

• "Suppose first that the market price is above the equilibrium price […] There is a surplus of the good: suppliers are unable to sell all they want at the going price. […] They respond to the surplus by cutting their prices. Prices continue to fall until the market reaches the equilibrium."

• Robustness Check

• A seller wants to sell \(y^*\) kilos of cheese each day. Today he charged price \(p_t\) and sold \(y_t\) kilos. How should he sets tomorrow's price \(p_{t+1}\)

• \(e_t = y^* -y_t\)

• \(p_{t+1} = a e_t + b \sum_0^t e_{\tau} d\tau + c \frac{de_t}{d_t} + p_0\)

• Absence of model knowledge

• Assume unsophisticated users

• Simple to code

• Simple to fit

• Reactive/Subsumption Architecture

• Zero-Intelligence (Plus)

• Probe and Adjust

• Gintis

• Making 50 kilos of cheese a day require action over multiple markets: milk, workers, sales. How do we generalize PID pricing over multiple markets?

• How do we decide how many kilos of cheese to produce in order to maximize profits?

• Profits are maximized when marginal benefits equal marginal costs

• \(\text{Marginal Benefit: } p_t = w_t \text{ :Marginal Costs}\)

• Use a PID controller to find how for which production target \(p_t = w_t\)

• Lower Frequency

• If you have market power, you need to take that into account

• \(\frac{\partial \Pi}{\partial q} = 0\)

• \(p + q \frac{\partial p}{\partial q} = w + q \frac{\partial w}{\partial q}\)

• \(p_t + \mu_p = w_t + \mu_w\)

• Use a PID with error \(p_t + \mu_p - w_t - \mu_w\)

• PI trial and error produce paired data \(p_t,y_t\)

• Can run a linear regression over them to discover \(\mu_p\)

• Use Kalman Filters

• Gunnery Control and Norbert Wiener

• "The world, understood cybernetically, was a world of goal-oriented feedback mechanisms with learning. Cybernetics,then, took computer-controlled gun control and layered it in an ontologically indiscriminate fashion across the academic disciplinary board."

• Two Large Literatures:
  • Price Stickiness
  • Bullwhip effects

• Naive trial and error stops working

• A model where sticky prices achieve equilibrium and flexible prices don't

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• Leijonhufvud "Keynes and the Keynesians"

• I mostly stay clear from macro ABM
• Demand equals wages paid
• No savings

• Economic Feedback Spectrum
• Tuning
• Thank you!