Agents in Economics: Pedagogy

1
Agents in Economics Pedagogy

• Rob Axtell

2
Against the Nash Program

• Nash claim (implicit) Observed macroscopic
  regularities result from agent-level equilibria
• Nash program Deduce agent-level strategies as
  equilibria that correspond to empirical
  regularities
• Alternative program 1 Nash claim is only
  sufficient, not necessary many empirical
  patterns result from agent dis-equilibria
• Alternative program 2 Nash claim is necessary
  but not sufficient as certain agent-level
  equilibria are not attainable from wide classes
  of ICs

CSED
3
Why Agents?

• Distinct uses
• Agent model animates conventional model
• Analytical difficulties make agents necessary
• Agent model only way to understand

4
Is Social Science Possible?(Buss, Papadimitriou
and Tsitsiklis, Complex Systems 1991)

• A identical automata each with S states
  (finite)
• Coupled through global rule, G, a first order
  sentence
• Initial condition, (s1, s2, ..., sA), specified
• Problem determine the state of the system at
  time T
• Analysis is useful if the number of computations
  is a polynomial in A, S, and log(T )
• Analysis is impotent if this is not the case and
  an automata (agent) model is the best one can do

5
Automata Theoretic Social Science

• Definition A poll, P(x), gives the number of
  automata in state x
• Definition Global rule G is constant-free if it
  does not refer to any particular state of the
  automata
• constant-free rule IF ?x ?y P(x) P(y) THEN 0
  ELSE 1
• not a constant-free rule IF P(s1) gt A/2 THEN 0
  ELSE 1
• sometimes hard to tell ?x P(x) P(s1) is
  equivalent to ?x?y P(x) P(y)
• Theorem 1 If G is constant-free then the state
  can be determined in polynomial time
• Theorem 2 If G is not constant-free then the
  system is PSPACE-complete.
• Theorem 3 The set of constant-free G is
  undecidable

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Why Not Agents?

• Today
• Build model but cant solve it
• Solve it computationally (maybe with agents)
• Find some special case that is analytically
  tractable
• Publish the latter with computation secondary
• Future?
• Build model from interacting agent perspective
• Make many realizations
• Find some special case that is analytically
  tractable
• Publish agent model with analysis in the appendix

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Upshot

• Take an economic principle and agentize it
• Possible results
• Agent model reproduces conventional result (rare)
• Agent model enriches basic result (common)
• Agent model overturns sub-field (???)
• Generalize the model, add a front end (user
  interface) and put it on your websitethis is
  already a contribution!

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The Canonical Experiment Adaptive agents
economic environment

• Standard results
• Theorem widening
• Analytical brittleness-theorem is special
  case/measure zero lack of generality
• Non-standard results
• Conventional result effectively uncomputable
• Conventional result simply fails to obtain
• Agent result qualitatively different
• Agent model generates new conceptualizations

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Example Gale-Shapley Matching

• Given a bipartite graph, with edges as
  preferences for the other nodes
• Gale and Shapley 1962 came up with an algorithm
  for matching nodes such that the resulting match
  is stable (no individuals in distinct pairs would
  prefer each other)
• Centralized matching
• Poor welfare properties
• Why is this used?

10
Two Schools Within theAgent Modeling Community

• Power of agent models is to extend the corpus of
  received results, mainly by a process of adding
  on
• For example, learning models, spatial games
• Early dominant view
• Power of such models lies in revisiting the
  foundations of social theory
• Relaxing the heroic assumptions (concerning
  behavior, connectivity of agents) of earlier
  results
• Riskier view, but higher payoffs if successful
• Today, elements of both schools flourish

11
Thinking in Agents

• When you catch the agent bug suddenly the whole
  world is just a multi-agent system
• Risk is that then you want to model the whole
  world!
• Particular risk for agent models is to build in
  too much
• Schelling you are done when there is nothing
  else that can be taken away
• KISS principle (Axelrod is well-known advocate)

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What is Not a Multi-Agent System?

• Is there any phenomenon that cannot be
  represented by
• arbitrary numbers of
• arbitrarily sophisticated automata
• connected together via arbitrary graphs
• running for arbitrary amounts of time?
• Power of models derive not from their generality
  but from their specificity

13
Agents and Policy

• Three big wins Traffic, military, disease
• How soon Economic policy, social policy?
• Need to teach analysts how to use tools
• Need to teach policy-makers about these new
  ideas, this new tool
• Last year Bielefeld
• Next year Pensacola?