Computational Approaches to Economic Valuation & Strategy Choice

1. Computational Approaches to Economic Valuation & Strategy Choice Colin Camerer Antonio Rangel Caltech

2. Outline • Brief history of the role of computation in Economics • Models of valuation and simple choice (Rangel) • Models of strategic choice and learning in games (Camerer) • Computational issues at different levels: individuals, firms, markets (Camerer) • Future directions of research

3. IBrief history of the role of computation in Economics

4. Computation is at the heart of economic problems Consider some typical problems: • Individual: What snack should I pick out of the buffet table? • Individual: Optimal investment portfolio? • Firm: Price setting and production selection problem • Market system: price formation Thus, one would expect computational based models of decision-making to be common in Economics

5. This is not the case:Traditional deliberate ignorance of computational detail • The triumph of “as if” modelling (economic behaviorism)-- Pareto (1987):“Pure political economy has therefore a great interest in relying as little as possible on the domain of psychology” -- Friedman (1953)Test predictions of theory rather than realism of assumptionsà can ignore computational detail • Fictional stand-ins for computation- Walrasian auctioneer- equilibrium in games • Underlying computational processes are modeled in REDUCED FORM

6. Traditional view (cte.) • Axioms are considered primitives (logic vs biology as constraint on choices) • A developed preference for general mathematical proof over simulation • Study of “procedural rationality” algorithms (Simon) did not gain traction • Distrust of complicated many-equation macroeconomic models & simulations • Little post-1990 taste for SFI agent-based modeling

7. Neuroeconomics: neurobiologically based computational models of decision-making Goals of Neuroeconomics: • What computations are carried out by the brain to make different types of economics decisions? • How are these computations implemented by the brain? • What are the implications of this knowledge for economics, finance, education, AI, marketing, … ?

8. BUSINESSAPPLICATIONS JUGDMENT & DM THERAPEUTICAPPLICATIONS ECONOMICAPPLICATIONS COMPUTAT. MODELS NEUROSCIENCE PSYCHOLOGY A.I. Computation is at the core of Neuroeconomics

9. IINeuroeconomic Models of Valuation and Simple Choice

10. Event: trial 1 trial 2 trial 3 … Time: 1 2 3 4 5 6 7 8 9 10 11 12 …. Cue wait Reward Cue wait Reward Cue wait Reward Example I: Reward Prediction Learning • Brain’s problem: learn to predict size & timing of rewards that follow each type of cue • Temporal-difference learning algorithms have been designed in CS to solve this problem (Sutton & Barto (1998))

11. How can the brain learn the reward function? Notation:- True value of state s: mean r(s)- pt(s) = computed predicted value at beginning of triat t (= brain’s best guess about the state’s true value)- t(s) = r(s) - pt(s) = error signal in trial tThis error term is extremely important: it serves as THE teaching signal!

12. Learning Algorithm • Step 1. Arbitrarily initialize the decision values p1(s) for all s • Step 2. Every trial t: • -- begin with pt(s) -- measure actual reward • -- Compute error (t) • -- Update the DV for a and c active in trial as follows: • pt+1(s) = pt(s) +  (t) • where • -> (0,1) is a learning rate • Under very general conditions, E(pt(a|c)) -> E(r(s)) for all s

13. How well do TD algorithms describe brain’s reward learning? Cue Reward TD-ErrorsBefore Learning TD-ErrorsDuring Learning TD-Errors AfterLearning if Unexpected Omission of reward

14. Can we find evidence of TD-error signals in monkeys’ brains? Single unit recordings from VTA dopamine neurons revealed that these neurons produce responses consistent with TD - learning: Schultz [1998]

15. What brain areas show activation that correlates w/ TD-error signals in humans? p<<0.001 +6 +3 R -3 -6  at time of CS CS+ trials -30 +54 From O’Doherty et.al. [2003]

16. ? Example II: Role of Visual Attention in Simple Choice

17. Visualattention DVscomputation Comparator Model: Three Parallel Processes • e=time elapsed since beginning of choice trial g(e)= L,R dL(e), dR(e) Choose L,R,or wait

18. Visualattention switch g(e) g(e) DVComputation Comparator dL(e), dR(e) choose g(e) or switch

19. Visual attention process • First fixation: Stochastic bottom-up process • P0 = Prob first fixation to L • Exponential latency: Pr(First fixation begins at t)= 1- B.e- t • Subsequent fixations: top-down process • Follow the commands of the comparator process

20. v+ 0 v- t Value construction process

21. Comparator process: • During each fixation, the comparator either chooses g(e) or sends a signal to the visual system to switch gaze • Length of each fixation stochastic:-- d = duration of current fixation-- Pr(comparator evaluates at d)= 1- A.e- d • Decision made as follows:-- rx(e) = d(tx(e)) - d(ty(e)) • -- Choose g(e) with probability-- Wait (and switch fixation) with prob • Always switch after first fixation

22. Model predictions • Behavioral: S-shaped choice probabilities • Process: RTs and #saccades increase with choice difficulty • Performance:- Importance of first fixation: P(choice=best|fist-fixation=best)> P(choice=best|fist-fixation=worse)- First look bias: for items with similar value P(choice=L|fist-fixation=L)> P(choice=L|fist-fixation=R)- …

23. Enforce2000 msfixation Present until a choiceis made 1000 ms + + + Collect eye-fixations @ 50 Hz Test

24. Results

25. Summary • Computation is at the core of the nascent field of Neuroeconomics • Goal is to (1) describe the computation and processes that the brain uses to make decisions and (2) establish their neural basis • Test the computational processes directly using modern neuroscience and psychology tools -- from fMRI to eye tracking • Feasibility of the research agenda has already been proven • Novel insights into DM are already being generated by this class of models.

26. IIIModels of Strategic Choice & Learning in Games

27. Some theoretical interest in computational models • Finite-state automata (Rubinstein, Neyman, et. al.) • Computational complexity (Gilboa-Zemel on NP-hard games) • Not linked to data or practical problems

28. Cognitive hierarchy models of limited strategic thinking • Selten (1998): • “The natural way of looking at game situations…is not based on circular concepts, but rather on a step-by-step reasoning procedure” • Cognitive hierarchy • “Level 0” use a heuristic (e.g. randomize) • “Level k” best-respond to choices of level 0-(k-1) • Axiom f(k)/f(k-1)  1/k (k-th step increasingly difficult)  f(k)=e-ttk/k! (Poisson) • Limit as t   often converges to equilibrium • Simpler than equilibrium in some ways easier to compute predictions no problem of multiple equilibria

29. Limited planning ahead in bargaining (Science, 03) 3-stage bargaining 1: $5 p1 offers 2: $2.50 p2 offers 3: $1.25 p1 offers (0,0) if rejected

30. E.g. “P-beauty contest” (Ho et al AER 98)pick x in [0,100], x closest to (2/3) of average wins

31. “Choosing” computations are different than “belief formation” computations Bhatt-Camerer GEB 2005

32. Field application: “Cold opening” of movies (unavailable to critics for Friday review) Studios do not let worst movies get reviewed… ”cold” opening increases box office

33. EWA learning in games: Generalized reinforcement • Reinforcement, fictitious play linked (Econometrica 99) • Update attractions to strategy j from payoff A ij (t) - A ij (t-1) = [*π(sij,s-i (t)) -A ij (t-1)]/(ϕN(t-1)+1) = prediction error/increasing weight  is “imagination” of counterfactual payoffs ϕ is recency weight Typical values: N(0)=1, ϕ=.8, weights go from .56  .20 • Can replace , ϕ with “self-tuning” functions (JET ’07) • Can add “sophistication”– players know others are learning (JET 02, GEB 06)

34. Example: Price matching with loyalty rewards (Capra, Goeree, Gomez, Holt AER ‘99) • Players 1, 2 pick prices [80,200] ¢ Price is P=min(P1,,P2) Low price firm earns P+50 High price firm earns P-50 • What happens? • Theory: competition drives prices to 80

36. IVComputational Issues at different levels:individuals, firms, markets

37. Levels of computational modelling in economics • Individuals (what you’ve seen) • Firms • Firms as hierarchies of imperfectly informed individuals (Radner-Van Zandt) Optimal hierarchies for aggregating formation • Mechanism design • Computability as an individual rationality constraint (Ledyard) • Markets • Markets as computational mechanisms • Computing equilibria (Judd, Kearns et al) • Smart markets: Hybrids of bids and optimal combination (e.g. combinatorial “package auctions” e.g. PCS spectrum) • Information aggregation • Markets ‘compute’ probabilities of events (e.g. prediction markets)

38. Prediction markets • Began with basic research: 20 yrs to wide use • Plott and Sunder (1982 Econometrica): • Markets for “contingent claims” • Pay $1 if an event occurs. Prices reveal probabilities • Markets are $-weighted opinion polls of self-selected respondents • Iowa Political Markets 1988 (http://www.biz.uiowa.edu/iem/) • Markets for political events predict surprisingly accurately • Tradesports 2002 (http://www.tradesports.com/) et al • Used by some companies, policy markets • See Wolfers & Zitzewitz J Econ Perspectives 04

39. Six hours earlier (9pm EST Oct 26 ‘06): Guess about Karl Rove non-indictment appears in Intrade price drop…36 hrs before Oct 28 Libby indictment

40. Google news at 1:46am EST Oct 27: Will Karl Rove be indicted? • Rove critics again turn up the volume • New York Daily News - Oct 27 1:18 AM • With rampant rumors of a soon-to-drop indictment in Special Counsel Patrick Fitzgerald 's CIA leak investigation, the Karl Rove literary business is booming. • Rove's Last Campaign • Washington Post - Oct 26 11:31 AM • Will Karl Rove, architect of President Bush's improbable political career, snatch one last victory from the jaws of defeat? (Or at least avoid getting indicted?) Something appears to have provoked special prosecutor Patrick J. Fitzgerald into a last-minute flurry of activity centered............ • Leak Counsel Is Said to Press on Rove's Role • New York Times - Oct 25 7:25 PM • Three days before the grand jury is set to expire, Patrick Fitzgerald appeared to be trying to determine Karl Rove's role in the outing of a C.I.A.'s officer's identity. • Libby, Rove Await Indictment Decisions By Martin Sieff, UPI Senior News Analyst Washington DC (UPI) Oct 25, 2005 • Space War - Oct 26 9:53 PM • Washington seethed with rumors and speculation Tuesday night on the eve of the expected announcement of possible indictments in the Valerie Plame CIA leak probe.

41. Current (3/15) “prices” of Scooter Libby pardon Mar 16 - 3:18AM GMT

42. VFuture of computational models of decision in Economics

43. @ the Individual level • It will look like theoretical neuroscience • Focus on modeling the neural and psychological processes involved in decision-making • Modeling constraints provided by neural, psychological, and behavioral data • Models will be tested with techniques such:- fMRI- electrophysiology- TMS- eyetracing- behavioral predictions

44. @ the firm and market levels • Will build on the properties of the individual level models • Model the interactions of many agents • Goal will be to improve our understanding of:- auctions- price formation in markets- financial markets dynamics- macroeconomic performance and policy