Conviction Learning in an Insecure Endless Diversion.

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Numerous vital recreations have vast methodologies. Duopoly, PG, bartering, ... Fit shifts by amusement, mistake measure. Issue #3: Belief Learning. On the off chance that subjects are framing ...
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Conviction Learning in an Unstable Infinite Game Paul J. Healy CMU

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Issue #3 Issue #2 Belief Learning in an Unstable Infinite Game Issue #1

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Issue #1: Infinite Games Typical Learning Model: Finite arrangement of systems Strategies get weight in light of "wellness" Bells & Whistles: experimentation, overflows… Many imperative recreations have unending procedures Duopoly, PG, bartering, barters, war of wearing down… Quality of fit delicate to framework size? Models don\'t utilize technique space structure

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Previous Work Grid size on fit quality: Arifovic & Ledyard Groves-Ledyard components Convergence disappointment of RL with |S| = 51 Strategy space structure: Roth & Erev AER \'99 Quality-of-fit/mistake measures What\'s the right metric space? Closeness in probs. on the other hand closeness in systems?

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Issue #2: Unstable Game Usually anticipating joining rates Example: p –beauty challenges Instability: Toughest test for learning models Most factual force

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Previous Work Chen & Tang \'98 Walker component & flimsy Groves-Ledyard Reinforcement > Fictitious Play > Equilibrium Healy \'06 5 PG instruments, foreseeing merging or not Feltovich \'00 Unstable limited Bayesian amusement Fit changes by diversion, blunder measure

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Issue #3: Belief Learning If subjects are framing convictions, measure them! Technique 1: Direct elicitation Incentivized surmises about s - i Method 2: Inferred from result table utilization Tracking result "lookups" may illuminate our models

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Previous Work Nyarko & Schotter \'02 Subjects BR to expressed convictions Stated convictions not very exact Costa-Gomes, Crawford & Boseta \'01 Mouselab to recognize sorts How players settle amusements, not learning

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This Paper Pick a temperamental endless diversion Give subjects a number cruncher instrument & track use Elicit convictions in a few sessions Fit models to information in standard way Study development of "convictions" "Convictions" <= adding machine apparatus "Convictions" <= inspired convictions

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The Game Walker\'s PG system for 3 players Added a "discipline" parameter

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Parameters & Equilibrium v i (y) = b i y – an i y 2 + c i Pareto ideal: y = 7.5 Unique PSNE: s i * = 2.5 Punishment γ = 0.1 Purpose: Not too wild, adjustments once in a while negative Guessing Payoff: 10 – |g L - s L |/4 - |g R - s R |/4 Game Payoffs: Pr(<50) = 8.9% Pr(>100) = 71%

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Choice of Grid Size S = [-10,10]

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Properties of the Game Best reaction: BR Dynamics: insecure One eigenvalue is +2

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Design PEEL Lab, U. Pittsburgh All Sessions 3 player bunches, 50 periods Same gathering, ID#s for all periods Payoffs and so forth normal data No express open great encircling Calculator constantly accessible 5 minute \'warm-up\' with mini-computer Sessions 1-6 Guess s L and s R . Sessions 7-13 Baseline: no speculations.

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Does Elicitation Affect Choice? All out Variation: No critical contrast ( p=0.745 ) No. of Strategy Switches: No huge distinction ( p=0.405 ) Autocorrelation (consistency): Slightly more without elicitation Total Earnings per Session: No critical contrast ( p=1 ) Missed Periods: Elicited: 9/300 (3%) versus Not: 3/350 (0.8%)

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Does Play Converge? Normal | s i – s i * | per Period Average | y – y o | per Period

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Does Play Converge, Part 2

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Accuracy of Beliefs Guesses show signs of improvement in time Average || s - i – s - i (t) || per Period Elicited guesses Calculator inputs

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Model 1: Parametric EWA δ : weight on methodology really played φ : rot rate of past attractions ρ : rot rate of past experience A(0): starting attractions N(0): introductory experience λ : reaction affectability to attractions

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Model 1\': Self-Tuning EWA N(0) = 1 Replace δ and φ with deterministic capacities:

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STEWA: Setup Only remaining parameters: λ and A 0 λ will be evaluated 5 minutes of \'Number cruncher Time\' gives A 0 Average result from adding machine trials:

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STEWA: Fit Likelihoods are "zero" for all λ Guess: Lots of close misses in expectations Alternative Measure: Quad. Scoring Rule Best fit: λ = 0.04 (past studies: λ >4) Suggests attractions are exceptionally focused

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STEWA: Adjustment Attempts The issue: close misses in technique space, not in time Suggests: change δ (weight on hypotheticals) unique particular : QSR* = 1.193 @ λ *=0.04 δ = 0.7 ( p - excellence est.): QSR* = 1.056 @ λ *=0.03 δ = 1 (conviction model): QSR* = 1.082 @ λ *=0.175 δ (k,t) = % of B.R. result: QSR* = 1.077 @ λ *=0.06 Altering φ : 1/8 weight on shocks: QSR* = 1.228 @ λ *=0.04

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STEWA: Other Modifications Equal starting attractions: more awful Smoothing Takes point of interest of system space structure λ spreads likelihood crosswise over methodologies uniformly Smoothing spreads likelihood to adjacent procedures Smoothed Attractions Smoothed Probabilities But… No Improvement in QSR* or λ * ! Provisional Conclusion: STEWA: not broken, or can\'t be settled…

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Other Standard Models Nash Equilibrium Uniform Mixed Strategy (\'Random\') Logistic Cournot BR Deterministic Cournot BR Logistic Fictitious Play Deterministic Fictitious Play k-Period BR

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"New" Models Best react to expressed convictions (S1-S6 just) Best react to adding machine passages Issue: how to total mini-computer utilization? Rotting normal of information Reinforcement in light of number cruncher settlements Decaying normal of adjustments

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Model Comparisons * Estimates on the lattice of whole numbers {-10,- 9,… ,9,10} In = periods 1-35 Out = periods 36-End

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Model Comparisons 2

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The "Take-Homes" Methodological issues Infinite procedure space Convergence versus Unsteadiness Right thought of blunder Self-Tuning EWA fits best . Surmises & adding machine information don\'t appear to offer any more prescient force… ?!?!

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