Teck-Hua Ho

Experience-weighted attraction learning in normal form games

In ‘experience-weighted attraction’ (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded, relative to reinforcement of chosen strategies according to received payoffs. The other key features are two discount rates, φ and ρ, which separately discount previous attractions, and an experience weight. EWA includes reinforcement learning and weighted fictitious play (belief learning) as special cases, and hybridizes their key elements. When δ= 0 and ρ= 0, cumulative choice reinforcement results. When δ= 1 and ρ=φ, levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs. Using three sets of experimental data, parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample. Estimates of δ are generally around .50, φ around .8 − 1, and ρ varies from 0 to φ. Reinforcement and belief-learning special cases are generally rejected in favor of EWA, though belief models do better in some constant-sum games. EWA is able to combine the best features of previous approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do.

Violations of the betweenness axiom and nonlinearity in probability

Betweenness is a weakened form of the independence axiom, stating that a probability mixture of two gambles should lie between them in preference. Betweenness is used in many generalizations of expected utility and in applications to game theory and macroeconomics. Experimental violations of betweenness are widespread. We rule out intransitivity as a source of violations and find that violations are less systematic when mixtures are presented in compound form (because the compound lottery reduction axiom fails empirically). We also fit data from nine studies using Guls disappointment-aversion theory and two variants of EU, which weight separate or cumulative probabilities nonlinearly. The three theories add only one parameter to EU and fit much better.

Redefine Statistical Significance

We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries.

Store Choice and Shopping Behavior: How Price Format Works

This article presents a perceived shopping utility framework for analyzing the impact of retail price format on store choice. This, in turn, determines three key performance metrics: number of shoppers; number of trips; and average spending per trip. When choosing a store, consumers evaluate both the fixed and variable utilities of shopping. The fixed utility does not vary from trip to trip whereas the variable utility depends on the size and composition of the shopping list. This article summarizes prior findings on store choice, analyzes how retailers can improve their performance, and interprets the practices of leading retailers. It presents a framework that can accommodate situations where retailers face multiple segments of buyers who have different sensitivities to fixed and variable utilities.

Self-tuning experience weighted attraction learning in games

Self-tuning experience weighted attraction (EWA) is a one-parameter theory of learning in games. It addresses a criticism that an earlier model (EWA) has too many parameters, by fixing some parameters at plausible values and replacing others with functions of experience so that they no longer need to be estimated. Consequently, it is econometrically simpler than the popular weighted fictitious play and reinforcement learning models. The functions of experience which replace free parameters “self-tune” over time, adjusting in a way that selects a sensible learning rule to capture subjects’ choice dynamics. For instance, the self-tuning EWA model can turn from a weighted fictitious play into an averaging reinforcement learning as subjects equilibrate and learn to ignore inferior foregone payoffs. The theory was tested on seven different games, and compared to the earlier parametric EWA model and a one-parameter stochastic equilibrium theory (QRE). Self-tuning EWA does as well as EWA in predicting behavior in new games, even though it has fewer parameters, and fits reliably better than the QRE equilibrium benchmark.

Evaluating replicability of laboratory experiments in economics

Another social science looks at itself Experimental economists have joined the reproducibility discussion by replicating selected published experiments from two top-tier journals in economics. Camerer et al. found that two-thirds of the 18 studies examined yielded replicable estimates of effect size and direction. This proportion is somewhat lower than unaffiliated experts were willing to bet in an associated prediction market, but roughly in line with expectations from sample sizes and P values. Science, this issue p. 1433 By several metrics, economics experiments do replicate, although not as often as predicted. The replicability of some scientific findings has recently been called into question. To contribute data about replicability in economics, we replicated 18 studies published in the American Economic Review and the Quarterly Journal of Economics between 2011 and 2014. All of these replications followed predefined analysis plans that were made publicly available beforehand, and they all have a statistical power of at least 90% to detect the original effect size at the 5% significance level. We found a significant effect in the same direction as in the original study for 11 replications (61%); on average, the replicated effect size is 66% of the original. The replicability rate varies between 67% and 78% for four additional replicability indicators, including a prediction market measure of peer beliefs.

Neural Correlates of Trial-to-Trial Fluctuations in Response Caution

Trial-to-trial variability in decision making can be caused by variability in information processing as well as by variability in response caution. In this paper, we study which neural components code for trial-to-trial adjustments in response caution using a new computational approach that quantifies response caution on a single-trial level. We found that the frontostriatal network updates the amount of response caution. In particular, when human participants were required to respond quickly, we found a positive correlation between trial-to-trial fluctuations in response caution and the hemodynamic response in the presupplementary motor area and dorsal anterior cingulate. In contrast, on trials that required a change from a speeded response mode to a more accurate response mode or vice versa, we found a positive correlation between response caution and hemodynamic response in the anterior cingulate proper. These results indicate that for each decision, response caution is set through corticobasal ganglia functioning, but that individual choices differ according to the mechanisms that trigger changes in response caution.

Information Sharing in a Long-Term Supply Chain Relationship: The Role of Customer Review Strategy

In this paper, we study the practice of forecast sharing and supply chain coordination with a game-theoretical model. We find that in a one-shot version of the game, forecasts are not shared truthfully by the customer. The supplier will rationally discount the forecast information in her capacity allocation. This results in Pareto suboptimality for both supply chain parties. However, we show that a more efficient, truth-sharing outcome can emerge as an equilibrium from a long-term relationship. In this equilibrium, forecast information is transmitted truthfully and trusted by the supplier, who in turn allocates the system-optimal capacity. This leaves both the customer and the supplier better-off, compared to the nontruthful-sharing equilibrium. We identify a multiperiod review strategy profile that supports the truthful-sharing equilibrium. The key element of this strategy is that the supplier computes a scoring index of the customers behavior that is updated over time and used to evaluate if the customer has sufficient incentive to share his private information truthfully in each transaction of the repeated game. Compared to trigger strategies, review strategies are more tolerant but require diligence and more monitoring effort.

Behavioral Game Theory: Thinking, Learning and Teaching

Game theory is a mathematical system for analysing and predicting how humans behave in strategic situations. Standard equilibrium analyses assume that all players: (1) form beliefs based on an analysis of what others might do (strategic thinking); (2) choose the best response given those beliefs (optimization); and (3) adjust best responses and beliefs until they are mutually consistent (equilibrium).

A Modeling Framework for Category Assortment Planning

The complexity of managing a category assortment has grown tremendously in recent years due to the increased product turnover and proliferation rates in most categories. It is an increasingly difficult task for managers to find an effective assortment due to uncertain consumer preferences and the exponential number of possible assortments. This paper presents an empirically based modeling framework for managers to assess the revenue and lost sales implication of alternative category assortments. Coupled with a local improvement heuristic, the modeling framework generates an alternative category assortment with higher revenue.This framework, which consists of a category-purchase-incidence model and a brand-share model, is calibrated and validated using 60,000 shopping trips and purchase records. Specifically, the purchase-incidence model predicts the probability of an individual customer who purchases (and who does not purchase) from a given product category during a shopping trip. The no-purchase probability enables us to estimate lost sales due to assortment changes in the category. The brand-share model predicts which brand the customer chooses if a purchase incidence occurs in the category. Our brand-share model extends the classical Guadagni and Little model (1983) by utilizing three new brand-width measures that quantify the similarities among products of different brands within the same category.We illustrate how our modeling framework is used to reconfigure the category assortment in eight food categories for five stores in our data set. This reconfiguration exercise shows that a reconfigured category assortment can have a profit improvement of up to 25.1% with 32 products replaced. We also demonstrate how our modeling framework can be used to gauge lost sales due to assortment changes. We find the level of lost sales could range from 0.9% to 10.2% for a period of 26 weeks.