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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.
Neural Evidence of Regret and Its Implications for Investor Behavior
We use neural data collected from an experimental asset market to measure regret preferences while subjects trade stocks. When subjects observe a positive return for a stock they chose not to purchase, a regret signal is observed in an area of the brain that is commonly active during reward processing. Subjects are unwilling to repurchase stocks that have recently increased in price, even though this is suboptimal in our experiment. The strength of stock repurchasing mistakes is correlated with the neural measures of regret. Subjects with high rates of repurchasing mistakes also exhibit large disposition effects.
Predictable Effects of Visual Salience in Experimental Decisions and Games
Bottom-up stimulus-driven visual salience is largely automatic, effortless, and independent of a person’s “top-down” perceptual goals; it depends only on features of a visual stimulus. Algorithms have been carefully trained to predict stimulus-driven salience values for each pixel in any image. The economic question we address is whether these salience values help explain economic decisions. Our first experimental analysis shows that when people pick between sets of fruits that have artificially induced value, predicted salience (which is uncorrelated with value by design) leads to mistakes. Our second analysis uses evidence from games in which choices are locations in images. When players are trying to cooperatively match locations, predicted salience is highly correlated with the success of matching (r = .57). In competitive hider-seeker location games, players choose salient locations more often than predicted by the unique Nash equilibrium. This tendency creates a disequilibrium “seeker’s advantage” (seekers win more often than predicted in equilibrium). The result can be explained by level-k models in which predicted stimulus-driven salience influences level-0 choices and thereby influences overall perceptions, beliefs, and choices of higher-level players. The third analysis shows that there is an effect of visual salience in matrix games, but it is small and statistically weak. Applications to behavioral IO, price and tax salience, nudges and design, and visually influenced beliefs are suggested.
Overconfidence and Excess Entry: An Experimental Approach
Psychological studies show that most people are overconfident about their own relative abilities, and unreasonably optimistic about their futures (e.g. Shelly E. Taylor and J.D. Brown, 1988; Neil D. Weinstein, 1980). When assessing their position in a distribution of peers on almost any positive trait-- like driving ability (Ola Svenson, 1981 ), income prospects, or longevity-- a vast majority of people say they are above the average, although of course, only half can be (if the trait is symmetrically distributed). This paper explores whether optimistic biases could plausibly and predictably influence economic behavior in one particular setting-- entry into competitive games or markets. Many empirical studies show that most new businesses fail within a few years. For example, using plant level data from the U.S. Census of Manufacturers spanning 1963-1982, Timothy Dunne et al. (1988) estimated that 61.5 percent of all entrants exited within five years and 79.6 percent exited within 10 years. Most of these exits are failures (see also Dunne et al., 1989a, 1989b; D. Shapiro and R.S. Khemani, 1987).
The Predictive Utility of Generalized Expected Utility Theories
Many alternative theories have been proposed to explain violations of expected utility (EU) theory observed in experiments. Several recent studies test some of these alternative theories against each other. Formal tests used to judge the theories usually count the number of responses consistent with the theory, ignoring systematic variation in responses that are inconsistent. We develop a maximum-likelihood estimation method which uses all the information in the data, creates test statistics that can be aggregated across studies, and enables one to judge the predictive utility-the fit and parsimony-of utility theories. Analyses of 23 data sets, using several thousand choices, suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit. The menu is: mixed fanning, prospect theory, EU, and expected value. Which theories are best is highly sensitive to whether gambles in a pair have the same support (EU fits better) or not (EU fits poorly). Our method may have application to other domains in which various theories predict different subsets of choices (e.g., refinements of Nash equilibrium in noncooperative games).
Neuroeconomics: How Neuroscience Can Inform Economics
Neuroeconomics uses knowledge about brain mechanisms to inform economic analysis, and roots economics in biology. It opens up the “black box” of the brain, much as organizational economics adds detail to the theory of the firm. Neuroscientists use many tools— including brain imaging, behavior of patients with localized brain lesions, animal behavior, and recording single neuron activity. The key insight for economics is that the brain is composed of multiple systems which interact. Controlled systems (“executive function”) interrupt automatic ones. Emotions and cognition both guide decisions. Just as prices and allocations emerge from the interaction of two processes—supply and demand— individual decisions can be modeled as the result of two (or more) processes interacting. Indeed, “dual-process” models of this sort are better rooted in neuroscientific fact, and more empirically accurate, than single-process models (such as utility-maximization). We discuss how brain evidence complicates standard assumptions about basic preference, to include homeostasis and other kinds of state-dependence. We also discuss applications to intertemporal choice, risk and decision making, and game theory. Intertemporal choice appears to be domain-specific and heavily influenced by emotion. The simplified ß-d of quasi-hyperbolic discounting is supported by activation in distinct regions of limbic and cortical systems. In risky decision, imaging data tentatively support the idea that gains and losses are coded separately, and that ambiguity is distinct from risk, because it activates fear and discomfort regions. (Ironically, lesion patients who do not receive fear signals in prefrontal cortex are “rationally” neutral toward ambiguity.) Game theory studies show the effect of brain regions implicated in “theory of mind”, correlates of strategic skill, and effects of hormones and other biological variables. Finally, economics can contribute to neuroscience because simple rational-choice models are useful for understanding highly-evolved behavior like motor actions that earn rewards, and Bayesian integration of sensorimotor information. Who knows what I want to do? Who knows what anyone wants to do? How can you be sure about something like that? Isn't it all a question of brain chemistry, signals going back and forth, electrical energy in the cortex? How do you know whether something is really what you want to do or just some kind of nerve impulse in the brain. Some minor little activity takes place somewhere in this unimportant place in one of the brain hemispheres and suddenly I want to go to Montana or I don't want to go to Montana. (White Noise, Don DeLillo)
Models of Thinking, Learning, and Teaching in Games
Noncooperative game theory combines strategic thinking, best-response, and mutual consistency of beliefs and choices (equilibrium). Hundreds of experiments show that in actual behavior these three forces are limited, even when subjects are highly motivated and analytically skilled (Camerer, 2003). The challenge is to create models that are as general, precise, and parsimonious as equilibrium, but which also use cognitive details to explain experimental evidence more accurately and to predict new regularities. This paper describes three exemplar models of behavior in one-shot games (thinking), learning over time, and how repeated “partner” matching affects behavior (teaching) (see Camerer et al., 2002b).
Looming Large or Seeming Small? Attitudes Towards Losses in a Representative Sample
We measure individual-level loss aversion using three incentivized, representative surveys of the U.S. population (combined N=3,000). We find that around 50% of the U.S. population is loss tolerant—they are willing to accept negative-expected-value gambles that contain a loss. This is counter to expert predictions and earlier findings—which mostly come from laboratory/student samples—that 70–90% of participants are loss averse. Consistent with the different findings in our study versus the prior literature, loss aversion is more prevalent in people with high cognitive ability. Further, our measure of gain–loss attitudes exhibits similar temporal stability and better predictive power outside our survey than measures of risk aversion. Loss-tolerant individuals are more likely to report recent gambling, investing a higher percentage of their assets in stocks, and experiencing financial shocks. These results support the general hypothesis that individuals value gains and losses differently, and that gain–loss attitudes are an important economic preference. However, the tendency in a large proportion of the population to emphasize gains over losses is an overlooked behavioural phenomenon.
Loss Aversion in Post-Sale Purchases of Consumer Products and their Substitutes
This paper considers the measurement of consumer loss aversion in product markets. We introduce a test based on a “substitution effect,” focusing on how the end of a sale affects sales not of the good itself, but a substitute good. Such an effect cannot be easily confounded with consumer stockpiling. Using a unique dataset from an online hardware retailer, we find evidence consistent with consumer loss aversion. Moreover, we find that less experienced consumers suffer a more prominent loss aversion bias compared to more experienced consumers.