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  • Meaningful learning and transfer of learning in games

    September 21, 2006

    Abstract:

    We explore a distinction among different ways in which people learn, in the

    context of games. Psychologists have long recognized an important distinction between

    two kinds of learning: one that is relatively shallow, domain-specific and operates

    through repeated association of stimuli and outcomes; and another that is deeper, requires

    the acquisition of concepts or meaning, and transfers more easily across domains. The

    literature on learning in games focuses almost exclusively on the former, which we term

    adjustment learning.

    We provide compelling evidence of the latter kind of learning, which we term

    meaningful learning. In two experiments, we demonstrate that learning – the acquisition

    of iterated dominance – occurs in the absence of any feedback, a kind of learning that

    cannot be explained by adjustment learning processes but that is consistent with

    meaningful learning. Moreover, we demonstrate that, consistent with the psychological

    literature, such meaningful learning transfers to new domains (games), and that such

    transfer does not occur with adjustment learning.

  • I. Introduction

    A considerable amount of research in economics attempts to understand how

    people learn in strategic environments. Several experimental studies on games

    demonstrate that players do not initially play equilibrium strategies, but that with

    repetition their behavior converges towards equilibrium, and several models attempt to

    provide a theoretical basis for this regularity (see Camerer, 2003, Chapter 6). While

    these models vary in the details of how they assume learning takes place, they all share

    the assumption that learning operates by players observing how well different strategies

    perform – either by playing those strategies, observing others playing them, or observing

    the (foregone) outcomes produced by unselected strategies – and then adjusting their

    behavior in the direction of better-performing strategies in subsequent plays of the game.1

    Thus, current economic models essentially conceptualize learning as a process best

    described as adjustment learning, or gradually figuring out what works in a specific game.

    While many papers in economics explore the above kind of learning,

    psychologists would consider this conceptualization of learning to be incomplete. For

    decades psychologists have recognized the existence of two kinds of learning, based on

    the way in which people learn, the kind of knowledge produced by learning, and the

    ability of individuals to transfer what they learn to new domains. This distinction – often

    described as “implicit” versus “explicit” learning (Reber, 1967) – is important because it

    1 For instance, in fictitious play models, players form beliefs of the likely payoffs of different strategies, on the basis of opponents’ prior choices, and select those strategies with relatively high expected payoffs given those beliefs (e.g., Cheung and Friedman, 1998; Fudenberg and Levine, 1998). In reinforcement-learning models, players’ propensities to select different strategies are based on what has been successful in the past (e.g., Erev and Roth, 1998). Camerer and Ho’s (1999) Experience Weighted Attraction model is a generalization of fictitious play and reinforcement models, in which players potentially assign different weights to strategies actually chosen and to those foregone. Merlo and Schotter (2003) provide evidence that players can learn by observing others’ outcomes (and that such “observational” learning may even outperform “first-hand” experience). There are also “rule learning” models (Stahl, 2000) in which higher- order rules for strategy selection, rather than strategies themselves, are reinforced through experience.

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  • highlights significant differences in the depth of what is learned and the ability of

    individuals to generalize their learning to new contexts.2

    A. The duality of learning

    What psychologists refer to as implicit learning is an unconscious process that

    yields knowledge that is usually neither accessible to cognition nor verbalizable (Reber,

    1989; Mandler, 2004). It is demonstrated, for instance, by showing that subjects exposed

    to massive amounts of information demonstrate improved performance in pattern

    matching, but that such performance improvement exceeds their ability to articulate or

    generalize their knowledge (e.g., Berry and Broadbent, 1984; Hayes and Broadbent,

    1988; Nissen and Bullemer, 1987).3 A key property of this kind of learning is that it

    operates through perceptual and associative processes, rather than through cognition, and

    therefore fails to produce cognitive or conceptual representations of what is learned, or

    meaningful knowledge (Mandler, 2004). An important consequence of the absence of

    such meaningful knowledge is that what is learned implicitly cannot be consciously

    manipulated or transferred to new domains (Holyoak and Spellman, 1993).

    Explicit learning, by contrast, is characterized as a conscious process through

    which individuals come to obtain meaningful cognitive representations of underlying

    concepts, structure, and relationships. Unlike the knowledge acquired via implicit

    learning, the knowledge acquired via explicit learning is consciously accessible, 2 This dichotomy goes by a number of different names in psychology, including unconscious/conscious, procedural/declarative, automatic/controlled, reflexive/reflective, and unselective/selective (Holyoak and Spellman, 1993; Hayes and Broadbent, 1988). 3 For example, in Arthur Reber’s (1967, 1989) artificial-grammar learning paradigm, subjects observe several text strings and are told that they have been generated according to certain rules. Subjects are then asked to determine whether a series of both old and novel strings have been generated according to those rules. Subjects typically distinguish grammatical from nongrammatical strings at a frequency greater than chance, though they cannot articulate the rules they were using to make those judgments.

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  • generalizable, and can be communicated. Moreover, explicit learning involves cognition,

    the evaluation of hypotheses, and often results in the development of improved general

    problem-solving ability (Hayes and Broadbent, 1988; Mandler, 2004). Thus, a key

    property that separates explicit from implicit learning is that the former is context-free

    and generates knowledge that can transfer to novel situations.

    It is surprising that this well-known distinction in psychology is not familiar to

    economists and game theorists, despite the considerable attention to the study of learning

    in games. This is perhaps because most studies of learning in games are ideally suited to

    the formation and measurement of implicit learning and are therefore not very likely to

    produce explicit, or meaningful, learning. Such studies typically rely on experiments in

    which subjects play a single game repeatedly, over many trials and with immediate

    feedback after each trial (see Camerer, 2003, Chapter 6), but with little time between

    trials to engage in cognitive reflection or the development of meaningful knowledge.

    Thus, the process of trial-and-error through which individuals learn in these experiments

    – which is well-represented by models of adjustment learning – is similar to the

    associative strengthening that drives implicit learning in the psychology literature.4

    The relationship between the adjustment learning usually studied in experimental

    games and implicit learning is perhaps most strongly illustrated by the lack of transfer of

    learning to new games. Despite many experiments on learning in games – in which

    subjects learn while playing an abstract game repeatedly with prompt outcome feedback

    – there is very little evidence that what is learned transfers to new strategically similar

    4 In fact, there is some evidence that learning similar to that which occurs in repeated games may be independent of cognition, and may operate through unconscious emotional reactions to payoffs. For instance, Bechara et al. (1994) demonstrate that learning in the “Iowa Gambling Task” (in which subjects choose between lotteries) more closely corresponds to subjects’ ability to emotionally “feel” good and bad payoffs than to their ability to store and cognitively manipulate payoff information.

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  • games. For instance, Ho et al. (1998) explicitly test for transfer in two closely-related

    dominance-solvable games, and find no transfer from the first game to the second.

    Similarly, in a series of papers, Cooper and Kagel (2003, 2005 & In press) find that

    transfer of learning does not occur when having individual subjects play two abstract

    signaling games sequentially.

    In fact, the minimal evidence of transfer of learning in games suggests that it

    occurs only when experiments include procedures

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