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Meaningful learning and transfer of learning in games
September 21, 2006
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
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.
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.
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.
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.
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