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SELF-CONFIDENCE
AND
PERSONAL MOTIVATION
Roland Bénabou and Jean Tirole^1
First version: June 1999
This version: June 2001
(^1) This paper was previously entitled “Self-Confidence: Intrapersonal Strategies.” We are grateful for help- ful comments and discussions to Dilip Abreu, Olivier Blanchard, Isabelle Brocas, Ed Glaeser, Dan Gilbert, Ian Jewitt, David Laibson, George Loewenstein, Andrew Postlewaite, Marek Pycia, Matt Rabin, Julio Rotem- berg and three anonymous referees, as well as conference and seminar participants at Chicago, Columbia, Cornell, MIT, the NBER, Northwestern, NYU, the Oxford Young Economists’ Conference, the University of Pennsylvania, Princeton, Stanford, and Yale. Bénabou gratefully acknowledges financial support from the National Science Foundation (SES—0096431).
SELF-CONFIDENCE AND PERSONAL MOTIVATION
Roland Bénabou and Jean Tirole^1
ABSTRACT
We analyze the value placed by rational agents on self—confidence, and the strategies employed in its pursuit. Confidence in one’s abilities generally enhances motivation, making it a valuable asset for individuals with imperfect willpower. This demand for self—serving beliefs (which can also arise fromhedonic or signalling motives) must be weighed against the risks of overconfidence. On the supply side, we develop a model of self-deception through endogenous memory that rec- onciles the motivated and rational features of human cognition. The resulting intrapersonal game of strategic communication typically leads to multiple equilibria. While “positive thinking” can improve welfare, it can also be self-defeating (and nonetheless pursued).
(^1) This paper was previously entitled “Self-Confidence: Intrapersonal Strategies.” We are grateful for helpful comments and discussions to Dilip Abreu, Olivier Blanchard, Isabelle Brocas, Ed Glaeser, Dan Gilbert, Ian Jewitt, David Laibson, George Loewenstein, Andrew Postlewaite, Marek Pycia, Matt Rabin, Julio Rotemberg and three anonymous referees, as well as conference and seminar participants at Chicago, Columbia, Cornell, MIT, the NBER, Northwestern, NYU, the Oxford Young Economists’ Conference, the University of Pennsylvania, Princeton, Stanford, and Yale. Bénabou gratefully acknowledges financial support from the National Science Foundation (SES—0096431).
and a motivation value. First, people may just derive utility from thinking well of themselves, and conversely find a poor self-image painful. Second, believing —rightly or wrongly— that one possesses certain qualities may make it easier to convince others of it. Finally, confidence in his abilities and efficacy can help the individual undertake more ambitious goals and persist in the face of adversity. While we shall mostly focus on this last explanation, all three should be seen as complementary, and for many purposes work equally well with the supply—side of our model (self—deception). The main reason why we emphasize the motivation theory is its substantially broader explana- tory power. Indeed, it yields an endogenous value of self—confidence that responds to the situations and incentives which the individual faces, in a way that can account for both “can-do” optimism and “defensive” pessimism. It also readily extends to economic and social interactions (altruistic or not), explaining why people generally prefer self—confident partners to self—doubting ones, and invest both time and effort in supporting the latter’s morale. The first premise of the motivation theory is that people have imperfect knowledge of their own abilities, or more generally of the eventual costs and payoffs of their actions.^2 The second one is that ability and effort interact in determining performance; in most instances they are complements, so that a higher self-confidence enhances the motivation to act. As demonstrated by the opening quote from James [1890], this complementarity has long been familiar in psychology. 3 It is also consistent with the standard observation that morale plays a key role in difficult endeavors; conversely, when people expect to fail they fail quite effectively, and failure leads to failure more readily for individuals characterized with low self-esteem (Salancik [1977]). The fact that a higher self-confidence enhances the individual’s motivation gives anyone with a vested interest in his performance an incentive to build up and maintain his self-esteem. First, the manipulator could be another person (parent, teacher, spouse, friend, colleague, manager) who is eager to see him “get his act together”, or otherwise apply himself to the task at hand. Such interpersonal strategies are studied in Bénabou and Tirole [2000]. Second, for an individual suffering from time inconsistency (e.g., hyperbolic discounting), the current self has a vested interest in the self-confidence of future selves, as it helps counter their natural tendency to quit too easily. It is in this context, which builds on Carrillo and Mariotti [2000], that we shall the investigate a variety of intrapersonal strategies of self—esteem maintenance. We shall thus see how and when people may choose to remain ignorant about their own abilities, and why they sometimes deliberately impair their own performance or choose overambitious tasks in which they are sure to fail (self-
(^2) The psychology literature generally views introspection as quite inaccurate (Nisbett and Wilson [1977]), and stresses that learning about oneself is an ongoing process. Furthermore, the self is constantly changing (e.g., Rhoden- walt [1986]): personal characteristics evolve with age, the goals pursued shift over one’s career and life cycle (often as the result of interactions with others), and the personal or economic environment in which these objectives are rewarded are pursued is typically variable. 3 Thus, Gilbert and Cooper [1985] note that “the classic attributional model of the causes of behavior ... [is described by] the well-known conceptual equation: (E × A) ± T D = B, in which effort times ability, plus or minus task difficulty equals the behavioral outcome.” Additional references are given in Section I. Note, however, that there are also instances where ability and effort are substitutes. As discussed below, we shall consider this case as well.
handicapping). Section II thus turns to the supply side of the self—confidence problem, and the “reality con- straints” that limit the extent to which people can engage in wishful thinking. In our model we maintain the standard assumption of individuals as rational (Bayesian) information processors. While almost universal in economics, this view is more controversial in psychology. On one hand, a lot of the classical literature has emphasized rationality and information-seeking in the process of self-identification, documenting the ways in which people update their beliefs according to broadly Bayesian principles.^4 On the other hand, the more recent cognitive literature abundantly docu- ments the less rational (or at least, motivated) side of human inference. For instance, a substantial body of evidence suggests that people tend to recall their successes more than their failures, and have self-servingly biased recollections and interpretations of their past performances.^5 Similarly, they tend to overestimate their abilities and other desirable traits, as well as the extent to which they have control over outcomes. They also rate their own probabilities as above average for favorable future life events, and below average for unfavorable ones; the more controllable these events through their future actions, the more so. 6 We shall capture this class of self-deception phenomena with a simple game—theoretic model of endogenous memory, or awareness-management, which represents one of the main contributions of this paper. Drawing on evidence about the mechanics and limitations of memory, it shows how to reconcile the motivated (“hot”) and rational (“cold”) features of human cognition, and could be used in any setting where a demand for motivated beliefs arises. The basic idea is that the individual can, within limits and possibly at a cost, affect the probability of remembering a given piece of data. At the same time, we maintain rational inference, so people realize (at least to some extent) that they have a selective memory or attention. The resulting structure is that of a game of strategic communication between the individual’s temporal selves. In deciding whether to try and repress bad news, the individual weighs the ben- efits from preserving his effort motivation against the risk of becoming overconfident. Later on, however, he appropriately discounts the reliability of rosy recollections and rationalizations. The implications of this game of asymmetric information are quite different from those of ex—ante de-
(^4) Thus attribution theory (Heider [1958] emphasizes the distinction between temporary (situational) and enduring (dispositional) characteristics. In economics parlance, the individual filters out noise in order to extract information from past events. In the social comparison process (Festinger [1954]), individuals assess their ability by comparing their performance with that of people facing similar conditions (familial, cultural, educational, etc.,). In other words, they use “relative performance evaluation”, or “benchmarking”, for self-evaluation. A good performance by others in one’s reference group is thus generally detrimental to self-esteem, and conversely some comfort is derived when others experience adversity (Schadenfreude). Relatively sophisticated updating also applies to the interpretation of praise and criticism: a person takes into account not only what others say (or do), but also their possible intentions. 5 Why they would want to do so in a social context is obvious. The interesting question is why they may bias their own inference process. 6 See, e.g. Taylor and Brown [1988]). Weinstein [1980], Alloy and Abrahamson [1979], and the many other references given in Section II. For recent overviews of the general phenomenon of self-deception, see Gilbert and Cooper [1985] and especially Baumeister [1998] on the psychological evidence, Elster [1999] and Mele [1999] for the philosophical debates and implications.
(see also Brocas and Carrillo [1999]). The central role played by memory also relates our model to Mullainathan [1999] and Laibson [2001], although one of its main features is to make recall endogenous.
I The demand for self-confidence
In most societies, self—confidence is widely regarded as a valuable individual asset. Going back at least to William James, an important strand in psychology has advocated “believing in oneself” as a key to personal success. Today, an enormous “self—help” industry flourishes, a sizeable part of which purports to help people improve their self—esteem, shed “learned helplessness” and reap the benefits of “learned optimism”. 7 American schools place such a strong emphasis on imparting children with self—confidence (“doing a great job!”) that they are often criticized for giving it preeminence over the transmission of actual knowledge. Hence the general question: why is a positive view of oneself, as opposed to a fully accurate one, seen as such a good thing to have?
Consumption value. A first reason may be that thinking of oneself favorably just makes a person happier: self—image is then simply another argument in the utility function. Indeed, psychologists emphasize the affective benefits of self—esteem as well as the functional ones on which we shall focus. One may also hypothesize that such preferences over beliefs could have been selected for through evolution: the overconfidence that typically results may propel individuals to undertake activities (exploration, foraging, combat) which are more risky than warranted by their private material returns, but confer important external benefits on the species. In Section V.B we shall explain how a hedonic self—image motive can readily be incorporated into our general framework.
Signalling value. A second explanation may be that believing oneself to be of high ability or morality makes it easier to convince others (rightly or wrongly) that one does have such qualities. Indeed, it is often said that to lie most convincingly one must believe one’s own lies. While the idea that people are “transparent” and have trouble misrepresenting their private information may seem unusual in economics, one could easily obtain an instrumental value of self—confidence from a signalling game where those who truly believe in their own abilities face lower costs of representing themselves favorably to others.
Motivation value. The explanation that we emphasize most is that self—confidence is valuable because it improves the individual’s motivation to undertake projects and persevere in the pursuit of his goals, in spite of the setbacks and temptations that periodically test his willpower. Morale is universally recognized as key to winning a medal, performing on stage, getting into college, writing a great book, doing innovative research, setting up a firm, losing weight, finding a mate, and so forth. The link between self—confidence and motivation is also pervasive in the psychology literature, from early writers like James [1890] to contemporary ones like Bandura [1977], according
(^7) These last two terms are borrowed from Seligman [1975], [1990].
to whom “beliefs of personal efficacy constitute the key factor of human agency” (see also, e.g., Deci [1975] or Seligman [1990]). The motivation theory also readily extends to economic (non altruistic) interactions, explaining why people typically prefer self—confident coworkers, managers, employees, teammates, soldiers, etc., to self—doubting ones; and why they spend substantial time and effort supporting the morale of those they end up matched with.^8
A The motivation problem
“Had I been less definitively determined to start working, I might have made an effort to begin right away. But because my resolve was absolute and, within twenty-four hours, in the empty frames of the next day where everything fit so well since I was not yet there, my good resolutions would easily be accomplished, it was better not to choose an evening where I was ill disposed for a beginning to which, alas! the following days would turn out to be no more propitious.”
Marcel Proust, Remembrance of Things Past. Consider a risk-neutral individual with a relevant horizon of three periods: t = 0, 1 , 2. At date 0, he selects an action that potentially affects both his flow payoff u 0 and his date-1 information structure.^9 At date 1, he decides whether to undertake a task or project (exert effort, which has disutility cost c > 0 ) or not (exert no effort). With some probability θ, which defines his ability, the project will succeed and yield a benefit V at date 2; failure generates no benefit. The individual’s beliefs over θ (defining his self—confidence or self—esteem) are described by distribution functions F (θ) at date 0 and F 1 (θ) at date 1. In the intervening period new information may be received, or previous signals forgotten; we shall focus here on the first, more standard case, and turn to memory in Section II. Note that with risk—neutrality the mean ¯θ 1 ≡ R^01 θdF 1 (θ) will be a sufficient statistic for F 1 ; for brevity we shall also refer to it as the agent’s date-1 self—confidence. Finally, we assume that the individual’s preferences exhibit time-inconsistency, due to quasi— hyperbolic discounting. There is indeed considerable experimental and everyday evidence that intertemporal choices exhibit a “salience of the present,” in the sense that discount rates are much lower at short horizons than at more distant ones.^10 Denoting ut and Et [·] the flow payoffs and expectations at t = 0, 1 , 2 , the intertemporal utility perceived by the individual as of date 1 is:
(1) u 1 + βδE 1 [u 2 ] = −c + βδ¯θ 1 V
when he undertakes the activity, and 0 when he does not. By contrast, intertemporal utility conditional on the same information set at date 1, but evaluated from the point of view of date
(^8) Note that this last observation cannot readily be accounted for by the “signalling” theory of self—confidence either. (^9) The simplest date 0 action is thus the choice of the amount of information that will be available at date 1 (e.g., soliciting feedback, taking a test, keeping or destroying records). Alternatively, this information may be derived from the outcome of some activity pursued for its own sake at date 0 (learning by doing, drinking a lot of wine).1 0 See Ainslie [1992], [2001] for the evidence, and Strotz [1956], Phelps and Pollack [1968], Loewenstein and Prelec [1992], Laibson [1994], [1997) and O’Donoghue and Rabin [1999] for formal models and economic implications.
region. If this confidence maintenance motive is strong enough (LF > GF ), the individual will prefer to remain uninformed: IF < 0. More generally, note that IF is lower, the lower is β. By contrast, in the absence of time inconsistency (β = 1) we have LF = 0 and thus IF ≥ 0 : in classical decision theory, information is always valuable. The overconfidence effect calls for more information, confidence maintenance for less. This tradeoff has been noted by empirical researchers. For instance, Leary and Downs [1995] summarize the literature by noting that: a) “persons with high self esteem perform better after an initial failure and are more likely to persevere in the face of obstacles”; b) “high self-esteem is not always functional in promoting task achievement. People with high self-esteem may demonstrate non- productive persistence on insoluble tasks, thereby undermining their effectiveness. They may also take excessive and unrealistic risks when their self-esteem is threatened”. To understand the last statement, let us turn to the case where ¯θF < c/βδV. Since Self 1 now always exerts (weakly) less effort than Self 0 would like him to, information can only help the individual restore his deficient motivation. Indeed,
IF =
Z 1
c/βδV
(6) (δθV − c) dF (θ) > 0.
Moreover, IF is now higher, the lower is β. In such situations the individual will avidly seek feedback on his ability, and his choices of tasks and social interactions will have the nature of “gambles for resurrection” of his self-esteem. Putting together the different cases, we see that the value of information is not monotonic with respect to initial self confidence. Indeed, for someone with confidence so low that ¯θF < c/βδV, IF is always positive and increasing with respect to (stochastic) increases in θ.^12 For an individual with F (c/δV ) = 0 but F (c/βδV ) < 1 , IF is always negative. Finally, for a person so self-assured that F (c/βδV ) = 0, motivation is not a concern (as if β were equal to 1), but neither is overconfidence: IF = GF = LF = 0. Therefore, there must exist some intermediate range where IF first declines and becomes negative, then starts increasing again towards zero.
C What types of people are most eager to maintain their self-confidence?
Let us now consider two individuals with different degrees of initial self-confidence, and ask: which one is least receptive to information? We denote their prior distributions over abilities as F (θ) and G (θ), with densities f (θ) , g (θ) and means
_ θF , ¯θG. To make confidence maintenance meaningful, let ¯θF > ¯θG > c/βδV. For comparing levels of self—confidence, however, just looking at expected abilities turns out not to be sufficient.
1 2 (^) Rewrite (6) as IF = R^01 1 {θ≥c/βδV } (δθV − c) dF (θ) , where (^1) {·} denotes the indicator function, and note that the integrand is increasing in θ.
Definition 1 An individual with distribution F over ability θ has higher self-confidence than another one with distribution G if the likelihood ratio f (θ) /g (θ) is increasing in θ.
Abstracting for the moment from any cost attached to learning or not learning the true ability, it is easy to see from (3) that IF ≥ 0 if and only if
Z (^) c/βδV 0
F (θ) F (c/βδV ) dθ^ ≥
μ 1 − β β
¶ ³ (^) c δV
The monotone likelihood ratio property (MLRP) implies that F (θ) /F (c/βδV ) ≤ G (θ) /G (c/βδV ) for all θ ≤ c/βδV. Therefore, the left—hand—side of (7) is smaller under F than under G, meaning that the person with the more positive self—assessment will accept information about his ability for a smaller set of parameters. Intuitively, he has more to lose from information, and is therefore more insecure.
Proposition 1 If an individual prefers not to receive information in order to preserve his self- confidence, so will anyone with higher initial self-confidence: if IG < 0 for some distribution G over θ, then IF < 0 for any distribution F such that the likelihood ratio f/g is increasing.
D Self-handicapping
A well-documented and puzzling phenomenon is that people sometimes create obstacles to their own performance.^13 In experiments, subjects with fragile self-confidence opt to take performance- impairing drugs before an intelligence test. In real life, people withhold effort, prepare themselves inadequately, or drink alcohol before undertaking a task. They also set themselves overambitious goals, where they are almost sure to fail. Test anxiety and “choking” under pressure are yet other common examples. Psychologists have long suggested that self—handicapping is often a self—esteem maintenance strategy (instinctive or deliberate), directed both at oneself and at others. 14 To examine this question, consider an individual with prior beliefs F (θ), faced at date zero with a choice between an efficient action that (for simplicity) will fully reveal his ability, and an inefficient, “self-handicapping” one which entails an expected cost h 0 (F ) ≥ 0 , but is totally uninformative about θ. Assuming ¯θF > c/βδV as before, equation (7) immediately generalizes to show that he
1 3 (^) See, e.g., Berglas and Jones [1978], Arkin and Baumgardner [1985], Fingarette [1985], or Gilovich [1991]. 1 4 (^) See, e.g. Berglas and Baumeister [1993]. Of course, self—handicapping involves both intrapersonal (self-esteem maintenance) and intrapersonal (self-presentation) motives; our model captures only the former. As Baumeister [1998] notes, “by self-handicapping, one can forestall the drawing of unflattering attributions about oneself. Self- handicapping makes failure meaningless, and so if people think you are intelligent the upcoming test cannot change this impression.” In particular, people apparently self-handicap more in public situations (Kolditz and Arkin [1982]). They then reap a double dividend, as this provides an excuse for poor performance both to themselves and to others.
We now turn to the supply side of the self—esteem problem. Given that a positive self—assessment may be desirable (whether for motivational, signalling or hedonic reasons), what are the means through in which it can be achieved, or at least pursued?
Wired—in optimism. A first hypothesis could be that evolution has selected for a particular cognitive bias in humans, causing them to systematically and involuntarily underweigh adverse signals about themselves, and overweigh positive ones. This explanation is rather problematic: the extent of overconfidence or overoptimism varies both over time and across tasks, and a great many people actually suffer from underconfidence (the extreme case being depression). Furthermore, individuals often “work” quite hard at defending their self—image when it is threatened, going though elaborate schemes of denial, self—justification, furniture—avoidance and the like.
Blissful ignorance. When self—confidence is a valuable capital, it may be preferable to remain uninformed than to put it at risk by exposing oneself to new information. In particular, as seen in the previous section, ex—ante strategic ignorance (Carrillo and Mariotti [2000]) or even self— handicapping may help a time—inconsistent individual safeguard his motivation. In a context of hedonic beliefs, workers in a hazardous job may not want to know about the exact risks involved (Akerlof and Dickens [1982]).
Self—deception. Most often, the relevant issue is not whether to seek or avoid information ex— ante (before knowing what it will turn out to say), but how to deal with the good and especially the bad news concerning one’s performances and abilities that life inevitably brings. This is where the mechanisms of defensive denial, repression, self—serving attributions and the like, so prominently emphasized in psychology, come into play. We shall capture this class of phenomena with a simple game—theoretic model of endogenously selective memory.
A Managing awareness: the role of memory
Psychologists, and before them writers and philosophers, have long documented people’s univer- sal tendency to deny, explain away, and selectively forget ego—threatening information. Freudian repression is the most obvious example, but various other forms of motivated cognition and self— deception feature prominently in contemporary psychology. Thus, a lot of research has confirmed that people tend to recall their successes more than their failures (e.g., Korner [1950], Mischel et al. [1976]), have self—servingly biased recollections of their past performances (Crary [1996]), and readily find “evidence” in their personal histories that they possess characteristics which they view (sometimes as the result of experimental manipulation) as correlated with success in professional or personal life (Kunda and Sanitioso [1989], Murray and Holmes [1993]). Similarly, they often engage in “beneffactance”, viewing themselves as instrumental for good but not bad outcomes (Zuckerman [1979]). When they commit a bad deed they reframe the facts to try and convince themselves that it was not so bad (“he deserved it”, “the damage was limited”), or attribute the responsibility to others (Snyder [1985]).
At the same time, the impossibility of simply choosing the beliefs we like has always stood in the way of a fully consistent theory of self—deception. Sartre [1953] argued that the individual must simultaneously know and not know the same information. Gur and Sackeim [1979] defined self—deception as a situation in which: a) the individual holds two contradictory beliefs; b) he is not aware of holding one of the beliefs; c) this lack of awareness is motivated. Our intertemporal model allows us to unbundle the “self that knows” from the “self that doesn’t know”, and thereby reconcile the motivation (“hot”) and cognition (“cold”) aspects of self—deception within a standard information—theoretic framework. The basic idea is that the in- dividual can, within limits, affect the probability of remembering a given piece of data. Under time—inconsistency, there is an incentive to try and recall signals that help sustain long-term goals, and forget those that undermine them. This is the motivation part.^16 On the other hand, we maintain the rational inference postulate, so people realize (at least to some extent) that they have a selective memory or attention. This is the cognition part.
Assumption 1 (memory or awareness management). The individual can, at a cost, increase or decrease the probability of remembering an event or its interpretation.
Formally, let λ ∈ [0, 1] denote the probability that a given information received at date 0 will be recalled or accessed at date 1. We define the natural rate of recall λN ∈( 0 , 1] as that which maximizes the date 0 flow payoff u 0. Increasing or decreasing λ thus involves a “memory cost” M (λ), i.e. a reduction in u 0 , with M (λN ) = 0, M^0 (λ) ≤ 0 for λ < λN and M^0 (λ) ≥ 0 for λ > λN.^17 Whether it refers to the subconscious or points to the differential accessibility and decay of memories stored in specialized parts of the brain, virtually all modern psychology recognizes that only part of the individual’s accumulated stock of information is readily available for conscious, purposive processing and decision-making. Furthermore, the encoding and retrieval process is subject to systematic influences, both internal and external: a) information that is rehearsed often is better remembered (indeed, that is why we cram for an exam); conversely, if one is preoccupied
1 6 (^) Alternatively, it could arise from an affective or signalling value of self—esteem. 1 7 (^) By definition, “forgetting” means that an actual loss of information (a coarsening of the informational partition) occurs. Thus, if at date 1 the individual does not remember a date-zero signal σ, he also does not recall any other piece of information that is perfectly correlated with σ, such as the costs M (λ) incurred in the process of forgetting. This complete forgetting is only a simplified representation of a richer attribution (signal extraction) problem, however. Let d measure the level of an action that affects recall but can also be undertaken for its own sake: amount of wine consumed, time spent with friendly rather than critical people, attention paid to the details of competing informations, effort in making, safekeeping or disposing of physical records, spatial or mental detours around certain potential cues, etc. Choosing d following an event σ leads to a recall probability λ = Λ(d) and has a direct utility u 0 (d, ε), where ε is a random taste shock. Later on, the agent may recall the action d∗(σ, ε) ∈ arg maxd {u 0 (d, ε) + βδE 0 [u 1 + δu 2 | d, σ]} that he took, and possibly the associated consequences u 0 (d∗(σ, ε), ε), but not the particular realization of ε that occurred (e.g., how much did I really want to drink wine, or sit next to that person at dinner?). Recalling d∗(σ, ε) is thus generally insufficient to fully reconstruct σ, or to separate out within realized utility the cost M (Λ(d∗(σ, ε), ε)) ≡ maxd u 0 (d, ε) − u 0 (d∗(σ, ε), ε) that was incurred purely for memory manipulation. This problem remains when the functions u 0 , Λ or M, or the distribution of ε, depend on σ.
of selective rehearsal afterwards, and again the choice of attention at the time the information is (voluntarily or accidentally) retrieved. 20 We shall therefore use the terms “memory” and “awareness of past informations” interchangeably.
Assumption 2 (metacognition) While the individual can manipulate his conscious self-knowledge, he is aware that incentives exist that result in selective memory.
As illustrated by the opening quotations from Nietzsche and Darwin, if a person has a systematic tendency to forget, distort or repress certain types of information he will likely become (or be made) aware of it, and not blindly take at face value the fact that most of what comes to his mind when thinking about his past performances and the feedback he received is good news. Instead, using (some) rational inference, he will realize that what he may have forgotten are not random events.^21 Formally, this introspection or skepticism with respect to the reliability of one’s own self-knowledge is represented by Bayes’ rule, which implies that a person cannot consistently fool himself in the same direction. Less sophisticated inference processes lead to similar results, as long as they are not excessively naive (see Section III.A).
B The game of self-deception
Let the agent receive, at date 0 , a signal σ about his ability θ. To make things simple, let σ take only two values: with probability 1 − q the agent receives bad news, σ = L, and with probability q he receives no news at all, σ = ∅. In other words, “no news is good news”. Let:
(9) θL ≡ E [θ | σ = L] < E [θ | σ = ∅] ≡ θH.
Since σ is informative about the return to date—1 effort, the agent’s Self 1 would benefit from having this signal. If it is ego-threatening, however, Self 0 may have an interest in suppressing it. The recollection at date 1 of the news σ will be denoted σˆ ∈ {∅, L}. We assume that memories can be lost but not manufactured ex-nihilo, so σ = ∅ always leads to ˆσ = ∅. A signal σ = L, on the other hand, may be forgotten due to natural memory decay or voluntary repression. Let λ denote the probability that bad news will be remembered accurately:
(10) λ ≡ Pr [ˆσ = L | σ = L].
As explained earlier, the agent can increase or decrease this probability with respect to its “natural” value λN ≤ 1; choosing a recall probability λ involves a “memory cost” M (λ). We shall now analyze the equilibrium in several stages.
2 0 (^) One could even adhere to a minimalist version of the model where the individual can only improve his rate of recall (through rehearsal, record-making, etc.), but never lower it (M(λ) = ∞ for all λ < λN ). All that matters is the potential for a2 1 differential rate of recall or awareness in response to desirable or undesirable informations. As Gilbert and Cooper [1995] note, “we are all insightful naive psychologists, well aware of human tendencies to be self-serving.”
- Inference problem of Self 1. Faced with a memory ˆσ ∈ {L, ∅}, Self 1 must first assess its credibility. Given that memories cannot be invented, unfavorable ones are always credible. When Self 1 does not recall any adverse signals, on the other hand, he must ask himself whether there were indeed no bad news at date 0, or whether they may have been lost or censored. If Self 1 thinks that bad news are recalled with probability λ∗, he uses Bayes’ rule to compute the reliability of a “no recollection” message as:
(11) r∗^ ≡ Pr [σ = ∅ | σˆ = ∅; λ∗] = (^) q + (1 − qq)(1 − λ∗).
His degree of self-confidence is then:
(12) θ(r∗) ≡ r∗θH + (1 − r∗)θL.
- Decisions and payoffs. We normalize the payoff in case of success to V = 1, and assume that the cost of date 1 effort is drawn from an interval [c, ¯c], with probability distribution Φ(c) and density ϕ(c) > 0. We assume ¯c > βδθH > βδθL > c, which means that at date 1 there is always a positive probability of no effort, and a positive probability of effort.^22 Given a signal σ at date 0 and a memory σˆ at date 1, Selves 0 and 1 respectively assess the productivity of date 1 effort as E [θ | σ] and E [θ |σˆ]. Self 1 only works when the realization of the effort cost is c < βδE [θ |σˆ] , so Self 0 ’s payoff is:
βδ
Z (^) βδE[θ |σˆ] 0
(13) (δE [θ | σ] − c) dΦ(c).
To build intuition, suppose for a moment that Self 0 could freely and costlessly manipulate Self 1’s expectation, E [θ |σˆ]. What beliefs would he choose for a naive Self 1? Maximizing (13), we find that Self 0 would like to set E [θ |σˆ] equal to E [θ | σ] /β. This makes clear how time-consistency gives Self 0 an incentive to boost or maintain Self 1’s self-confidence; the problem, of course, is that Self 1 is not so easily fooled. These two effects are consistent with the common view in psychology that a moderate amount of “positive illusion” about oneself is optimal, but that many people find it quite difficult to strike this desirable balance.
- Costs and benefits of selective memory or attention. Focussing on the “bad news” case, denote as UC (θL | r∗) the expected utility of Self 0 (gross of memory—management costs) when the adverse information is successfully forgotten, and as UT (θL) the corresponding value when it is accurately recalled. The subscripts C and T stand for “censored” and “truth” respectively. Hiding from Self 1 the signal σ = L raises his self—confidence from θL to θ(r∗), leading him to exert effort in the additional states of the world where βδθL < c < βδθ(r∗). As with ex-ante ignorance, this
2 2 (^) In Section I we took the distribution of θ to be continuous, and c was fixed. In this section c has a continuous distribution and θ can take only two values. The two formulations are actually isomorphic (even if the latter happens to be more convenient here): all that really matters is the distribution of δθV /c.
Because PBE’s are related to the solutions r∗^ ∈ [q, 1] to the nonlinear equation obtained by substituting (11) into the first-order condition for (15), namely
ψ(r, β) ≡ βδ
Z (^) βδ(rθH +(1−r)θL) βδθL
(δθL − c) dΦ(c) + M^0
μ 1 − q/r 1 − q
we shall use a sequence of simpler cases to demonstrate the main points which emerge from our model. Note, for further reference, that ψ(r, β) represents Self 0’s (net) marginal incentive to forget.
C Costless memory or awareness management
“Repression is automatic forgetting.” Laughlin, The Ego and Its Defenses [1979].
We first solve the model in the case where the manipulation of memory is costless, M ≡ 0. While it does not capture the psychological costs of repression (as opposed to the informational ones), this case already yields several key insights, and is very tractable. 23
Proposition 2 When M ≡ 0 , there exist β and ¯β in (0, 1), β < β¯, with the following properties. For low degrees of time inconsistency, β > β¯, the unique equilibrium involves minimum repression (λ∗^ = 1); for high degrees, β < β, it involves maximum repression (λ∗^ = 0). For intermediate degrees of time inconsistency, β ∈ [β, β¯], there are three equilibria, including a partially repressive one: λ∗^ ∈ { 0 , Λ(β), 1 }, where Λ(β) decreases from 1 to 0 as β rises from β to β¯.
These results are illustrated on Figure 1. The intuition is simple, and apparent from (14). When β is high enough overconfidence is the dominant concern, therefore adverse signals are systematically transmitted. Conversely, for low values of β the confidence-building motive dominates, so ego- threatening signals are systematically forgotten. For intermediate values both effects are relevant, allowing multiple equilibria, including one where memory is partially selective. What makes all three equilibria self-fulfilling is precisely the introspection or “metacognition” of the Bayesian individual, who understands that his self—knowledge is subject to opportunistic distortions. The more censoring by Self 0, the more Self 1 discounts the “no bad news to report” recollection, and therefore the lower the risk that he will be overconfident. As a result, the greater is Self 0’s incentive to censor. Conversely, if Self 0 faithfully encodes all news in memory, Self 1 is more likely to be overconfident when he cannot recall any bad signals, and this incites Self 0 to be truthful. Note that in the censoring equilibrium (λ∗^ = 0), none of Self 0’s information is ever transmitted to Self 1: r∗^ = q. In the language of communication games, this is a “babbling equilibrium”. The mechanism at work here is nonetheless very different from the ex ante suppression of information
2 3 (^) While we assume here that λ can be freely varied between 0 and 1, the results would be identical if it were constrained to lie in some interval [λ, ¯λ]. With λ > 0 one can never forget (or avoid undesired cues) for sure.
considered earlier when analyzing self-handicapping, or in Carrillo and Mariotti [2000]. Self 0 does not want to suppress good news, only bad news; but in doing the latter he cannot help but also do the former. As we shall see later on, this may end up doing him more harm than good, whereas the usual “strategic ignorance” is only chosen when it improves ex-ante welfare. The last observation to be drawn from Figure 1 is that, as β rises from 0 to 1, there is necessarily (i.e., for any equilibrium selection) at least one point where λ∗^ has an upward discontinuity. Small differences in the psychic or material costs of memory management, repression, etc., can thus imply large changes in the selectivity of memory, hence in the variability of self-confidence, and ultimately in performance.
D Costly memory or awareness management
“To break down the renewed assaults of my memory, my imagination effectively labored in the opposite direction.” Marcel Proust, Remembrance of Things Past.
In this section we use specific functional forms to study the problem set up in Section II.B. The memory cost function is:
(17) M (λ) = a(1 − ln λ) + b(1 − ln(1 − λ)),
with a > 0 and b ≥ 0. It minimized at the “natural” recall rate λN = a/(a + b), and precludes complete repression. When b > 0 perfect recall is also prohibitively costly, and M is U—shaped. As to the distribution of effort costs, we take it to be uniform, ϕ(c) = 1/¯c on [0, ¯c], with c >¯ βδθH. With these assumptions the incentive to forget, namely UC (θL | r∗) − UT (θL) in (16), is propor- tional to a third degree polynomial in r, with either one or three roots in [q, 1] (see the appendix). Therefore, for any (a, b) there are again either one or three equilibria. One can go further, and obtain explicit comparative statics results, by focussing on the simpler case where recall is costless but repression is costly. These following proposition is illustrated on Figures 2.1 to 2.3.
Proposition 3 Let b = 0. A higher degree of time inconsistency or a lower cost of repression increases the scope for memory manipulation, generating partially repressive equilibria and possibly even making perfect recall unsustainable. Formally:
- For any given β there exist thresholds a and ¯a with 0 ≤ a ≤ ¯a, and continuous func- tions λ 1 (a), λ 2 (a) respectively increasing and decreasing in a, such that: (i) for a ∈ (0, a), the unique equilibrium corresponds to λ∗^ = λ 1 (a); (ii) for a ∈ (a, a¯), there are three equilibria: λ∗^ ∈ {λ 1 (a), λ 2 (a), 1 }; (iii) for a ∈ (¯a, +∞), the unique equilibrium corresponds to λ∗^ = 1.
- There exist critical values β 1 < β 2 < β 3 such that: (i) for β ≥ β 3 , ¯a = 0; (ii) for β ∈ [β 2 , β 3 ), a = 0 < ¯a, as in Figure 2.1; (iii) for β ∈ (β 1 , β 2 ), 0 < a < ¯a, as in Figure 2.2; (iv) for β ≤ β 1 , 0 < a = ¯a, as in Figure 2.3.
