3. Self-Control in Peer Groups (Bénabou et al. [2002])

Set-Up of a general model for willpower and self-control:

• Imagine a situation, where an individual I lives in 2 periods and can

decide at the beginning of each period whether he carries out

(a) a no willpower activity (NW) or

(b) a willpower dependent activity (W).

• It is assumed that I opts for W.

• He has then the option to

(a) Persevere (P) or

(b) Give up (G).

• G gives an immediate payoff of A whereas G pays B in the future.• Present Value of B > A. 20

But:

• Individual has a self-control problem.

• He does not only discount with a standard discount rate but with a

hyperbolic discount rate (he uses a higher discount rate for earlier

periods than for later periods)

• Not giving-in is costly. There exist two types of Individuals:

cL = strong-willpower type (low cost)

cH = low-willpower type (high cost)

• Individual does not know his c. He can only learn it from self-

monitoring.

3. Self-Control in Peer Groups (Bénabou et al. [2002])

21

• Individual compares

payoffs from P and G.

• To compare he needs to

know about the

probability of being a

strong-willpower type.

• There exists some level

of confidence p* where

individual always opts

for P.

3. Self-Control in Peer Groups (Bénabou et al. [2002])

X-Axis: p = level of confidence of being cL

Y-Axis: x (p) = probability that I plays strategy P 22

Model which includes effects from peer groups:

• Two Individuals face the same self-control problem.

• Two agents have the same level of confidence in their willpower

(pi=pj) at beginning.

• Individual can observe actions of other agent and learn from it.

• By observing another agent, he can either

(1) become more encouraged, if the other agent successfully resists

temptation (-> plays P).

(2) become less encouraged, if the other agent cannot resist temptation (->

plays G).

3. Self-Control in Peer Groups (Bénabou et al. [2002])

23

• Decision by one agent to persevere now leads to two possible different

states of the world :

– Agent 1 plays P ; Agent 2 plays P as well (PP).

– Agent 1 plays P ; Agent 2 plays G (PG).

• New key element: expected return to resisting one‘s impulses now

depends on what the other agent is likely to do.

3. Self-Control in Peer Groups (Bénabou et al. [2002])

24

3. Self-Control in Peer Groups (Bénabou et al. [2002])

3 Situations possible:

(1) Agent 1 plays P, Agent 2 plays P

XPP (p) > X (p)

(2) Agent 1 plays P, Agenst 2 plays G

XPG (p) < X (p)

(3) Agent 1 plays P, Agent 2 plays with

some probability P and with some

other probability G.

25

• main results from paper:

– With respect to self-control group membership is preferable, when :

• group members have at least a minimal level of confidence in

their own and their peers‘ ability to resist temptation.

• partner is someone with a slightly worse self-control problem

(a „too perfect“ partner“ is problematic because one does not learn

anything from his actions).

3. Self-Control in Peer Groups (Bénabou et al. [2002])

26

• Bénabou, R. and Tirole J. (2000), „Willpower and Personal Rules“, Princeton

University mimeo

• Bénabou, R. , Battaglini, M. and Tirole, J. (2002), „Self-Control in Peer

Groups“

• Freud, S. , „The Ego and the Id.“ (London: Hogarth)

• Stigler, George J. , „The Theory of Price“, 3d ed. New York : Macmillan, 1966

• Thaler, R.H. and H.M. Shefrin (1981), „An Economic Theory of Self-Control“,

Journal of Political Economy, 89 (2), 392 – 406

Papers from Bénabou can be downloaded from

http://www.princeton.edu/~rbenabou

4. Literature:

27