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1 CIRJE-J CIRJE
2 The Erosion and Sustainability of Norms and Morale KANDORI, Michihiro The initially high performance of a socioeconomic organization is quite often subject to gradual erosion over time. We present a simple model which captures such a phenomenon. We assume that players are partly motivated by certain psychological factors, norms and morale, and they are willing to exert extra effort if others do so. This results in a "continuum" of equilibrium effort levels, whose minimum corresponds to the Nash equilibrium with respect to the material incentives. We show that repeated random shocks induce the erosion of equilibrium effort levels, but they do not completely decay; in the long run a certain range of efforts are sustainable. Our model shows that different organizations typically enjoy diverse norms and morale, which persist for a long time, in the vicinity of the equilibrium determined by material incentives. JEL Classification Numbers: A12, A13, C70, C72, C73, C91, C92, D63, D64, H41.
3 2003 Kandori (2003) Japanese Economic Review
4
5
6
7 Isaac (1994) 60 Andreoni (1988) M. Rabin 2
8 , (coordination game) 3 Rabin (1993,98)) Rabin Kandori, Mailath and Rob (1993) Young (1993) 3
9 Ellison(2000) N i=1,2,,n ei = 0,1,,L t=0,1,2, e(t) = (e1(t),,en(t)) (1) ui(e(t),k(t),m(t)) = Σjej(t) c(ei(t)) k(t)[m(t) ei(t)]+ Σjej(t) c(ei(t)) 1 Σjej(t) 2 c(ei(t)) c(e) = c(e) c (e 1) > 0 e ei(t) ei(t) c(ei(t)) (N 1) ei(t)
10 k(t)[m(t) ei(t)]+ m(t) k(t) m(t) [m(t) ei(t)]+ m(t) ei(t) m(t) [m(t) ei(t)]+ k(t) m(t) k(t) m(t) (2) m(t) = median{e1(t 1),, en(t 1)} (median) N (N+1)/2 4 k(t) K( ) N (3) k( t) = K [ m( t) e i ( t 1)] + i= 1 4 N
11 e = (e1,,en) (10,10,,10) (3,10,,10) (0,0,2,7,7,8,8,8,9,9,10) 7 10 (1,5,5,5,10) (1,5,2,5,10) = e*=(e*,,e*) i ei ui(e*,k,m) ui(e i*,ei,k,m), m = e*, k = K(0). e*
12 m k = K(0) e* ei i ei e* c c(e) = c(e) c (e 1) ei (= ei ) 1 m = e* 1 k(0) m = e 1+k(0) c e* e c e c e* c e* e m e c 1 e e e m = = c m
13 [e m, e ] t=1,2 1 ε e(t 1) m(t) (2) k(t) (3) (1) ei(t) 5 ε > e(0) 6
14 e(t) µ µ µ (i) µ (ii) µ ε µ(ε) µ * = lim µ ( ε ) ε 0 (i), (ii) Kandori, Mailath, and Rob (1993) Young (1993) 2 5 e 5
15 e 2 e 3 e 2 e =9 80 Freidlin Wentzell 7 Kandori, Mailath, and Rob (1993) Young (1993) Ellison Fudenberg and Levine (1998) 5
16 5 1 3 e c n < (N+1)/2 e e = n K(0) K(n (e 0)) = K(ne ) e c 1+K(ne) e n c e (< e n ) c 1+K(ne) e n n e (< e n ) n n (N 1)/2 e n, n=1,2,,(n-1)/2 [ e 1, e] [e 2, e 1 ] n n (N
17 1)/2 [e n, e n 1 ] n e (N 1)/2 [e m, e (N 1)/2 ] e = (40,40,40,40,40) 3 (41,41,41,40,40) = [e m, e (N 1)/2 ] (N+1)/2 [e m, e (N 1)/2 ],
18 [e m, e (N 1)/2 ] (N+1)/2 [e m, e (N 1)/2 ] [e m, e (N 1)/2 ] 8 7 e = 0,1,,100 c(e) = e 2 /80 K(D) = 80/(80+D)
19 10000 Akerlof Akerlof-Yellen
20 Akerloff Yellen (1985)
21 k Rubinstein Critique 20
22 Rubinstein (2001) Lucas Lucas critique (2002) Rubinstein critique 10 Rabin
23 (2001) NTT. (2002). (2002). Akerlof, G. and J. Yellen (1985) "Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?", American Economic Review, Vol. 76, pp Andreoni, J. (1988) "Why Free Ride? Strategies and Learning in Public Goods Experiments", Journal of Public Economics, Vol. 37, pp Ellison, G. (2000) "Basin of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution", Review of Economic Studies, Vol. 67, pp Fudengerg, D. and D. Levine (1998) The Theory of Learning in Games, MIT Press. Isaac, M., J. Walker, and A. Williams (1994) "The Group Size and the Voluntary Provision of Public Goods", Journal of Public Economics, Vol. 54, pp Kandori, M. (2003) The erosion and Sustainability of Norms and Morale, Japanese Economic Review, Vol 54, pp
24 Kandori, M., G. Mailath, and R. Rob (1993) "Learning, Mutation, and Long Run Equilibria in Games", Econometrica, Vol. 61, pp Rabin, M. (1993) "Incorporating Fairness into Game Theory", American Economic Review, Vol. 83, pp Rabin, M. (1998) "Psychology and Economics", Journal of Economic Literature, Vol. XXXVI, pp Rabin, M. (2002) "A Perspective on Psychology and Economics", European Economic Review, Vol. 46, pp Rubinstein, A. (2001) "Is it "Economics and Psychology"?: The Case of Hyperbolic Discounting", NAJ Economics, Vol Young, P. (1993) "The Evolution of Conventions", Econometrica, Vol. 61, pp
25 c 1+K(0) 1 e m e* ē e
26
27
28 c 1+K(0) 1 M 1+K(e) 1+K(2e) N 1 1+K( e) 2 e m N 1 2 e L e 2 e 1 ē e
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