Subjective Expected Utility Theory with Costly Actions - Economics ...

where (¹a; ¹w) denotes the “outside option,” that is, the best course of action
available to the agent in case he declines the contract. This outside option is
the best action-contract pair attainable by the agent.
Typically the principal-agent problem is stated in terms of the utility representation
of the preferences of the two parties and not in terms of their preference
relations. To obtain such a representation let S (x; a) =fs 2 S j ta (s) · xg for
every x 2 T and a 2 A. For every a de…ne j 0 s subjective cumulative distribution
function, ¦ j (¢; a) on T by
¦ j (x; a) =¼ j (S (x; a)) ; j 2fP; Ag; (31)
where ¼j is j0s subjective probability derived from the corresponding preference
relation. Using these notations and Theorem 3, the principal-agent problem
(28) - (30) may be restated in its conventional form as follows: Choose an
action-contract pair (a ¤ ;w ¤ ) such that
(a ¤ ;w ¤ ) 2 arg max
A£W
subject to the incentive compatibility constraints
Z
Z
u
T
A (x ¡ w ¤ (x)) d¦ A (x; a ¤ )+v (a ¤ ) ¸
and the participation constraint
Z
Z
u
T
P (x ¡ w ¤ (x)) d¦ P (x; a ¤ ) (32)
u
T
A (x ¡ w ¤ (x)) d¦ A (x; a)+v (a) ; 8a 2 A
(33)
u
T
A (x ¡ w ¤ (x)) d¦ A (x; a ¤ ) ¸ u0; (34)
where u0 is the reservation utility level associated with the outside option.
Note that the similar representations apply under the conditions of Theorems
1 and 2 with the corresponding utility functions.
An alternative formulation of agency theory, the parameterized distribution
formulation, pioneered by Mirrlees (1974, 1976), avoids the use of a state space
as a primitive concept. In a recent paper Karni (2003b) I developed an axiomatic
foundation of the parameterized distribution formulation of agency theory.
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