Bayesian efficiency is an analog of

Pareto efficiency Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engi ...

for situations in which there is

incomplete information In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies ...

.Palfrey, Thomas R.; Srivastava, Sanjay; Postlewaite, A. (1993)
Bayesian Implementation.
' Pg. 13-14. Under Pareto efficiency, an allocation of a resource is Pareto efficient if there is no other allocation of that resource that makes no one worse off while making some agents strictly better off. A limitation with the concept of Pareto efficiency is that it assumes that knowledge about other market participants is available to all participants, in that every player knows the payoffs and strategies available to other players so as to have complete information. Often, the players have types that are hidden from the other player.

Overview

The lack of complete information raises a question of when the efficiency calculation should be made. Should the efficiency check be made at the

ex ante The term ''ex-ante'' (sometimes written ''ex ante'' or ''exante'') is a phrase meaning "before the event". Ex-ante or notional demand refers to the desire for goods and services that is not backed by the ability to pay for those goods and servic ...

stage before the agent sees their types, at the interim stage after the agent sees their types, or at the ex post stage where the agent will have complete information about their types? Another issue is incentive. If a resource allocation rule is efficient but there is no incentive to abide by that rule or accept that rule, then the

revelation principle The revelation principle is a fundamental principle in mechanism design. It states that if a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of ...

asserts that there is no mechanism by which this allocation rule can be realized. Bayesian efficiency overcomes problems of the

by accounting for incomplete information, by addressing the timing of the evaluation (ex ante efficient, interim efficient, or ex post efficient), and by adding an incentive qualifier so that the allocation rule is incentive compatible.Baltagi, Badi Hani. (2001)
A Companion to Theoretical Econometrics.
' Blackwell Publishing. Bayesian efficiency separately defines three types of efficiency: ex ante, interim, and ex post. For an allocation rule

x:T\to A

: ''Ex ante efficiency'':

x

is incentive compatible, and there exists no incentive compatible allocation rule

y:T\to A

that :

\int U^i(y(t),t)dG^i(t) \geq \int U^i(x(t),t)dG^i(t)

for all

i

, with strict inequality for some

i

. ''Interim efficiency'':

x

is incentive compatible, and there exists no incentive compatible allocation rule

y:T\to A

that :

\int U^i(y(t),t)dG^i(t_, t_i) \geq \int U^i(x(t),t)dG^i(t_, t_i)

for all

i

and

t_i

, with strict inequality for some

i

and

t_i

. ''Ex post efficiency'':

x

is incentive compatible, and there exists no incentive compatible allocation rule

y:T\to A

that :

U^i(y(t),t) \geq U^i(x(t),t)

for all

i

, with strict inequality for some

i

. Here,

G^i

are beliefs,

U^i

are utility functions, and

i

are agents. An ex ante efficient allocation is always interim and ex post efficient, and an interim efficient allocation is always ex post efficient.

References

{{game theory Bayesian statistics Pareto efficiency Game theory Law and economics Mathematical optimization Optimal decisions Electoral system criteria Welfare economics