Citizen’s response depends on
expected response of the state
Examples:
Stimulus
Loyalty
Exit
Voice
Increase in
taxes
Pay taxes, keep
mouth shut
Reallocate
portfolio to avoid
tax increase
Organize tax
revolt
Local
jursidiction
outlaws hand
gun
Turn in guns,
keep mouth shut
Move to Idaho
Join NRA, militia
group, etc.
Mangos start to
taste “lousy”
Eat mangos…
keep mouth shut
Buy kiwis
Complain to store
owner
Government
places $1,000
withdrawl limit
on bank
accounts
Lose weight
Insist on being
paid in cash, keep
money under
mattress, use
credit cards,
barter, emigrate,
Set fire to
government
buildings, throw
President out of
office,
(?)
Voice
C
State’s response depends on its
expectation of citizen’s response
Respond
Loyalty
Exit
(State keeps benefit
of new situation;
Citizen opts for
some substitute)
(State keeps benefit
of new situation;
Citizen suffers loss)
Exit Voice Game with Outcomes
Respond
(O3: State returns benefit to citizen)
(State returns benefit to citizen)
Loyalty
S
S
Voice
Voice
Ignore
C
(?)
C
C
Exit
Loyalty
Exit
Loyalty
Exit
(State keeps benefit
of new situation;
Citizen opts for
some substitute)
(O1: State keeps
benefit of new
situation but loses
support of citizen;
Citizen opts for
some substitute)
(State keeps benefit
of new situation;
Citizen suffers loss)
Turning outcomes into pay-offs
(O2: State keeps
benefit of new
situation; Citizen
suffers loss)
(O4: State keeps
benefit of new
situation; Citizen
suffers loss)
(O5:State keeps
benefit of new
situation but loses
support of citizen;
Citizen opts for
some substitute)
Exit-Voice Game With Pay-offs
Respond
(1;S)
Value assigned by
Outcome
Description
Citizen
State
1
State keeps benefit of new situation;
Citizen opts for some substitute
E
1
2
State keeps benefit of new situation and
support of citizen; Citizen suffers loss
0
1+S
3
State returns benefit but keeps support
of citizen
1-c
S
4
Same as 2
0-c
1+S
5
Same as a 1
E-c
1
Loyalty
S
Voice
Ignore
C
Exit
(E;1)
C
Exit
Loyalty
(0;1+S)
(E; 1)
(0;1+S)
1
State’s response to voice when exit threats are credible (E>0)
End Game
Respond
(1;S)
Loyalty
S
Voice
Ignore
Voice
Exit
Loyalty
Exit
(E;1)
Respond
Loyalty
S
Voice
Ignore
(0;1+S)
Eq. Strategy:
Equilibrium behavior when:
1.) value citizen places on a substitute
is more than what it gets from loyalty,
but not so high that its better than a
return the status quo ante (0<E<1)
(C’s 1st action, C’s 2nd action; S’s action)
(V,E;R) is a sub-game perfect equilibrium
and
(1-c;S)
Respond
2.) State depends on support (S>1)
C
Loyalty
(E;1)
(0;1+S)
Loyalty
S
Exit
C
Exit
Exit
(E;1)
(1;S)
C
Loyalty
Exit
(0;1+S)
Citizen’s choice when it has credible exit threats (E>0) and the state depends on
the citizen’s support S>1
Ignore
C
(E;1)
(0;1+S)
Loyalty
S
C
C
(1;S)
Respond
(0;1+S)
Voice
(E;1)
Ignore
C
Exit
C
(E;1)
(0;1+S)
(E;1)
Definitions
A strategy is a complete plan that specifies what an
actor would do at any conceivable decision point
(node).
A Nash equilibrium is a set of strategies that are best
replies to each other on the equilibrium path
A subgame is a part of a game beginning at one node
and including all succeeding nodes that forms a
game by itself.
A subgame perfect equilibrium is a set of strategies
such that each player plays a Nash equilibrium in
every subgame
(E-c;1)
Loyalty
Exit
(0-c;1+S)
(0;1+S)
Equilibrium behavior when citizen has credible exit threat
(0<E<1) and state is dependent (S>1).
Respond
(1-c;S)
(0-c;1+S)
Loyalty
S
Voice
Ignore
C
Exit
(E;1)
C
Exit
Loyalty
(0; 1+S)
(E-c; 1)
(V,E;R) is
subgame perfect
2
Equilibrium behavior when citizen has no credible exit threat
(E<0) and state depends on citizen’s support (S>1).
Respond
(1-c;S)
Ignore
(E;1)
(0-c;1+S)
Exit
Ignore
C
C
(E-c; 1)
Exit
(E-c; 1)
Loyalty
Exit
(L,L;I) is subgame
pefect
(0; 1+S)
Loyalty
S
Voice
Loyalty
Exit
(0-c; 1+S)
C
C
(1-c;S)
Respond
Loyalty
S
Voice
Equilibrium behavior when citizen has no credible exit threat
(E<0) and state is relatively autonomous (S<1).
(E;1)
(L,L;I) is subgame
pefect
(0;1+S)
Summary of subgame perfect equilibria
State is:
Equilibrium behavior when citizen has a credible exit threat
(E>0) and state is relatively autonomous (S<1).
Dependent
Relatively autonomous
S<1
S>1
Respond
(1-c;S)
Citizen has:
Has
credible
exit
threats
(1>E>0)
(Exit, Exit; Ignore)
(Voice,Exit;Respond)
(Loyalty,Loyalty;Ignore)
(Loyalty,Loyalty;Ignore)
(0-c;1+S)
Loyalty
S
Voice
Ignore
C
C
Exit
Loyalty
Exit
(E;1)
Does not
have
credible
exit
threats
(E-c; 1)
(E,E;I) is subgame
pefect
(0;1+S)
Equilibrium behavior when citizen prefers substitute to the
benefit of state response (E>1-c) and state is dependent (S>1)
Respond
(E<0)
Equilibrium behavior when citizen prefers substitute to the
benefit of state response (E>1-c) and state is relatively
autonomous (S<1)
(1-c;S)
Respond
(1-c;S)
(0-c;1+S)
Voice
Ignore
C
Exit
(E;1)
(0;1+S)
Loyalty
S
Voice
C
Exit
Loyalty
(0-c;1+S)
Loyalty
S
(E-c; 1)
(E,E;R) is subgame
perfect
Ignore
C
Exit
(E;1)
C
Exit
Loyalty
(0;1+S)
(E-c; 1)
(E,E;I) is subgame
perfect
3
Summary of subgame perfect equilibria
State is:
Relatively autonomous
S<1
Dependent
When voice is intrinsically beneficial to the citizen
(c<0), the citizen has not credible exit threat (E<0),
and the state is relatively autonomous (S<1)
S>1
Preference
for
substitute
Citizen has:
Has
credible
exit
threats
Does not
have
credible
exit
threats
Respond
(E>1-c)
(-C;1+S)
(1>E>0)
(Voice,Exit;Respond)
(Exit, Exit; Ignore)
(E<0) (Loyalty,Loyalty;Ignore)
Voice
Ignore
C
(0;1+S)
State is:
Relatively autonomous
S<1
Dependent
(E>1)
(Voice,Exit; Ignore)
(Voice,Exit; Respond)
(1>E>0)
(Voice,Exit; Ignore)
(Voice,Exit;Respond)
(Voice,Loyalty;Ignore)
(Voice,Loyalty;Ignore)
S>1
Preference
for
substitute
Loyalty
C
Citizen has:
Exit
Loyalty
(E-C; 1)
Summary of subgame perfect equilibria when voice
is intrinsically beneficial c<0
(-C;1+S)
Voice
Exit
(1-C;S)
S
C
Loyalty
Exit
Respond
Ignore
C
(Loyalty,Loyalty;Ignore)
When voice is intrinsically beneficial to the citizen
(c<0), the citizen has a credible exit threat (E>0), and
the state is relatively autonomous (S<1)
(E;1)
Loyalty
S
(E;1)
Exit
(1-C;S)
(Exit,Exit; Respond)
(Exit,Exit; Ignore)
(E-C; 1)
Has
credible
exit
threats
Does not
have
credible
exit
threats
(E<0)
(0;1+S)
Conclusions
• Influence is relevant only when perfect
substitues are not available (I.e. when exit is
costly)
• When voice is likely to be effective states
have an incentive to prevent bad shocks
• Voice is effective only when it is costly
Conclusions – when voice is
costly
• Voice is used only when exit threats are credible
and the state depends on citizen’s support
• Loyalty is used when exit threats are not credible
• Exit is used when state is relatively autonomuous
and exist threats are credible
– Thus, when the state observes the use of voice, it can
learn something about the citizen
4
Conclusions – when voice is
intrinsically beneficial
Life in the state of nature is like a
prisoner’s dilemma (Hobbes, Rousseau)
• Voice is used all the time
– So the state can not learn anything about the
citizen by observing voice
(D;d) is a Dominant Strategy
Equilibrium in Prisoner’s Dilemma
– A strategy is a list of actions that states what a player
will do at every point in a game when that player can
act.
– A strategy (Si) is a dominant strategy for actor i if i’s
pay-off is higher when playing that strategy than it
would be if i played any other strategy (~Si) no matter
what all the other players do. That is, a dominants
strategy is a “best response” to all the strategies that all
the other actors in the game.
– A Dominant strategy equilibrium is strategy
combination such that all players play a dominant
strategy.
Pareto Optimality in Prisoner’s
dilemma
• An outcome is Pareto optimal if no other outcome
exists such that at least one player would be made
better off, and no player is made worse of.
• An outcome is Pareto inferior if there
exisotherwise.
• Pareto optimal outcomes are said to Pareto
dominate Pareto inferior outcomes
• C,C is the pareto optimal outcome in singleshot
PD
C
D
C
(3,3)
(1,4)
D
(4,1)
(2,2)
Nash equilibrium in Prisoner’s
dilemma
• A set of strategies form a Nash Equilibrium when
each player’s strategy is a best response to what
the other players are conjectured (by the
equilibrium) to do.
• Thus, a Nash equilibrium is a “self-enforcing”
agreement. It is “self-enforcing” in that if the
players share a common conjecture about what the
others will do, no player has an incentive to
unilaterally depart from the conjectured behavior.
Life in Civil Society: If the state punishes,
cooperation between citizens is possible
C
D
C
(3-t,3-t)
(1-t,4-p-t)
D
(4-p-t,1-t)
(2-p-t,2-p-t)
5
And if the state doesn’t charge too much tax
(3-t>2, or 1>t), life is better in civil society
Without the state
With the state
C
D
C
(3,3)
(1,4)
D
(4,1)
(2,2)
C
D
C
(3-t,3-t)
(1-t,4-p-t)
D
(4-p-t,1-t)
(2-p-t,2-p-t)
What states do:
1.War making: Eliminating or neutralizing their own
rivals outside the territories in which they have
clear and continuous priority as wielders of force.
2. State making: Eliminating or neutralizing their
rivals inside those territories.
3.Protection: Eliminating or neutralizing the enemies
of their clients
4. Extraction: Acquiring the means of carrying out
the first three activities.
Conclusion
In so doing, the approach it:
This “predatory state” approach is instructive
because it:
1. gives view of rulers as egoistic
maximizing rational actors
2. shows how goal oriented behavior leads to
changes in institutional environment
3. shows how changes in institutional
environment might change behavior
1. explains why units grew larger over time increasing economies of scale in violence
And
2. has potential of explaining why rulers
would share power and/or limit extraction
6