Repeated Interaction and Reputation Effects

Repeated Interaction

• Creates possibility for reputation effects– reputations for resolve– reputations for honesty/dishonesty

• Creates possibility for endogenizing “audience costs”

Theory vs. Empirics• A theoretical model of a single crisis:

• The data: Observations on multiple plays of the same game by same population of actors

A

ThreatenDon’t Threaten

B

A

AcquiesceResist

StandFirm

SQA

SQB

ACQA

ACQB

BDA, BDB WARA, WARB

BackDown

Implications

• Strategies and equilibria in a repeated interaction may be different from what holds in the isolated stage game

• Payoffs in any one interaction are actually “continuation values”: the expected value of the future given that you reached this outcome node in this iteration of the game.

• Standard assumptions of independence and/or homogeneity of shocks over time may be violated

Persistent vs. Temporary Shocks A

ThreatenDon’t Threaten

B

A

Acquiesce Resist

StandFirm

SQA,t

SQB,t

ACQA,t

ACQB,t

BDA,t

BDB,t

BackDown

, , ,

, , ,

A t A t A A t

B t B t B B t

WAR w

WAR w

, ,

Persistent: ,

Temporary: , ~ i.i.d.A B

A t B t

Persistent Shocks

• If persistent shocks are known to the participants, but not to us as analysts, then we might be able to correct for them with random or fixed effects

• If the persistent shocks are a source of incomplete information in the game– strategies in the repeated game may be influenced by

incentives to develop reputations and/or learn over time

– the prior distribution of types going into each iteration depends on the history (e.g., the amount of uncertainty could decrease over time)

A

ThreatenDon’t Threaten

B

A

Acquiesce Resist

StandFirm

(0,1)

(1,0)

(0, 1)

BackDown

A Long-Run Player with a Persistent Type

(wA, wB,t)

A Long-Run Player with a Persistent Type

• A faces N opponents in (possibly quick) sequence

• A’s type is same in all interactions– A is tough if wA > 0, meaning that it always

prefers to fight

– soft types (for whom wA < 0) prefer not to fight in the one-shot game

• Each B is strong (wB,t > 0 ) or weak (wB,t < 0 )

Equilibrium(Kreps-Wilson, Milgrom-Roberts)

• When = 1, unique equilibrium:

• For B– strong B always resists– weak B resists if A has ever backed down or not threatened– weak B acquiesce if more than n opponents remain– some weak B resist if less than n opponents remain

wA

0k(n)

Threaten,Back Down

Threaten, Stand Firmif at least n opponents remain

Threaten,Stand Firm

Implications

• The more opponents that remain to be faced, the more (some) soft types of A have incentive to mimic tough types by standing firm.– the cost of fighting strong opponents is outweighed by the

benefit from deterring resistance by the weak ones

• The more opponents that remain, the lower the probability that B will resist.

• If A ever backs down, it is revealed as soft, and all opponents will resist in the future.

Walter, “Building Reputation”

• Question: Why do governments accommodate some separatist groups but not others?

• Observation: The most intractable civil conflicts occur over territory.

• Puzzle: Territory is a pie that is easy to divide. Why don’t governments buy off separatists rather than fighting them?

The Implicit Model

Government (A)

SQ Challenge

Fight (1,0)

(0, 1)

Accommodate

(wA, wB,t)

Separatist (B)

Hypotheses

1. A government’s decision to accommodate demands for self-determination will be negatively related to the number of challengers it expects to face in the future.

2. A government’s decision to grant territorial autonomy or independence will be inversely related to the cumulative value of all the land within its borders that could come under dispute.

Data

• Observations: Self-determination movements that made non-violent or violent demands for autonomy or independence in 1956-2000.

• Dependent variable: Level of accommodation by government (4-point scale)

• Main independent variables:– number of ethnic or ethnopolitical groups in the country

– total strategic, psychological and economic value of all land occupied by all ethnopolitical groups

Results

1. Accommodation by government decreases with• number of ethnopolitical groups• total strategic and economic value of land occupied by

ethnopolitical groups

2. Accommodation by government not influenced by • value of land involved in current challenge• capabilities of government relative to current challenger

3. Building reputation seems to work:• Refuse to accommodate or offer only modest reforms to

first challenger subsequent challenge 27% of the time• Grant autonomy or independence to first challenger

subsequent challenge 59% of the time.

A Game with Non-Persistent Types

A

ThreatenDon’t Threaten

B

A

Acquiesce Resist

StandFirm

(0,1)

(1,0)

(0, 1)

BackDown

(wA,t, wB,t)

…

A Game with Non-Persistent Types

• Infinitely repeated game

• A’s and B’s matched randomly in each period

• Values for war, wA,t and wB,t, are i.i.d.

• Notice: In the stage game, threats are costless.– Audience costs are not assumed; if audience costs

arise, they must do so endogenously, from concerns about future

– In single shot game, A will fight iff wA,t > 0.

Equilibria

• History independent:– A always challenges and stands firm iff wA,t > 0

– B acts based on prior probability– no learning, no conditioning on past behavior

Equilibria

• Temporary punishment for dishonesty (Sartori 2002):– A has an honest reputation at the outset and in all

subsequent periods until it backs down after making the threat

– If A backs down, then it has a dishonest reputation for N periods, after which its reputation for honesty is restored

Equilibria

• Temporary punishment for dishonesty (Sartori 2002):– When A’s reputation is honest:

– B updates in response to threat and acts based on posterior

wA,t

ThreatenStand Firm

ThreatenBack Down

Don’t ThreatenBack Down

Equilibria

• Temporary punishment for dishonesty (Sartori 2002):– When A’s reputation is dishonest:

– B ignores the threat and acts based on prior

wA,t

ThreatenStand Firm

ThreatenBack Down

Equilibria• Temporary punishment for dishonesty (Sartori

2002):– states have reputations for honesty or dishonesty

based on past behavior• if the state currently has an honest reputation, it can

make informative signals• if a state currently has a dishonest reputation, it cannot

communicate information

– “audience costs” arise from the fact that backing down deprives the state the ability to use diplomacy for N periods

– strategies are history contingent even though history contains no information about type

Equilibria

• Grim Trigger (Guisinger and Smith 2004):– reputations as in Sartori (2002)– once a state loses its reputation for honesty, it is

never restored– in this equilibrium, it is possible to have a

separating equilibrium (when A has an honest reputation):

wA,t

ThreatenStand Firm

Don’t ThreatenBack Down

Equilibria

• Agent-Specific Grim Trigger (Guisinger and Smith 2004):– as before, but reputations belong to leaders

(agents), not the state– if the leader in A backs down, that leader has a

reputation for dishonesty– A can only restore its ability to use diplomacy by

replacing the leader with a new one (at some cost)– this means that voters may have an incentive to

remove leaders that are caught bluffing

Substantive Implications

1. Repeated interaction can cause audience (domestic and/or international) to arise endogenously

2. Possible role of reputations/past behavior• reputations for resolve• reputations for honesty

Methodological Implications

1. Assumption of non-persistent shocks preserves independence and homogeneity of type distributions across plays of the game

2. Equilibria in repeated game with non-persistent shocks have similar cut-point form as in single-shot game

3. But: multiple equilibria in repeated game with non-persistent types

• not all equilibria have history-dependent strategies

• in equilibria with history-dependent strategies, punishment regimes of any length can be supported