QR 38

4/3/07, Uncertainty

I. Risk

II. Agency problems

III. Asymmetric information and perceptions

I. Risk

Uncertainty means lack of certainty about the outcomes of a game. Many possible sources:

• Outcomes inherently risky (effect of weather on a battle)

• Actions difficult to observe

• Preferences of other player unknown

• All are important in IR

Incomplete and imperfect information

• Imprecise information about outcomes is incomplete information.

• Imprecise information about past moves is imperfect information.

• In practice, the way that we deal with incomplete information is to transform it into a game of imperfect information.

Risk

Risk: some probability distribution over outcomes

• Payoffs are probabilistic.

• Risk is inherent in the situation, not due to the strategic actions of others.

Commodity supplier exampleConsider OPEC (or coffee or bauxite

suppliers):

• Price of commodity fluctuates depending on consumer demand, weather, etc.

• This creates risk for both the supplier and consumer.

• Assume that a coffee grower makes $150,000 in a good year, $50,000 in a bad year

Commodity example• Assume a 50-50 distribution over these

two possible outcomes

• The expected profit is then $100,000

• Consider the consumer (U.S. distributor): a good year for the grower is a bad year for the consumer.

• So a “good” year leads to profits of $50,000 for the consumer; a “bad” year to profits of $150,000

Commodity example• The consumer’s expected profit is

$100,000.

Can the consumer and grower collaborate to reduce the risk to which they are exposed?

• Yes, by pooling their risks.

• In general, pooling works as long as risks are not perfectly positively correlated.

Commodity example

• Here, since the risks are negatively correlated, pooling should help both.

• Their combined income is always $200,000.

• They could enter into a contract in which the grower gives the consumer $50,000 in good years, and the consumer gives the grower $50,000 in bad years.

Commodity example

• Then each is guaranteed a payoff of $100,000

• Risk has been eliminated• There is no advantage to this arrangement

if the players are risk-neutral, but it increases their utility if they are risk-averse.

• Because of the perfect negative correlation, the risk disappears completely.

Risk pooling in IRProblems with risk-pooling schemes:• Enforceability

– Commodity arrangements often short-lived; a PD (ICA and OPEC exceptions)

• Moral hazard– If insured against risk, may not take

precautions you otherwise would (fertilizer)

• Adverse selection– Those most likely to need insurance will

purchase it (incompetent growers)

II. Agency problems

Moral hazard problem is linked to a general class of informational problems known as agency issues.

• Examples: employer hiring an employee – the employee is the employer’s agent. Choosing leader for an IO.

Using an agent has many advantages, but also problems, such as whether the agent’s actions are observable.

Observability of actions

Consider allowing the IMF to negotiate a bail-out arrangement with Argentina (U.S. the principal, IMF the agent).

• Negotiations won’t be entirely public• Even if a good agreement is reached, it

may not help Argentina’s economy (risk)• If the economy doesn’t improve, is this the

result of the agent not doing a good job or bad luck? U.S. can’t tell.

Observability of actions

How to address this problem? • If agent’s actions observable, just pay IMF

more for negotiating well.• Otherwise have to make the payoff

contingent on the observed outcomes and use incentive schemes.

• Solutions have to meet the incentive-compatibility constraint and the participation constraint.

Incentive schemes

Incentive-compatibility constraint:

• How big the payment would have to be to induce good effort.– Have to make the expected payoff big enough

to induce good effort. – Because outcomes are risky, this can mean

the actual payment must be very large.– Even if the agent does a good job, by bad

luck he might get paid nothing.

Incentive schemes

Participation constraint:• Have to offer enough that the agent will

choose to work with you at all• How big this payment must be depends on

the agent’s exit options.The principal’s lack of information means

that he must pay more than under complete information.

• This inefficiency falls on the least-informed player, the principal.

III. Asymmetric information and perceptions

Agency problems are an example of information asymmetry (above, the IMF knew if it negotiated in good faith, but the U.S. didn’t).

• Asymmetric information is a general problem in IR.– Players may know their own

preferences, but not others’– Players know their own past behavior,

but not others’

Asymmetric information

• When asymmetric information exists, perceptions or beliefs become central to the play and resolution of the game.

• Now the equilibrium has to be described in terms of both strategies and beliefs, because they depend intimately on one another.

Beliefs

• Beliefs are not random: a rational player will update beliefs in response to events.– A player that stubbornly stuck to beliefs that

were at odds with observed behavior wouldn’t be acting rationally.

• Definition of belief: a probability attached to some quantity, such as others’ payoffs.

U.S.-North Korea example

Consider the U.S. trying to convince NK to give up its nuclear program by offering aid in exchange.

• NK could put either a high or a low value on aid

• This is NK’s type: a type that values aid highly, or that puts a low value on it

• NK’s type is private information; NK knows, U.S. only has an estimate.

U.S.-North Korea example

• E.g., U.S. might believe there is a 70% probability that NK puts a high value on aid, and a 30% probability that it puts a low value on aid.

• This probability distribution is the U.S. belief about NK’s type.

• We usually assume that beliefs are common knowledge: NK knows what probabilities U.S. assigns, U.S. knows NK knows this, etc.

Showing asymmetric information in an extensive-form game

How to capture asymmetric information in an extensive-form game?

• Trade sanctions example. – U.S. is considering the use of trade sanctions

to convince Japan to open its market.– U.S. is not sure whether Japan is cooperative

or not.– A cooperative Japan prefers open markets to

a trade war; an uncooperative Japan does not.

– U.S. believes Japan is cooperative with probability p.

U.S.-Japan games

US

J

Sanctions

No

Cooperate

No

Openmarkets3, 2

Trade war0, 1

Status quo2, 3

Japan cooperative (p)

US

NoSQ2, 3

Sanctions

J

Coop

No

OM3, 1

TW0, 2

Japan uncooperative (1-p)

Game with uncertainty

To show the U.S. decision problem, we include an initial move by Nature.

• Japan can be of two types• Each type has different payoffs• Nature is not strategic, just rolls the dice• An information set ties together nodes

where the player making the decision at that node is uncertain about which node has been chosen.

Game with uncertainty

Nature

Cooperative,prob p

Uncooperative,prob 1-p

US

US

Sanction

No

Coop

No

J

Open market, 3, 2

Trade war, 0, 1

SQ 2, 3

Sanction

No

No

CoopOpen market, 3, 1

Trade war, 0, 2

SQ 2, 3

Game with uncertainty

• The dashed line indicates the U.S. information set: it doesn’t know precisely which of these nodes it is at when it makes its decision– Could also indicate this by circling the nodes

• How does the U.S. decide what to do?– It calculates its expected payoff for each

strategy (sanction, don’t sanction)– Then chooses the strategy with the highest

expected payoff

Critical value of p

The U.S. looks for the critical value of p: the value at which it switches to the sanctioning strategy.

• US payoff from choosing sanctions:

p3+(1-p)0 = 3p

• US payoff from no sanctions: 2

• So sanction if 3p>2; p>2/3

• 2/3 is the critical value of p.

Adding domestic politics

BdM then extends the game by considering an interest group that punishes the president if he doesn’t adopt their preferred strategy.

• This just changes the president’s payoffs, so that the critical value for sanctioning becomes higher

• Work through this calculation for yourself

Analyzing uncertainty

• This is a game of one-sided uncertainty: Japan knows U.S. payoffs with certainty.

• Two-sided uncertainty would get a little messier, but solving the game would involve the same logic.

Signaling

What if the players have the opportunity to try to influence the other’s beliefs?

• This is known as signaling.

• This opportunity may create incentives to bluff.

Signaling

• E.g., assume J has the chance to pass a law that makes it easier to impose retaliatory tariffs before US moves.

• US, on observing passage of this law, may change its probability estimate about J’s type.

• Knowing this, even a cooperative J may have an incentive to bluff.

• But US knows this, and so will discount J’s actions.

Appeasement example

Appeasement as an example: should a declining power appease a rising power by making repeated concessions to demands?

• The challenger gets to decide in each period whether to make demands

• Then the declining power concedes or says no.

Appeasement example

• There is one-sided uncertainty about the demands of the challenger: declining doesn’t know whether demands are limited or not (how determined the challenger is).

• If demands are unlimited, war is inevitable, and the declining power would rather fight sooner than later.– Then no concessions made

Appeasement example• But because of uncertainty, sometimes the

declining power will end up making concessions but still fighting.

• This is an inefficient outcome.

• Incomplete information has a cost, and it falls on the less-informed player (as in the agency example).