Bilateral Negotiations 0 - University of Queenslandcupid.economics.uq.edu.au/mclennan/Classes/Ec3430/lecture04.pdf · I Key negotiation variable: ... (or bilateral monopoly) examples

Bilateral Negotiations

Andy McLennan

August 18, 2016

Chapter Outline

I Added value approach to bargaining.

I Only two players (bilateral bargaining).

I Two types of transactions:

1. Buyer-seller exchange: the seller owns an asset, produces agood or provides a service and the buyer values that asset, goodor service.

2. Cost-sharing arrangements: both players want to share anasset, good or service in order to realize some value, but one orboth do not generate sufficient value on their own to cover thecosts.

Making predictions

In many sequential games, we need to have some (rough) predictionabout what the outcome of negotiations will be:

I If I enter this market and bargain with suppliers, what prices andquantities will they agree to, roughly?

I If I make an investment that raises demand for my product, howwill that change the outcome of negotiations?

I If I make an investment that ties me to just one customer, whatprice will result?

Bargaining power

We’ve had a flavor of what is coming. . .

We have already seen that you will get a greater share of the pie if:

I You have a better outside option (it affects WTP or WTS).

I You have credible alternatives (e.g. credible threat example).

I You can commit to a strategy (e.g. ultimatum game is equivalentto not accepting counter-offer).

Complete information

I For the moment, we continue to assume complete information.I In particular, sellers know buyers’ WTP and buyers know sellers’

WTS.

I Incomplete information in bargaining can explain:I Bargaining breakdowns (e.g., strikes)I Inefficient outcomes (e.g., no trade even though WTP > WTS)

Buyer-seller exchange (or bilateral monopoly)

Key elements:

I Seller: player who owns an asset, produces a good or provides aservice.

I Buyer: player who values that asset, good or service, but musttrade with the seller to get it (and realize value).

I Key negotiation variable: price.

The negotiation is over how to divide the surplus:

I There is always an inefficient outcome: no agreement.

I But many efficient outcomes: any agreement to split the surplusby use of a price in the feasible range (Gans, Chapter 3).

Buyer-seller exchange (or bilateral monopoly) examples

I Electricity generating plant and coal mine.

I TV networks and leading actor.

I Pharmaceutical companies (specializing in specific therapeuticcategory) and researchers in those companies.

Common feature: both parties made investments that arerelationship-specific. These investments have no value outside thatrelationship.

Running example: buyer-seller exchange

I Niles does not have tickets to the opera and they are all sold out.I Niles values two opera tickets at $200 ($100 a piece).

I Frasier has two opera tickets but has a cold and decides he maynot want to go after all.

I Frasier will go if he has the tickets but only values going at $50($25 per ticket).

Will they negotiate and reach an agreement? If Frasier agrees to sellthe tickets to Niles, what can we say about the price?

What is total surplus?

Definition

Total surplus is the sum of individual surpluses from trade.

Note: It is defined on the basis that trade occurs.

I Niles’ (buyer) surplus: WTP−p = $200−p

I Frasier’s (seller) surplus: p−WTS = p−$50

I Thus, total surplus (from trade) is:

WTP−p︸ ︷︷ ︸buyer surplus

+ p−WTS︸ ︷︷ ︸seller surplus

= WTP−WTS = $150

Gains from trade view

Valuecreated

(total surplus)= $150

WTP = $200

WTS = $50

Price

Seller (Frasier)

Buyer (Niles)

Who captures value?

Change in bargaining power

I Consider the same example, but now suppose the opera is notsold out.

I Niles can purchase tickets for $100 ($50 each).

Will they negotiate and reach an agreement? If Frasier agrees to sellthe tickets to Niles, what can we say about the price?

Gains from trade view

Valuecreated

(total surplus)= $50

WTP = $100

WTS = $50

Price

Seller (Frasier)

Buyer (Niles)

Who captures value?

Note: Niles will not pay more than $100 for Frasier’s tickets.

Added value

Definition

Your added value = total surplus when you are engaged in trade - totalsurplus when you are not

Added value is a measure of what a player is bringing to the table.

Added value

I Important determinant of division of the pie.

I Two player case:I Added values are easy to compute.I Each players’ AVs are equal and are equal to total surplus.

I Many players case:I Requires careful computation.

Added value in the example (when opera is sold out)

I Total value when both Niles and Frasier agree to negotiate= $200

I Total value if Niles refuses to negotiate = $50

I Total value if Frasier refuses to negotiate = $50

I ThusI Niles’ AV = $200−$50 = $150I Frasier’s AV = $200−$50 = $150

I Makes sense: with 2 people, if either refuses to trade, all surplusis lost.

What does this mean for price?

Total surplus= $150

WTP = $200

WTS = $50

Price

Frasier = p - WTS

Niles = WTP - p

Who captures value?

Maximum price

Total surplus= $150

WTP = $200

WTS = $50

Price

Frasier = p - WTS= $150

Niles = WTP - p

= $0

Who captures value?

Frasier cannot gain more than $150 in surplus.

Minimum price

Total surplus= $150

WTP = $200

WTS = $50

PriceFrasier = p - WTS

= $0

Niles = WTP - p= $150

Who captures value?

Niles cannot gain more than $150 in surplus.

Added value in the example (when opera is not sold out)

I Total value created when both Niles and Frasier agree tonegotiate = $200

I Total value if Niles refuses to negotiate = $150

I Total value if Frasier refuses to negotiate = $150

I ThusI Niles’ AV = $200−$150 = $50I Frasier’s AV = $200−$150 = $50

Price range

Total surplus= $50

$200

WTS = $50

PriceFrasier = p - WTS

Niles = WTP - p

Who captures value?

WTP = $100

I Maximum price: $100I Minimum price: $50I Niles is likely to get a better deal compared to the case when

opera is sold out.

Example: Home Alone

Example

When Macaulay Culkin was picked for Home Alone, he took the rolefor little more than $100,000. Twentieth Century-Fox released the filmin 1990. It grossed $286 million in the home market alone and went onto become the sixth highest grossing movie ever.The story of the sequel, Home Alone 2: Lost in New York, was verydifferent. This time, Macaulay got paid around $5 million, plus fivepercent of the domestic gross. The sequel rapidly grossed $174million, and that added another $8.7 million to Macaulay’s paycheck,helping him become the youngest of Hollywood’s top-40 grossingartists.

Price range

Totalsurplus

WTS

Price HA IMacaulay

Studio

Who captures value?

WTP HA I

WTP HA II

Price HA IIStudio

Macaulay

Specific price predictions

Consider the example:

I Catherine has a power transformer (from when she first came toAustralia from the US) in like-new condition but for which she nolonger has any use.

I Hilary just moved to Australia from the US with an expensivestereo and, so, needs a transformer.

I A new transformer costs $200.

I It is unlikely anyone else will buy the used transformer.I What agreement will be reached?

I Intuition is that they quickly agree on something near $100.I Economic profit of C = $100−$0 = $100.I Economic profit of H = $200−$100 = $100.I So, each gets an equal share of the available value.

Why is this the “intuitive” outcome?

BATNA

BATNA = “Best alternative to a negotiated agreement”

Definition

The BATNA is what you get if negotiations break down for good, thatis, your payoff in the totally non-cooperative state.

I BATNA is just another name for “next-best alternative”, oropportunity cost.

I It is used specifically in the context of negotiations.I BATNA determines:

I WTP/WTS, andI Agreeable cost- or revenue-sharing arrangements.

I Outside option is an equivalent term to BATNA.

BATNAs bound range of possible value transfers (prices)

I If your bargaining partner insists you get less than your BATNA,you are better off breaking off negotiations and taking your nextbest alternative.

I This is what you will do.

I No one gets less than their BATNA from a freely madeagreement.

“If parties reach agreement, fine. Otherwise, they do the best theycan.”

Credibility and BATNA

It only works if BATNA is credible:

I You have to know about your best BATNA,. . .

I . . . , the other side has to know that you have a temptingBATNA,. . .

I . . . and you have to know that the other side knows that you knowabout your BATNA.

Why half the surplus?

I If nothing specific tilts things in favor of one negotiator, it issensible to assume an even split of the surplus.

I Often considered “unreasonable” when one party tries to get morein an evenly matched situation.

I In business, negotiators are often evenly matched.I Many people have an inherent sense of “fairness”.

I If you get a better outside alternative,your next-best alternative changes,which changes the surplus,which should affect what you get!

In the example

I When opera is sold out:

p =WTP +WTS

2=

$200+$502

= $125

I Niles’ (buyer) surplus: WTP−p = $200−$125 = $75I Frasier’s (seller) surplus: p−WTS = $125−$50 = $75

I When opera is not sold out:

p =WTP +WTS

2=

$100+$502

= $75

I Niles’ (buyer) surplus: WTP−p = $100−$75 = $25I Frasier’s (seller) surplus: p−WTS = $75−$50 = $25

Sources of bargaining strength

I To say that you did well in a negotiation because you were in astrong bargaining position is not very informative.

I The interesting question is: what are the sources of bargainingstrength?

When does one player get more?

Forces that tilt the bargaining balance:1. Negotiating skill: is one party more experienced?

I No deceit – remember, this is a complete information situation.I Still, agents may be skilled at getting others to part with value.

2. Specific bargaining process (large effect!!)I Auctions are the best example of a specific process.I Outside of auctions, most negotiations are free-form.

3. Agents’ sense of fairness (i.e., emotional responses)I People can behave “irrationally” if “provoked”.I Sometimes sending in a negotiator with a (known) hair-trigger

temper can be useful (have to be careful not to provoke others).

4. Cost of delay: is one party more vulnerable?I Time is money: the relative cost of delay of the bargainers is a

determinant of their bargaining power.I The more impatient your opponent is to settle, the better for you is

the agreement you can push for.

When does one player get more?

5. Focal points: is there anything about the bargaining situation thatserves to highlight a particular outcome?

I precedent (always here before)I convention (take turns)I arithmetical symmetry (fifty-fifty)I fairness (fifty-fifty)I suggestion from an impartial party

6. Credible commitments (all-or-nothing offer):I Leaving the outcome beyond your controlI Mandated negotiating agentsI Burning your bridgesI Cutting off communicationI ReputationI Rational irrationality (method in one’s madness)I ContractsI Brinkmanship

Be aware of when these are important!

What drives players to reach agreement?

Offers/counter-offers could, in principle, go on forever.

I The cost of delay in reaching agreementI Costs to using staff to negotiate (or prepare offers)I Costs to one (or both) firms if the agreement is not in placeI Other firms may take advantage of the business opportunity

I The risk of (irrational) breakdown in negotiationsI If the other negotiator keeps making unreasonable demands, you

may become exasperated and break off negotiations, even if it’snot in your economic interest

Timing issues have real effects

I The patient player extracts more surplus.I If costs and risks are very bad for one party, the other benefits.I If I know you’re losing money because of delay, I can extract more

surplus.

I Similar timing issues push toward symmetric solutions (splittingthe surplus equally).

I As long as delay is bad for both players.

I Symmetric or not, people reach agreement more quickly undercomplete information.

I Value wasted due to delays is inefficient.

Cost-sharing arrangement

Key elements:I Two players: both wish to share an asset, good or service in

order to realize some value.I It might be the case that they both generate enough value on their

own to cover the costs.I It might be that one or both do not generate enough value to cover

the costs on his own.

I Returns: joint use of the asset does not diminishes the quality ofits use.

I Key negotiation variable: share of the costs.

The negotiation is over how to divide the costs:

I There is always an inefficient outcome: no agreement.

I But many efficient outcomes: any agreement to share the costswithin the feasible range.

Cost-sharing arrangement examples

I Joint ventures to cover R&D costs (even if companies compete inother markets).

Analysis extends to implicit cost-sharing arrangements, that do notinvolve monetary transfers.

Common feature: players are complementors on the supply-side.The costs of usage of the resource do not rise considerably whenmore than one player is involved.

Classifying cost-sharing surplus

Where is the source of surplus in this joint relationship?

1. Low asset costs: avoid duplication of costs.

2. Medium asset costs: make venture feasible for a small player.

3. High asset costs: make venture feasible for all players.

It’s useful to calculate total surplus to figure out where it’s comingfrom. . .

Running example: cost-sharing

I Two players, Ann and Bob.I There is a resource that can give each player some revenue if

they have access to it:I Revenue for Ann: $100I Revenue for Bob: $200

I There is a cost to acquire the resource: (1) $250, (2) $150, (3)$50.

I Joint use of the resource does not reduce the revenue it yields toAnn and Bob.

It’s clear that they are better off by jointly using the resource.

But the question is: how much of the resource’s cost should Ann andBob pay respectively?

High asset costs (1)

I Start with the case when the resource costs $250.

I Neither Ann nor Bob could cover it alone.

I The only way to make positive profit is to agree with a jointacquisition of the resource: both are essential to the partnership.

I Total surplus of the exchange = $100+$200−$250 = $50I Both are essential⇒ their respective added values are identical

and equal to total surplus:I Ann’s AV: $50I Bob’s AV: $50

Range of feasible cost allocations

I Highest contribution Ann can make: $100 (leaving Bob with $150)

I Highest contribution Bob can make: $200 (leaving Ann with $50)

I Range of cost allocations:I Ann: $50−$100I Bob: $200−$150

Range of cost allocations: high cost asset

$250

Bob

Ann

$200

$50

$150

$100

Bob’s revenue(WTP)

Ann’s revenue(WTP)

Range of Bob’s

contribution

Range of Ann’s

contribution

Medium asset costs (2)

I Case when the resource costs $150.

I Ann could not cover it alone, but Bob could.

I If the joint partnership does not happen, Bob would still earn avalue of $50.

I If the joint partnership happens, the total surplus would be$100+$200−$150 = $150.

I The value created by the partnership is then $150−$50 = $100:I Ann’s AV: $100I Bob’s AV: $100

Range of feasible cost allocations

I Highest contribution Ann can make: $100 (leaving Bob with $50)

I Highest contribution Bob can make: $150 (leaving Ann with $0)

I Range of cost allocations:I Ann: $0−$100I Bob: $150−$50

Range of cost allocations: medium cost asset

$150

Bob

Ann

$200

$0

$50

$100

Bob’srevenue

Ann’s revenue(WTP)

Range of Bob’s

contribution

Range of Ann’s

contribution

$150

Bob’sWTP

Low asset costs (3)

I Case when the resource costs $50.

I Both Ann and Bob could cover the costs alone.

I If the joint partnership does not happen, Ann earns a value of$100−$50 = $50 and Bob earns a value of $200−$50 = $150.

I If the joint partnership happens, the total surplus would be$100+$200−$50 = $250.

I The value created by the partnership is then$250− ($150+$50) = $50:

I Ann’s AV: $50I Bob’s AV: $50

Range of feasible cost allocations

I Highest contribution Ann can make: $50 (leaving Bob with $0)

I Highest contribution Bob can make: $50 (leaving Ann with $0)

I Range of cost allocations:I Ann: $0−$50I Bob: $50−$0

Range of cost allocations: low cost asset

$50

Bob

Ann

$200

$0

$0

$100

Bob’srevenue

Ann’srevenue

Range of Bob’s

contribution

Range of Ann’s

contribution

$50

$50

Bob’sWTP

Ann’sWTP

Difference among the three cases

Surplus created SourceHigh cost $50 Only way to earn revenueMedium cost $100 Allowed Ann her revenue of $100Low cost $50 Avoided duplication of costs of $50

Specific cost-sharing rules

If we assume equal bargaining power, what would be the equivalent to“half the surplus”?

I How about splitting the costs evenly?I Makes sense in the case of low cost asset.I However, it would prevent agreement in the case of high cost

asset (even if the joint partnership is worthwhile).

I How about equi-proportional rules (contributions are proportionalto the relative benefits)?

I In the example: Bob would contribute with 23 of the costs.

I Still might not be a good prediction of a bargaining outcome: eventhough it reflects some fairness notion, it does not reflects theeconomics of the situation, the incentives.

I Equal bargaining power should lead to cost-sharing rules thatequate surpluses of each player.

Contributions when players have equal bargaining power

(1) High cost asset: $250

I Total surplus from trade: $100+$200−$250 = $50

I Value without trade: $0I Players should get the same surplus:

I Bob’s surplus is WTP− cB = $200− cB .I Ann’s surplus is WTP− cA = $100− cA.I The sum of their contributions has to add up to the cost:

cA + cB = $250.

Solve the system of equations:

200− cB = 100− cA

cB + cA = 250

I cB = $175

I cA = $75

Contributions when players have equal bargaining power

(2) Medium cost asset: $150

I Total surplus from trade: $100+$200−$150 = $150

I Value without trade: $200−$150 = $50I Players should get the same surplus:

I Bob’s surplus is $200− cB−$50 = $150− cB .I Ann’s surplus is $100− cA.I The sum of their contributions has to add up to the cost:

cA + cB = $150.

Solve the system of equations:

150− cB = 100− cA

cB + cA = 150

I cB = $100

I cA = $50

Contributions when players have equal bargaining power

(3) Low cost asset: $50

I Total surplus from trade: $100+$200−$50 = $250

I Value without trade: $200−$50+$100−$50 = $200I Players should get the same surplus:

I Bob’s surplus is $200− cB−$150 = $50− cB .I Ann’s surplus is $100− cA−$50 = $50− cA.I The sum of their contributions has to add up to the cost:

cA + cB = $50.

Solve the system of equations:

50− cB = 50− cA

cB + cA = 50

I cB = $25

I cA = $25

Concluding remarks

Bottom line:I Two person trade:

I AV of each person is identicalI AV of each person = total surplus from trade

I Range of prices is determined by willingness-to-pay andwillingness-to-sell and by looking at each player’s added value.

I Total surplus is reduced if one person has an alternative option(e.g., Frasier and box office compete to sell to Niles).

I Price moves in favor of the person with a tempting BATNA (e.g., alower price to Niles who has an alternative).

I You should seek alternatives and think about what you could do ifthe negotiations fail.

I Know what can change bargaining balance: commitment, focalpoints, delay costs.

More generally: know yourself, know the other, and know the situation.

“In business, you don’t get what you deserve, you getwhat you negotiate.”

– Chester L. Karrass