Strategic Game Theory for Managers

R.E.Marks © 2003 Lecture 1-1

S TR A TEGIC GAME THEOR Y FOR MAN A GER S

Ou tlin e of su bje ct:

Lecture Topic1. 1. Strate g ic De c is ion Makin g2. Firms Behaving Badly.3. Duopoly Behaviour4. More Examples.5. 2. De c is ion An alys is :

Gam e s Again st Natu re6. Eva lua t ion .7. Gain ing Insight .8. Ut ility.9. 6. Un pre dictability

10. 7. Bargain in g11. 8. Us in g In form ation Strate g ica lly12. Screening, Signa lling.


13. 9. Biddin g an d Au ction De s ign14. Concluded.15. 10. Con tractin g ,

or th e Ru le s of th e Gam e16. Employing, Financing, Franchising.17. 13. Ch oos in g th e Righ t Gam e : Coope tit ion18. Concluded.19. Stu de n t pre se n tation s20. Concluded.


Books

Recommended (but not required) text :

Bierman H.S. & Fernandez L., Gam e Theory with Econom ic Applications,Reading: Addison-Wesley, 2nd ed., 1998.

Dixit A., and Skea th S., Gam es of S trategy, New York: Nor ton , 1999.

As well, the following books will be found usefu l:Gin t is H., Gam e Theory Evolving: A Problem -Centered In troduction to Modeling

S trategic In teraction , Pr inceton: P.U.P., 2000.Watson J., S trategy: An In troduction to Gam e Theory, N.Y.: Nor ton , 2002.Rasmusen E ., Gam es and In form ation: An In troduction to Gam e Theory,

Oxford: B. Blackwell, 3rd edit ion , 2001.Gardner R., Gam es for Business and Econom ics, N.Y.: Wiley, 2nd. ed., 2003.Ghemawat P., Gam es Businesses Play: Cases and Models, Camb.: MIT Press,

1997.PackageAsse ssm e n t


Qu otable Qu ote s

Game theory:“the grea test auct ion in h istory”

The N ew York Tim es, March 16, 1995, p.A17.“When government auct ioneers need wor ldly advice, where can they turn? To

mathemat ica l economist s, of course ... As for the firms tha t want to get theirhands on a sliver of the a irwaves, their best bet is to go out first and h irethemselves a good game theor ist .”The Econom ist, J u ly 23, 1994, p.70.

the “most dramat ic example of game theory’s new power ... It was a t r iumph,not on ly for the FCC and the taxpayers, bu t a lso for game theory (and gametheor ist s).”Fortune, February 6, 1995, p.36.

“Game theory, long an in tellectua l past ime, came in to it s own as a businesstool.”Forbes, J u ly 3, 1995, p.62.

“Game theory is hot .”The Wall S treet J ournal, February 13, 1995, p.A14.


On -lin e Re fe e n ce s

. . . bu t game theory is not new!

For a history of game theory, seewww.econ.canterbury.ac.nz/hist.htm

For more game theory on the Web, seewww.economics.harvard.edu/∼aroth/alroth.html

For a glossary of t erms you should be familia r with a fter Chongwoo’s SETint roduct ion , seewww.agsm.edu.au/∼bobm/teaching/SGTM/glossary.html


Gam e Th e ory

❝Convent iona l economics takes the st ructure of markets as fixed.People a re thought of as simple st imulus-response machines.Sellers and buyers assume tha t products and pr ices a re fixed, andthey opt imize product ion and consumpt ion accordingly.Convent iona l economics has it s place in descr ibing the opera t ion ofestablished, mature markets, bu t it doesn’t capture people’screa t ivity in finding new ways of in teract ing with one another.

Game theory is a differen t way of looking a t the wor ld. In gametheory, noth ing is fixed. The economy is dynamic and evolving.The players crea te new markets and take on mult iple roles. Theyinnova te. No one takes products or pr ices as given . If th is soundslike the free-form and rapidly t ransforming marketplace, tha t ’swhy game theory may be the kernel of a new economics for thenew economy.❞

— Brandenburger & NalebuffForeword to Co-opetition


1. Strategic Decision MakingBu sin e ss is w ar an d pe ace .

➣ Coopera t ion in crea t ing va lue.➣ Compet it ion in dividing it up.➣ No cycles of War, Peace, War, ....

bu t simultaneously war and peace.

“You have to compete and coopera te a t the same t ime.”— Ray Noorda of Novell.

➪ Co-opet it ion

(See Lectures 17 and 18 la ter and Brandenburger & Nalebuff in the Package.)


Man u al for “Co-ope tit ion ”

How to:— coopera te without being a sa in t— compete without killing the opposit ion .

➪ Game Theory


1.1 Business is a Game, of Sor ts

Business is a game, but differen t from st ructured board games or a rcade gamesor computer games:

➣ it is not win-lose (not zero-sum): possible for a ll players to win

➣ apar t from the law, there is no ru le book

➣ others will change the game to their advantage

➣ the game is made up of five PARTS (see below)

➣ success comes from playing the righ t gam e

So game theory provides a framework for an ever-rapidly changing wor ld.


Wide r issu e s .

In Lectures 17 and 18 we go beyond the more micro issues → wider issues:

Which gam e should your firm / organisation be in?

It ’s no good st icking toyour kn it t ing if there’s

no demand for jumpers.


Qu e stion : High or low ?

You can choose Left or Right :Profits:

Left RightYou $40 m $80 mRiva l $20 m $160 m


Th e PARTS of th e Gam e

Players: customers, suppliers, r iva ls, a llies;Change any, including yourself.

Added Values: what each player adds to the game (taking the player ou twould subt ract their added va lue).Wa ys to ra ise yours, or lower their s.

R ules: give st ructure to the game; in business — no universa l set of ru lesfrom law, custom, pract ica lity, or cont ract sCan revise exit ing ru les, or devise new ones

Tactics: moves to shape the way:— players perceive the game, and hence— how they playTact ics to reduce mispercept ion , or to crea te or main ta inmispercept ion .

S cope: the bounds of the game: expand or shr ink.

PARTS gives more than a framework, it provides a complete set of levers.

PARTS provides a method to promote non-rout ine th inking, see la ter.


A Case : Th e Ne w York Post v. th e Ne w York Ne w s

N.Y. Post N.Y. N ews

J anuary 1994 40¢ 40¢February 1994 50¢ 40¢

March 1994 25¢ 40¢(in Sta ten Island)

J u ly 1994 50¢ 50¢

Unt il Feb 1994 both papers were sold a t 40¢. Then the Post ra ised it s pr ice to50¢ but the N ews held to 40¢ (since it was used to being the first mover ). So inMarch the Post dropped it s Sta ten Island pr ice to 25¢ but kept it s pr iceelsewhere a t 50¢, un t il N ews ra ised it s pr ice to 50¢ in J u ly, having lost marketshare in Sta ten Island to the Post and having accepted tha t the Post wouldhencefor th be the leader in any pr ice h ike. So both were now pr iced a t 50¢everywhere in NYC.


1.2 A gentle introduction

Piemax Inc. bakes and sells desser t pies.It s decision :

— price high or low for today’s pies?

Things to be considered:— prices of r iva ls’ pies?— prices of non-pie subst itu tes?

A naïve opt ion :simply opt imise it s pr icing policy given it s beliefs about r iva ls’ pr ices, or


Th in k s trate g ica lly...

Alterna t ive:t ry to predict those pr ices,using P iemax’ knowledge of the indust ry,in par t icu la r : it s knowledge tha t it s r iva ls will choose their pr ices basedon their own predict ions of the market environment , including P iemax’own pr ices.

Game Theory →

• P iemax should bu ild a m odel of the behaviour of each individua lcompet itor,

• Which behaviour would be most reasonable to expect?

Later : what is an equilibr ium?

Later : ought P iemax to believe tha t the market ou tcome → equilibr ium?

Now: what kind of model?


Th e s im ple st k in d of m ode l.

— All bakers opera te for one day only (a so-ca lled one-shot model)— All bakers know the product ion technologies and object ives of the

others— Study with the tools of:

➣ payoff m atrix games and➣ Nash e qu ilibriu mN ash Equilibrium : no player has any incent ive to change h is or heract ion , assuming tha t the other player (s) have chosen their bestact ions for themselves.Nash equilibr ia a re self-rein forcing.In two-player games, a Nash equilibr ium prescr ibes st ra tegies tha ta re mutua lly best response (not un iversa lly best responses, as withdominant st ra tegies).


Re pe ate d in te raction s .

If m ore than one day (a repea ted game or in teract ion):— then P iemax’s object ives?

(more than maximising today’s profits)e.g. low pr ice today may:

→ customers switch from a r iva l brand→ increase P iemax’ market share in the fu ture

e.g. baking a la rge ba tch of pies may→ a llow learn ing by doing by the sta ff& lower product ion cost s in the fu ture


Bu t th e re are dan ge rs!

It s r iva ls may be influenced by P iemax’s pr ice today→ a low Piemax pr ice may t r igger→ a price war.

Such dynamic games can be dea lt with using— extensive-form game t rees and— the solu t ion concept of subgam e perfection

S ubgam e Perfect Equilibrium :a Nash equilibr ium tha t does not rely on non-credible th rea ts (tha tsa t isfies backwards induct ion).


How abou t in form ation ?

• What if P iemax is uncertain of the cost funct ions or the long-termobject ives of it s r iva ls?

— Has Cupcake P ty Ltd just made a breakthrough in la rge-ba tchproduct ion?

— Does Sweetstuff plc ca re more about market share than aboutcur ren t profits?

— And how much do these r iva ls know about P iemax?

Incom plete in form ation games.

Act ing in a fog: percept ions ru le!


An d le arn in g?

➣ If the indust ry cont inues for severa l per iods,then P iemax ought to learn about Cupcake’s and Sweetstuff’s pr iva teinformat ion from their curren t pricing behaviourand use th is in format ion to improve it s fu ture st ra tegy.

➣ In an t icipa t ion , Cupcake and Sweetstuff may be loa th to let theirpr ices revea l in format ion tha t enhances P iemax’s compet it iveposit ion :

➣ They may at tempt to m anipulate Piem ax’s in form ation .


In a n u tsh e ll ...

Game theory is the study of ra t iona l behaviour in situa t ions involvingin terdependence:➣ May involve common in terest s: coordination➣ May involve compet ing in terest s: rivalry➣ R ational behaviour: players do the best they can , in their eyes;➣ Because of the players’ in terdependence, a ra t iona l decision in a game

must be based on a predict ion of others’ responses.Put yourself in the other’s shoes and predict ing what act ion the otherperson will choose, you can decide your own best act ion .


1.3 Strategic Interaction

• Game theory → a game plan , a specifica t ion of act ions cover ing a llpossible eventua lit ies in st ra tegic in teract ions.

• S trategic situations:involving two or more par t icipants, each t rying to influence, to

outguess, or to adapt to the decisions or lines of behaviour tha t othershave just adopted or a re expected to adopt (Tom Schelling).

Look forward and reason backwards!


Th e fl at tyre an d m yopia ...

Two college students, very confident about their mid-term exam per formance ina subject , decided to a t tend a par ty the weekend before the fina l exam. Thepar ty was so good tha t they overslept the whole Sunday.Instead of taking the exam unprepared on Monday, they pleaded to theprofessor to give them a make-up exam. Their excuse was a fla t tyre without aspare and any help. The professor agreed.On Tuesday morning, the professor placed them in separa te rooms and handedthem the test . The test had just one quest ion :Which tyre?


An d th e application s ...

— a procurem ent m anager t rying to induce a subcont ractor to search for cost -reducing innova t ions

— an entrepreneur negot ia t ing a roya lty a r rangement with a manufactur ingfirm to license the use of a new technology

— a sales m anager devising a commission− payments scheme to mot iva tesa lespeople

— a production m anager deciding between piece-ra te and wage payments toworkers

— designing a m anagerial incentive system— how low to bid for a government procurement cont ract— how h igh to bid in an auct ion— a takeover raider’s decision on what pr ice to offer for a firm— a negotiation between a mult ina t iona l and a foreign government over the

set t ing up of a manufactur ing plan t— the haggling between a buyer and seller of a used car— collective bargain ing between a t rade un ion/employees and an employer


1.4 Some Interactions1.4.1 Auctioning a Five-Dollar Note

Rules: ➣ First bid: 20¢➣ Lowest step in bidding: 20¢

(or mult iples of 20¢)➣ Auct ion last s un t il the clock sta r t s r inging.➣ Highest bidder pays bid and gets $5 in return .➣ Second-h ighest bidder a lso pays, bu t gets noth ing.

Write down the situa t ion as seen by1. the h igh bidder, and2. the second h ighest bidder.

What happened?

Esca la t ion and en t rapment

Examples? (See O’Neal’s paper in the package.)


1.4.2 Schelling’s Game

Rules:➣ Single play, $4 to play: by wr it ing your name on the slip➣ Vote “C” (Coopera te) or “D” (Defect ).➣ Sign your ba llot . (and commit to pay the en t ry fee.)➣ If x% vote “C” and (100 − x)% vote “D”:

• then “C”s’ payoff = (x

100× $6) − $4

• then “D”s’ payoff = “C” payoff + $2

➣ Or: You needn’t play a t a ll.


Sch e llin g’s Gam e

Percentage of par t icipants vot ing C

$pe

rpa

rtic

ipan

t

0 25 50 75 1000

2

4

6

8

“C”

“D”

Note: the game cost s $4 to join .


Sch e llin g’s Gam e

WHAT HAPPENED?➣ numbers & payoffs.➣ previous years?

Dilemma:⎧⎨⎩

coopera te for the common good ordefect for oneself

Public/pr iva te in format ion

Examples?


1.4.3 The Ice-Cream Sellers

(See Marks in the Package)

L

ˆ

R

ˆ

C

ˆ

➣ Demonst ra t ion➣ Pa yoff mat r ix➣ Incent ives for movement?➣ Examples?


Mode llin g th e ice -cre am se lle rs .

We can model th is in teract ion with a simplifica t ion : each seller can either :➣ move to the cen t re of the beach (M), or➣ not move (stay put ) (NM).The share of ice-creams each sells (to the tota l popula t ion of 80 sunba thers)depends on it s move and tha t of it s r iva l.Since each has two choices for it s loca t ion , there a re 2 × 2 = 4 possibilit ies.We use arrows and a payoff m atrix , which clear ly ou t lines the possible act ionsof each and the resu lt ing outcomes.

What a re the sa les if neither moves (or both NM)? Each sells to ha lf the beach .What a re the sa les if You move to the cen t re (M) and your r iva l stays pu t a t thethree-quar ter poin t?What if you both move?Given the ana lysis, what should you do?


Th e Ice -Cre am Se lle rs

The other seller

M NM

40, 40 50, 30M

NM 30, 50 40, 40You

TABLE 1. The payoff mat r ix (You, Other )

A non-coopera t ive, zero-sum game,with a dom in an t s trate gy ,

or dominant move.


Re al-World Ice -Cre am Se lle rs

Think of the beach as a product spect rum, each end represen t ing a par t icu la rn iche, and the cen t re represen ta t ing the most popula r product .

Demand is la rgest for the most popula r product , bu t so is compet it ion .

This simple model: a t endency to avoid ext remes, especia lly with bar r iers toen t ry for new players.

Examples: — the convergence of fash ions?— the simila r ity of commercia l TV and radio programming?— the copy-ca t policies of polit ica l par t ies?— the para llel scheduling of Anset t (and perhaps Virgin) and

Qantas?

A twist : What if the cen t re is too fa r for some ba thers (a t the ends of the beach)to walk?

Then the tendency for the sellers to offer the same product (a t the cen t re) isreduced, and they might differen t ia te their products.


1.4.4 The Prisoner’s Dilemma(See Marks in the Package)Case : Te ls tra an d Optu s an d adve rtis in g .

David Ogilvy: Half the m oney spent on advertising is wasted; the problem isidentifying which half.

Telst ra and Optus independent ly must decide how heavily to adver t ise.Adver t ising is expensive, bu t if one telco chooses to adver t ise modera tely whilethe other adver t ises heavily, then the first loses ou t while the second does well.Let ’s assume if both Adver t ise Heavily then Telst ra nets $70,000, while Optusnets $50,000.But if Telst ra Adver t ises Heavily while Optus Adver t ises Modera tely on ly, thenTelst ra nets $140,000 while Optus nets on ly $25,000, and vice versa .If both Adver t ise Modera tely, then Telst ra nets $120,000 and Optus nets$90,000.What to do?


Th e Adve rtis in g Gam eOptus

Heavy Modera te

70, 50 140, 25Heavy

Modera te 25, 140 120, 90Telstra

TABLE 2. The payoff mat r ix (Telst ra , Optus)

Ranking outcomes is OK: 4 = best → 1 = worst .

OptusHeavy Modera te

2, 2 4, 1HeavyModera te 1, 4 3, 3Telstra


Th e Tradition al, Sym m e tric Payoffs for th e P rison e r’s Dile m m a:

The Payoff Mat r ix:➣ The Chea ter ’s Reward = 5➣ The Sucker ’s Payoff = 0➣ Mutua l defect ion = 2➣ Mutua l coopera t ion = 4

These a re chosen so tha t : 5 + 0 < 4 + 4so tha t C,C is e ffi c ie n t in a repea ted game.


Th e P rison e r’s Dile m m a

A need for :✸ communica t ion✸ coordina t ion✸ t rust✸ or?

Effi cie n t Ou tcom e : there is no other combina t ion of act ions or st ra tegies tha twould make a t least one player bet ter off without making any other playerworse off.


Th e P rison e r’s Dile m m aThe other player

C D

4, 4 0, 5C

D 5, 0 2, 2You

TABLE 3. The payoff mat r ix (You, Other )

A non-coopera t ive, posit ive-sum game,with a dominant st ra tegy.

Efficien t a t _____

Nash Equilibr ium a t _____


1.4.5 The Capacity Game

Case : Du Pon t’s Titan iu m doxide capacity.

Titan ium dioxide is a whitener for pa in t , paper, and plast ics.In 1972 du Pont , with 34% of the U.S. market for t it an ium dioxide, announcedaddit iona l capacity which would a fter six years resu lt in it s share r ising to 65%.Du Pont resisted others’ pr ice r ises, bu t slackening demand growth meant it splans were reduced in size and delayed.But it s preempt ive st ra tegy has been very profitable: it is now the globa l leaderin t it an ium dioxide supply and it s exclusive ilmenite product ion is the lowest -cost t echnology.

A Sim ple r Mode l:

Two firms each produce ident ica l products and each must decide whether toExpand (E) it s capacity in the next year or not (DNE).A larger capacity will increase it s share of the market , bu t a t a lower pr ice.The simultaneous capacity game between Alpha and Beta can be wr it ten as apayoff mat r ix.


Th e Capacity Gam eBeta

DNE Expand

$18, $18 $15, $20DNE

Expand $20, $15 $16, $16Alpha

TABLE 4. The payoff mat r ix (Alpha , Beta )

A non-coopera t ive, posit ive-sum game,with a dominant st ra tegy.

Efficien t a t _____

Nash Equilibr ium a t _____


Equ ilibriu m .

At a Nash e qu ilibriu m , each player is doing the best it can , given thest ra tegies of the other players.We can use arrows in the payoff mat r ix to see what each player should do, giventhe other player ’s act ion .The Nash equilibr ium is a self-reinforcing foca l poin t , and expecta t ions of theother ’s behaviour a re fu lfilled.The Nash equilibr ium is not necessar ily efficien t .The game above is an example of the Pr isoner ’s Dilemma: in it s one-shotversion there is a conflict between collect ive in terest and self-in terest .


1.5 Modelling Players’ Preferences

Without uncer ta in ty or any dice-rolling,we need only rank the four combina t ions:

best, good , bad , worst:→ payoffs of 4, 3, 2, and 1, respect ively, in a 2 × 2 in teract ion .


Com plication s

Larger numbers of possible act ions:harder to rank the la rger number of ou tcomes(with th ree act ions there a re 3 × 3 = 9),bu t ranking sufficien t .(i.e. ordinal preferences, instead of asking “by how much is one outcomeprefer red to another?”)Later, with m ixe d s trate g ie s (probabilist ic or dice-throwing) andunpredictability:

• use probabilities over act ions and• the expected values of the possible ou tcome• use cardinal m easures over the amounts, usua lly dolla r amounts, which

are unambiguous, and the num bers m atter!


1.6 More Interactions1.6.1 Battle of the Bismark SeaIt ’s 1943: Actors:➣ Admira l Imamura : ordered to t ranspor t J apanese t roops across the Bismark

Sea to New Guinea , and➣ Admira l Kenney: wishes to bomb Imamura’s t roop t ranspor t s.Decisions/ Actions:➣ Imamura :

— a shor ter Nor thern rou te (2 days) or— a longer Southern rou te (3 days)

➣ Kenney: where to send h is planes to look for Imamura’s sh ips; he can reca llh is planes if the first decision was wrong, but then loses one day of bombing.

Some sh ips a re bombed in a ll four combina t ions.Kenney and Imamura each have the same act ion set — {N orth , S outh} — buttheir payoffs a re never the same. Imamura’s losses a re Kenney’s ga ins: a ze ro-su m gam e .


Th e Battle of th e Bism ark Se a

➣ Does any player have a dominant st ra tegy?➣ What is the most obvious way the game should be played?


Th e Battle of th e Bism ark Se a

Im am ura

North South

2, −2 2, −2Nor th

South 1, −1 3, −3Kenney

TABLE 5. The payoff mat r ix (Kenney, Imamura)A non-coopera t ive, zero-sum game,

with an it era ted dominant st ra tegy equilibr ium.

There is no other equilibr ium combina t ion : with a ll other combina t ions, a t leastone of the players stands to ga in by changing h is act ion , given the other ’sact ion .

For Imamura . going N weakly domina tes going S.Neither player has a dom inant strategy.


P laye rs’ ch oice s .

Neither player has a dom in an t s trate gy :➣ Kenney would choose

— N orth if he thought Imamura would choose N orth , bu t— S outh if he thought Imamura would choose S outh .— So Kenney’s best response is a funct ion of what Imamura does.

➣ Imamura would choose— N orth if he thought Kenney would choose S outh , bu t— either if he thought Kenney would choose N orth .— For Imamura , N orth is w e akly dom in an t.

And Kenney knows it and chooses N orth too.


Equ ilibriu m .

The st ra tegy combina t ion (N orth , N orth ) is an i te rate d dom in an t s trate gye qu ilibriu m . (It was the ou tcome in 1943.)

(N orth , N orth ) is a (Nash) equilibr ium, because:➣ Kenney has no incent ive to a lter h is act ion from N orth to S outh so long as

Imamura chooses N orth , and➣ Imamura ga ins noth ing by changing h is act ion from N orth to S outh so long

as Kenney chooses N orth .➣ And neither player has a (st r ict ly) dominant st ra tegy.➣ S outh is a (weakly) domina ted st ra tegy for Imamura .


A m arke t an alogu e ?

Two companies, K and I, t rying to maximise their shares of a market ofconstan t size by choosing between two product designs N and S .

K has a market ing advantage, and would like to compete head-to-head with I,while I would ra ther ca rve ou t it s own n iche instead of head-to-headcompet it ion .


1.6.2 The Battle of the Sexes

(A coordina t ion game: video VHS v. Sony’s Betamax;now the compet ing standards for digita l audio disks: SACD (Sony & Philips) v.DVD-A (Toshiba , Matsush ita , P ioneer etc.)and DVD recording: DVD+R, DVD-R, DVD-RAM.))

The Players & Actions:➣ a man (Hal) who wants to go to the Thea t re and➣ a woman (Shir l) who wants to go to a Concer t .While selfish , they a re deeply in love, and would, if necessary, sacr ifice theirpreferences to be with each other.The payoff mat r ix (measur ing the sca le of happiness) is below.What a re a ll equilibr ia?(Which pa irs of act ions a re mutua lly best response?)


Th e Battle of th e Se xe s

S hirl

Theat re Concer t

2, 1 −1, −1Thea t re

Concer t −1, −1 1, 2Hal

TABLE 6. The payoff mat r ix (Hal, Sh ir l)A non-coopera t ive, posit ive-sum game,

with two Nash equilibr ia .


Th e Battle of th e Se xe s

There is no it era ted dominant st ra tegy equilibr ium.There a re two N ash equilibria:➣ (Theatre, Theatre): given tha t Hal chooses Theatre, so does Shir l.➣ (Concert, Concert), by the same reasoning.How do the players know which to choose?

(A coordina t ion game.)


P laye rs’ ch oice s .

If they do not t a lk beforehand, Hal might go to the Concer t and Shir l to theThea t re, each mistaken about the other ’s beliefs.Foca l poin ts?Repet it ion?Each of the Nash equilibr ia is collect ively ra t iona l (efficien t ): no other st ra tegycombina t ion increases the payoff of one player without reducing tha t of theother.There is a fi rst-m ove r advan tage in th is sequent ia l-move game.


Marke t an alogu e ?

➣ An indust ry-wide standard when two dominant firms have differen tpreferences bu t both want a common standard.

➣ The choice of language used in a cont ract when two firms want to formalisea sa les agreement bu t prefer differen t t erms.

➣ Bought a DVD player recent ly?DVD, CDV, MP3, CD, DVD-V, DVD+, etc.Emerging standards mean choice and decisions for ea r ly adopters.


1.6.3 The Ultimatum Game➣ Your daughter, Maggie, asks for your sage advice.➣ She has agreed to par t icipa te in a lab exper iment .➣ The exper iment is two-player barga in ing, with Maggie as P layer 1.➣ She is to be given $10, and will be asked to divide it between herself and

Player 2, whose ident ity is unknown to her.➣ Maggie must make P layer 2 an offer,➣ Then Player 2 can either :

— accept the offer, in which case he will receive whatever Maggie offeredhim, or

— he can reject , in which case neither player receives anyth ing.➣ How much should Maggie offer?


Maggie ’s ch oice s .

➣ Dist inguish :➀ the rationalist’s answer from➁ the likely agreem ent in pract ice from➂ the just agreem ent.

The ra t iona list :➣ Player 1 should offer P layer 2 5¢ (the smallest coin).➣ Player 2 will accept , since 5¢ is bet ter than noth ing.➣ But offer ing only 5¢ seems r isky, since, if P layer 2 is insu lted, it would cost

h im only 5¢ to reject it .➣ Maybe Maggie should offer more. But how much more?In-class exercise.


1.6.4 The Inheritance Game

The players:➣ Elizabeth , an aged mother, wishes to give an heir loom to one of➣ her severa l daughters.The gam e:➣ E. wants to benefit the daughter who va lues it most .➣ But the daughters may be dishonest : each has an incent ive to exaggera te it s

wor th to her.


A se con d-price au ction .

➣ so E . devises the following scheme:— asks the daughters to tell her confident ia lly (i.e. a sea led bid) their

va lues, and— promises to give it to the one who repor t s the h ighest va lue— the h ighest bidder gets the heir loom, bu t on ly pays the second-h ighest

repor ted va lua t ion .Will E lizabeth’s scheme (a Vickrey1 auct ion , or second-price auct ion) makehonesty the best policy?

Yes.

1. The la te Bill Vickrey shared the Nobel pr ize in economics in 1996.


Wh y? Th in kin g th rou gh th e option s .Consider your reasoning as one of the daughters:➣ th ree opt ions: tru th fu lness, exaggeration , or understatem ent.➣ The amount you pay is independent of what you say it ’s wor th ,

so the on ly effect of your repor t is to determine whether or not you win theheir loom, and hence what you must pay.

➣ Exaggeration : the possibility tha t you make the h ighest repor t when youwould not otherwise have, had you been honest .i.e., tha t the second-h ighest repor t , the one you now exceed, is h igher thanyour t rue va lua t ion .But → tha t what you must pay (the second-h ighest repor t ) is more thanwhat you th ink the heir loom is wor th .∴ Exaggera t ion not in your in terest .

➣ Understating changes the ou tcome only when you would have won with anhonest repor t ;bu t now you repor t a va lue lower than tha t of one of your sisters, so you donot win the heir loom.∴ Not in your in terest either.


It w orks .

So the mother ’s scheme works, and the t ru th is obta ined—but a t a pr ice, toElizabeth , the Mum.E. receives a payment less than the successfu l daughter ’s va lua t ion ,so th is daughter ea rns a profit := her va lua t ion − the 2nd-h ighest va lua t ion .= the premium the mother forgoes to induce honesty


Marke t An alogu e ?Think: how can the neighbours who propose bu ilding a park overcome eachhousehold’s tempta t ion to free-ride on the others’ effor t s by cla iming not to careabout the park, when cont r ibu t ions should reflect the household’s va lua t ion ofthe park?

How can the users of a sa tellit e be induced to revea l their profits so tha t theopera t ing cost of the sa tellit e can be divided according to the profit each userearns? \ &

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Strategic Game Theory for Managers

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