G?m? Th??ry 101 D?finiti?n, Ex?l?in?d, Ex?m?l??

G?m? Th??ry 101 D?finiti?n, Ex?l?in?d, Ex?m?l?? Ev?r? ?hild understands wh?t g?m?? ?r?. Wh?n ??m??n? ?v?rr???t?, we sometimes say “it’? ju?t a g?m?.”Games ?r? ?ft?n not ??ri?u?. G?m?? theories ?n th? other h?nd are mu?h different. They ?r? u?u?ll? ??ri?u? business.Th? ?ur???? of game theory fr?m it? b?ginning? in 1928 w?? t? be ???li?d to serious situations in ???n?mi??, politics, bu?in???, ?nd ?th?r areas.Ev?n w?r? ??n b? analysed by g?m? theory. G?m? th??r? i? u?u?ll? ???n ?? a m?th?m?ti??l g?m? where ?v?r? m?v? i? calculated ??r?full? in other to achieve th? ?x???t?d r??ult.HERE ARE SOME COMPONENTS OF A GAMERulesM?th?m?ti??l g?m?? h?v? ?tri?t rul??. Th?? specify wh?t i? allowed ?nd wh?t i?n’t.Th?ugh m?n? r??l-w?rld g?m?? ?ll?w for discovering n?w m?v?? ?r w??? to act, games th?t ??n b? analysed mathematically h?v? a rigid ??t ?f ????ibl? m?v??, u?u?ll? ?ll known in ?dv?n??.Outcomes ?nd payoffsChildr?n (?nd gr?wn-u?? too) play games f?r h?ur? for fun. M?th?m?ti??l g?m?? may h?v? many possible ?ut??m??, ???h ?r?du?ing pay offs f?r th? ?l???r?.Th? payoffs may b? m?n?t?r?, ?r th?? m?? express ??ti?f??ti?n. Y?u w?nt t? win the g?m?.Un??rt?int? ?f th? OutcomeA m?th?m?ti??l game i? “thrilling” in th?t its ?ut??m? ??nn?t b? predicted in ?dv?n??.Sin?? its rul?? are fix?d, this im?li?? th?t a g?m? must ?ith?r ??nt?in ??m? random ?l?m?nt? or h?v? m?r? than ?n? ?l???r.D??i?i?n makingA g?m? with n? decisions might be boring, at l???t f?r th? mind. Running a 100 m?t?r race d??? n?t r??uir? m?th?m?ti??l ?kill?, only fast l?g?.H?w?v?r, most ???rt g?m?? ?l?? inv?lv? decisions, and can therefore ?t l???t ??rtl? b? ?n?l?z?d by g?m? theory.N? ?h??tingIn r??l-lif? g?m?? ?h??ting i? ????ibl?. Ch??ting m??n? n?t ?l??ing by th? rul??.If, when ??ur ?h??? ????n?nt i? distracted, ??u t?k? ??ur ?u??n ?nd ?ut it on a b?tt?r ??u?r?, ??u are ?h??ting, as in ??k?r, wh?n you exchange ?n 8 in your h?nd with ?n ??? in your ?l??v?.G?m? theory doesn’t even ??kn?wl?dg? th? ?xi?t?n?? ?f ?h??ting.BASICS OF GAME THEORY: GAME, PLAY, MOVEA play i? an instance of th? game. In ??rt?in ?itu?ti?n?, called ???iti?n?, a ?l???r has d? m?k? a decision, ??ll?d a m?v? ?r an ??ti?n. Thi? i? not th? same ?? ?tr?t?g?. A ?tr?t?g? i? a ?l?n th?t tells th? player wh?t m?v? to choose in every ????ibl? ???iti?n.R?ti?n?l behaviour i? usually ???um?d for all ?l???r?. Th?t is, ?l???r? ?r? ???um?d to h?v? ?r?f?r?n???, styles ?nd beliefs ?b?ut th? w?rld ?nd then th?? tr? t? ?l?? th?ir game ?? th?? b??t ??? fit.It i? ???um?d th?t th? opposite play wants t? win and f?r th?t t? h????n, he h?? t? b? very rational with hi? ?r h?r b?h?vi?ur.M?r??v?r, ?l???r? ?r? ?w?r? that other players ?r? tr?ing t? ??timiz? th?ir payoffs ?nd beat th?m and thi? inf?rm? th?ir d??i?i?n m?king.First let’s get a ??r????tiv? of wh?t game th??r? is all aboutW?, humans cannot survive with?ut interacting with ?th?r hum?n?, and ir?ni??ll?, it sometimes ???m? th?t w? h?v? ?urviv?d despite th??? int?r??ti?n? in th? ??n?? th?t th??? int?r??ti?n? h?v? included w?r?, fighting, killing? ?t?.Pr?du?ti?n and exchange require cooperation b?tw??n individu?l? at ??m? l?v?l but th? same int?r??ti?n? m?? also lead to di???tr?u? confrontations. Hum?n hi?t?r? i? ?? mu?h a hi?t?r? of fight? ?nd w?r? ?? it i? a hi?t?r? ?f ?u?????ful ?????r?ti?n ?nd fri?nd?hi??.Many hum?n int?r??ti?n? carry the ??t?nti?l? of ?????r?ti?n ?nd h?rm?n? ?? w?ll ?? conflict, di?tru?t ?nd sometimes outright di???t?r.Ex?m?l?? in?lud?: r?l?ti?n?hi?? ?m?ng ??u?l??, ?ibling?, countries, m?n?g?m?nt ?nd labor uni?n?, n?ighb?r?, ?m?l???r ?nd ?m?l?????, and ?? on.On? ??n ?rgu? th?t th? in?r???ingl? ??m?l?x technologies, in?tituti?n?, ?nd ?ultur?l n?rm? that have ?xi?t?d in human ???i?ti?? have been there in ?rd?r t? facilitate ?nd r?gul?t? th??? int?r??ti?n?.F?r ?x?m?l?, internet t??hn?l?g? gr??tl? facilitates buyer-seller tr?n???ti?n?, but ?l?? ??m?li??t?? th?m furth?r by increasing ????rtuniti?? for ?h??ting ?nd fr?ud.Workers and managers h?v? usually opposing interests wh?n it ??m?? to w ?g?? ?nd working ??nditi?n?, ?nd labour uni?n? ?? w?ll ?? l?b?ur l?w? ?r?vid? ?h?nn?l? ?nd rul?? through which ?n? potential ??nfli?t between them can be ?ddr????d.T?n?’? ???id?ntWh?n ?n? of us (Steve) w?? a ??ll?g? ?tud?nt, hi? fri?nd T?n? ??u??d a minor traffic ???id?nt. W?’ll l?t him t?ll th? ?t?r?:The car ?f th? vi?tim, wh?m I’ll ??ll Vic, w?? slightly scraped. T?n? didn’t w?nt t? t?ll hi? in?ur?n?? company. The n?xt m?rning, T?n? ?nd I w?nt with Vi? t? vi?it ??m? b?d? shops. Th? u??h?t was th?t th? r???ir w?uld ???t $80.Tony ?nd I had lunch with a bottle of wine, ?nd thought ?v?r th? ?itu?ti?n. Vic’s ??r was far fr?m new ?nd h?d ???umul?t?d m?n? ??r????. R???iring the f?w th?t T?n? h?d caused w?uld improve th? ??r’? ?????r?n?? ?nl? a littl?.W? figur?d that if Tony ??nt Vi? a ?h??k f?r $80, Vi? w?uld ?r?b?bl? ju?t ???k?t it. Perhaps, we thought, Tony ?h?uld ??k t? see a receipt ?h?wing th?t th? r???ir? h?d ??tu?ll? b??n performed b?f?r? he ??nt Vi? the $80.A g?m? th? ?ri?t w?uld represent thi? ?itu?ti?n b? a game tr??. For definiteness, w?’ll ???um? that th? v?lu? to Vic ?f r???iring th? d?m?g? is $20.Explanation ?f th? game tree:T?n? goes first. H? h?? a ?h?i?? of two ??ti?n?: send Vic a ?h??k f?r $80, or d?m?nd a r???i?t ?r?ving that th? work h?? b??n d?n?.If T?n? sends a check, th? g?m? ?nd?. Tony i? ?ut $80; Vi? will no doubt k??? the m?n??, so he h?? g?in?d $80. W? r??r???nt th??? ????ff? b? th? ?rd?r?d ??ir (-80, 80); the fir?t numb?r i? Tony’s ????ff, the ????nd i? Vi?’?.If T?n? d?m?nd? a r???i?t, Vi? has a ?h?i?? ?f two ??ti?n?: r???ir the ??r and send T?n? th? r???i?t, ?r just forget th? wh?l? thing.If Vi? r???ir? th? car ?nd ??nd? T?n? th? r???i?t, th? g?m? ?nd?. T?n? ??nd? Vi? a ?h??k f?r $80, so he i? ?ut $80; Vi? u??? th? check t? ??? for the r???ir, ?? his g?in is $20, the v?lu? ?f the r???ir.If Vi? decides to forget th? wh?l? thing, h? ?nd Tony each ?nd u? with a g?in ?f 0Assuming that we h?v? ??rr??tl? sized u? th? ?itu?ti? n, w? ??? th?t if Tony demands a receipt, Vi? will have to d??id? between tw? ??ti?n?, one th?t giv?? him a ????ff ?f $20 ?nd one that giv?? him a payoff ?f 0. Vic will ?r??um?bl? ?h???? t? repair th? ??r, which giv?? him a better payoff. T?n? will th?n b? ?ut $80.Our ??n?lu?i?n was th?t Tony w?? out $80 wh?t?v?r he did. We did n?t like thi? game.When th? bottle w?? n??rl? finished, w? th?ught ?f a third ??ur?? ?f ??ti?n th?t T?n? could t?k?: ??nd Vi? a check for $40, ?nd t?ll Vi? th?t h? would ??nd th? r??t when Vi? provided a r???i?t ?h?wing th?t th? w?rk h?d ??tu?ll? b??n d?n?. The game tr?? n?w l??k?d lik? this:Most ?f th? g?m? tr?? l??k? lik? th? fir?t ?n?. H?w?v?r:If Tony t?k?? hi? new ??ti?n, ??nding Vic a check f?r $40 ?nd asking f?r a receipt, Vi? will have a ?h?i?? ?f two ??ti?n?: repair the ??r, ?r don’t.If Vic r???ir? the ??r, th? game ?nd?. Vi? will ??nd Tony a r???i?t, ?nd T?n? will send Vi? a ????nd check f?r $40. Tony will b? ?ut $80. Vi? will use b?th ?h??k? to pa y for th? r???ir, ?? he will h?v? a n?t g?in ?f $20, the v?lu? ?f the r???ir.If Vi? d??? n?t repair the ??r, ?nd ju?t ???k?t? th? the $40, th? g?m? ends. T?n? i? ?ut $40, ?nd Vi? h?? g?in?d $40. Ag?in ???uming th?t w? have ??rr??tl? ?iz?d u? th? ?itu?ti?n, w? ??? th?t if T?n? sends Vi? a check f?r $40 and asks f?r a r???i?t, Vic’s best ??ur?? ?f action i? t? keep th? m?n?? ?nd n?t m?k? th? repair. Thu? T?n? is ?ut only $40.T?n? ??nt Vic a ?h??k for $40, t?ld him h?’d ??nd th? r??t when he saw a receipt, ?nd n?v?r h??rd from Vi? ?g?in.E??n?mi??, sociology, ????h?l?g?, ?nd ??liti??l ??i?n?? ?r? ?ll d?v?t?d to studying hum?n b?h?vi?ur in different realms of social life.H?w?v?r, in m?n? in?t?n??? th?? tr??t individu?l? in i??l?ti?n, f?r convenience if n?t f?r ?n?thing ?l??. In ?th?r w?rd?, th?? ???um? th?t to understand ?n? individual’s b?h?vi?r.It i? safe to ???um? that his or her b?h?vi?r d??? not h?v? a significant ?ff??t ?n ?th?r individu?l?. In some cases, and d???nding u??n th? ?u??ti?n ?n? i? ??king, this assumption m?? b? w?rr?nt?d.For ?x?m?l?, wh?t a small f?rm?r in a l???l market, l?t’? ??? in M?nt?n?, ?h?rg?? for wheat i? n?t likely t? have ?n effect on the w?rld wh??t prices.Simil?rl?, th? probability th?t m? vote will ?h?ng? th? ?ut??m? ?f th? U.S. presidential ?l??ti?n? is n?gligibl? small.So, if we ?r? interested in the w?rld wh??t ?ri?? or th? r??ult ?f th? ?r??id?nti?l ?l??ti?n?, w? m?? ??f?l? ???um? th?t ?n? individu?l ??t? ?r b?h?vi?r will n?t ?ff??t th? outcome.In many cases, however, thi? ???um?ti?n m?? l??d to wrong ??n?lu?i?n?. F?r ?x?m?l?, h?w mu?h ?ur f?rm?r in M?nt?n? ?h?rg??, ??m??r?d t? th? ?th?r f?rm?r? in Montana, ??rt?inl? ?ff??t? h?w mu?h h? ?r ?h? and other f?rm?r? make. If ?ur f?rm?r ??t? a ?ri?? that i? l?w?r th?n th? prices set by th? ?th?r f?rm?r? in th? local m?rk?t, ?h? w?uld ??ll m?r? than th? others, and vi?? versa.Th?r?f?r?, if we ???um? th?t they d?t?rmin? th?ir prices with?ut t?king thi? ?ff??t int? ????unt, w? a re not lik?l? to get ?n?wh?r? n??r und?r?t?nding their b?h?vi?r.Simil?rl?, the v?t? of ?n? individual m?? r?di??ll? ?h?ng? the ?ut??m? ?f voting in ?m?ll ??mmitt??? and ???uming th?t they v?t? in ign?r?n?? ?f th?t f??t i? likely t? be mi?l??ding.Aft?r ?ll, ?v?n ?du??t?d ??n?t?r? ??m?tim?? turn their votes b???d on ?n? ??r??n’? idea.S? what i? g?m? th??r??Game th??r? i? ?x??tl? th??? interactions within a gr?u? of individuals (?r g?v?rnm?nt?, firm?, ?t?.) wh?r? th? actions ?f ???h individual have ?n ?ff??t on th? ?ut??m? th?t i? of interest t? everybody.Yet, thi? is n?t ?n?ugh f?r a ?itu?ti?n t? be a ?r???r ?ubj??t ?f game th??r?: th? w?? th?t individu?l? act has to be ?tr?t?gi?, i.?., they ?h?uld b? ?w?r? ?f the f??t th?t th?ir ??ti?n? ?ff??t others.Th? fact th?t m? ??ti?n? h?v? ?n ?ff??t on th? ?ut??m? does n?t n??????ril? translate t? strategic b?h?vi?ur if I ?m n?t aware ?f th?t f??t. Therefore, w? say th?t game th??r? ?tudi?? strategic int?r??ti?n within a group of individuals .B? strategic int?r??ti?n w? m??n th?t individu?l? kn?w th?t th?ir ??ti?n? will have an ?ff??t on th? ?ut??m? and th?n ??t? accordingly. It b??i??ll? m??n? acting in such a w?? t? m?ni?ul?t? ?n ?ut??m? in ??ur favour. Look ?t th? ?x?m?l? ?b?v?â€"“J?hn’? ???id?nt”Having determined the t???? ?f situations th?t g?m? th??r? d??l? with, w? h?v? to now di??u?? h?w it ?n?l???? these ?itu?ti?n?.Like ?n? ?th?r th??r?, the objective ?f g?m? th??r? i? t? ?rg?niz? ?ur knowledge ?nd in?r???? ?ur understanding of th? outside w?rld.A scientific th??r? tri?? t? abstract th? m??t ????nti?l aspects ?f a giv?n ?itu?ti?n, analyze them using ??rt?in ???um?ti?n? ?nd ?r???dur??, and ?t th? end derive ??m? g?n?r?l ?rin?i?l?? and ?r?di?ti?n? th?t can b? ???li?d to individual in?t?n???.F?r it to h?v? ?n? ?r?di?tiv? ??w?r, game theory has t? assume some rules according t? whi?h individu?l? m?? ??t. If w? d? n?t d???rib? how individu?l? behave, what th?ir ?bj??tiv?? ?r? ?nd h?w they tr? to ??hi?v? th??? ?bj??tiv?? w? ??nn?t derive ?n? ?r?di?ti?n? at ?ll in a giv?n ?itu?ti?n.F?r example, ?n? w?uld get ??m?l?t?l? diff?r?nt ?r?di?ti?n? r?g?rding th? ?ri?? of wh??t in a local m?rk?t if one ???um?? th?t farmers simply flip a ??in and ?h???? b?tw??n $1 ?nd $2 a pound ??m??r?d t? if ?n? assumes they tr? t? m?k? as mu?h m?n?? ?? ????ibl?.Therefore, t? bring ??m? discipline t? th? ?n?l??i? ?n? has t? intr?du?? ??m? ?tru?tur? in terms of th? rules ?f the game. Th? most important, and m??b? ?n? of th? m??t controversial, assumption ?f game theory whi?h brings ?b?ut this di??i?lin? i? th?t individuals ?r? rational.Rationality im?li?? that individu?l? know the strategies ?v?il?bl? t? ???h ?f th?m, h?v? ??m?l?t? and ??n?i?t?nt ?r?f?r?n??? over ????ibl? outcomes, ?nd th?? ?r? ?w?r? ?f th??? ?r?f?r?n???.Furth?rm?r?, they ??n determine the b??t strategy f?r themselves ?nd flawlessly im?l?m?nt it.If t?k?n literally, th? ???um?ti?n of rationality i? ??rt?inl? ?n unr??li?ti? ?n?, ?nd if applied to ??r ti?ul?r ????? it m?? ?r?du?? r??ult? that are ?t ?dd? with r??lit?. We ?h?uld fir?t note th?t game th??ri?t? ?r? ?w?r? of th? limit?ti?n? im????d b? this ???um?ti?n ?nd th?r? is ?n active r????r?h area ?tud?ing th? implications ?f l??? d?m?nding f?rm? ?f rationality, ??ll?d bounded r?ti?n?lit?.It i? n?t enough th?t I know th?t m? ??ti?n?, as w?ll ?? ??ur?, affect the outcome, but I mu?t ?l?? kn?w th?t you kn?w this fact. T?k? th? example ?f tw? wheat f?rm?r? b?th farmer A and B kn?w th?t their respective ?h?i??? of ?ri??? will ?ff??t their profits f?r the d??.But suppose, A d??? not kn?w that B kn?w? thi?.Now, from the ??r????tiv? of f?rm?r A, f?rm?r B i? ??m?l?t?l? ign?r?nt of what is g?ing ?n in th? market ?nd h?n?? f?rm?r B might ??t any ?ri??.Thi? makes f?rm?r A’? d??i?i?n quite difficult in itself because he h?? n? r?ti?n?l ground t? stand on to compete with f?rm?r B b???u?? f?rm?r B ??uld set ?n? price (he could set a ?ri?? lower than the ???t ?ri?? whi?h will m?k? it imposs ible f?r f?rm?r A t? compete).T? model th? ?itu?ti?n more r??li?ti??ll?, w? then have t? assume th?t th?? b?th kn?w th?t th?? kn?w th?t their prices will affect their ?r?fit?.On? ??tu?ll? h?? t? ??ntinu? in this f??hi?n ?nd assume th?t the rul?? ?f the game, in?luding h?w ??ti?n? ?ff??t th? ??rti?i??nt? ?nd individuals’ r?ti?n?lit?, ?r? ??mm?n kn?wl?dg?.A fact “X” i? common kn?wl?dg? if everybody knows it, if ?v?r?b?d? kn?w? that ?v?r?b?d? kn?w? it, if everybody kn?w? th?t ?v?r?b?d? kn?w? th?t ?v?r?b?d? kn?w? it, ?nd so on.Thi? has ??m? philosophical im?li??ti?n? ?nd is ?ubj??t t? a l?t ?f controversy, but f?r the m??t part w? will ?v?id th??? di??u??i?n? and take it as giv?n.In sum, we m?? define g?m? theory ?? f?ll?w?: Game th??r? i? a ???t?m?ti? study ?f ?tr?t?gi? interactions ?m?ng r?ti?n?l individu?l?.It? limit?ti?n? ??id?, game theory h?? b??n fruitfull? ???li?d to m?n? situations in th? r??lm ?f ???n?mi??, political ??i?n??, bi?l?g?, l?w, ?t?.In the rest ?f thi? ?rti?l? , w? will illu?tr?t? th? m?in ideas ?nd ??n???t? of g?m? th??r? ?nd ??m? ?f it? ???li??ti?n? using simple ?x?m?l??.An ?x?m?l?Su????? th?t B??ing ?nd Airbu? are asked t? ?ubmit ???l?d bid? on th? ?ri?? ?f t?n jet ?irlin?r? t? a f?r?ign n?ti?n?l ?irlin?. B?th ??m??ni?? d?ubt that th?? will ??m??t? in ?imil?r w??? in th? futur?. Both companies ??n ??l??t ?ith?r a high price ?r a l?w price.If ?n? ??m??n? bid? high and th? ?th?r bids l?w, the ?rd?r goes t? th? low bidder; if b?th ??m??ni?? submit th? same bid, they ??lit the order. E??h firm h?? the capacity t? build ?ll t?n ?ir?l?n??.B?th companies privately ?h???? their bids ?t th? ??m? tim?. Th? r??ulting ????ff? (profits ?x- pressed in milli?n? ?f dollars) d???nd ?n both firms’ choices.L?w ?ri??â€"100 milli?n each High ?ri??â€"150 million ???hCONCEPTS IN GAME THEORYDominant Str?t?gi?? A d?min?nt strategy ?xi?t? wh?n it i? optimal for a firm t? ?h???? th?t ?tr?t?g? n? m?tt?r what its rival d???. In the ?x?m?l? above, b?th firm? have a d?min?nt ?tr?t?g?â€"?h???? the l?w ?ri??.To illu?tr?t?, consider B??ing’? position. If Airbu? chooses a high ?ri??, B??ing ???tur?? th? entire ?rd?r b? submitting a l?w ?ri??. The resulting payoff of $1 billi?n is high?r th?n the payoff ?f $750 milli?n if both firm? ?ri?? high ?nd ??lit th? order.If Airbus ?h????? a l?w ?ri??, B??ing i? clearly b?tt?r ?ff t? ?ri?? l?w ?nd ??lit the order instead of l??ing ?ut entirely. It? alternative is t? ?ri?? high and sell n? ?l?n??.Examining the r?w?, the ??m? l?gi? h?ld? for Airbus. Giv?n th??? strong incentives, th? likely ?ut??m? is f?r b?th firms to ?ubmit a l?w ?ri??. N?t? th?t the firm? w?uld b? better ?ff if th?? j?intl? were t? ?ubmit high ?ri???. But thi? ?ut??m? i? unlikely with?ut r????t?d int?r??ti?n?. (Thi? ?r?bl?m h?? the same ?tru?tur? ?? th? well-known prisoners’ Dilemma)Nash Equilibrium M?n? ?f th? w?rld’? markets ?r? lik? the ??mm?r?i?l ?ir?r?ft industry in that th?r? ?r? a f?w l?rg? firms wh? ?r? th? m?j?r players. I n thi? type of market, it i? g?n?r?ll? important f?r m?n?g?r? t? consider riv?l?’ r????n??? wh?n making m?j?r decisions.Firms d? n?t always h?v? d?min?nt ?tr?t?gi??. For in?t?n??, suppose in ?ur ?x?m?l?, the U.S. g?v?rnm?nt ?l???? ?r???ur? ?n th? foreign ??untr? to have its n?ti?n?l ?irlin? purchase planes fr?mB??ing (governments ??tu?ll? have d?n? thi? for their d?m??ti? producers). Th? ?irlin? still ??lit? th? ?rd?r when the bid? are the ??m? ?nd awards B??ing th? entire ?rd?r if B??ing is th? low bidd?r. But du? t? this ??liti??l ?r???ur?, if B??ing bids high and l???? th? bid, the ?irlin? will bu? f?ur ?l?n?? fr?m B??ing ?t th? high ?ri?? on a ?id? deal ?ft?r purchasing the t?n ?l?n?? from Airbu? ?t the low ?ri??.Ch???ing a low price i? still a d?min?nt ?tr?t?g? for Airbus. Boeing, h?w?v?r, does not have a d?min?nt ?tr?t?g?. If Airbu? ?ri??? high, it i? ??tim?l f?r Boeing to ?ri?? l?w t? capture th? entire ?rd?r, wh?r??? if Airbu? ?ri??? l?w, it is b?tt?r for Boeing to price h igh ?nd make the side deal.When d?min?nt strategies d? not exist, th? ??n???t ?f a Nash equilibrium is useful in ?r?di?ting th? ?ut??m?. A Nash equilibrium i? a set ?f ?tr?t?gi?? (?r ??ti?n?) in whi?h each firm i? doing th? b??t it ??n, giv?n the ??ti?n? of it? rival.Th? ??mbin?ti?n ?f a l?w Airbu? ?ri?? ?nd a high Boeing price i? a Nash ??uilibrium. Neither firm w?uld w?nt t? ?h?ng? it? ?ri?? given the price ?ubmitt?d by th? ?th?r firmA ??rti?ul?r problem might have multiple Nash ??uilibri?Nash equilibria ?r? not n??????ril? th? ?ut??m?? th?t maximize the j?int payoff ?f the ?l???r?.F?r in?t?n??, fr?m th? ?x?m?l? ?b?v?, th? ?ut??m? where both firm? ?ubmit l?w prices i? a N??h ??uilibrium.Y?t b?th firms w?uld b? b?tt?r ?ff if th?? j?intl? ?ubmitt?d high prices.M?n?g?m?nt ImplicationsTh? ??w?r of a Nash equilibrium t? ?r?di?t the ?ut??m? in strategic ?itu?ti?n? ?t?m? fr?m the f??t th?t N??h ??uilibri? ?r? ??lf-?nf?r?ing: They are stable ?ut??m??. For instance, if Boeing can forecast Airbu?’? ?h?i?? (??rh??? b???u?? it und?r?t?nd? that Airbu? has a dominant ?tr?t?g?), it i? ??tim?l for Boeing t? choose it? ??uilibrium ??ti?n, a high ?ri??.And Airbus h?? n? in??ntiv? t? ?v?id its ??uilibrium choice, a l?w ?ri??. Thu?, ?v?n if b?th firms can forecast the outcome, neither firm h?? ?n in??ntiv? to ?h???? ?n? other ??ti?n.Alth?ugh th? id?? ?f a N??h ??uilibrium i? ?uit? useful, it is n?t ?? ??w?rful in ?r?di?ting the ?ut??m?? ?f strategic int?r??ti?n? ?? th? ??n???t of a dominant ?tr?t?g?. Wh?n dominant ?tr?t?gi?? exist, th?r? ?r? ?tr?ng ?riv?t? in??ntiv?? t? choose them r?g?rdl??? of wh?t th? ?th?r player d???.Thu?, it i? ?uit? predictable th?t riv?l? will ?h???? d?min?nt ?tr?t?gi??. With a Nash ??uilibrium, your best choice g?n?r?ll? i? ??nting?nt ?n wh?t you ?x???t ??ur rival t? do.In m?n? ????? it i? r????n?bl? to expect that a Nash ??uilibrium will occur. Thi? is more likely to b? true wh?n th? rivals have m?r? ?x??ri?n?? in similar ?tr?t?gi? ?r?bl?m?, h?v? b? tt?r inf?rm?ti?n ?b?ut ???h ?th?r, or wh?n the N??h equilibrium is what i? ??ll?d a n?tur?l f???l ??int.F?r example, ??n?id?r the ?r?bl?m again.If Boeing has r????n?bl? inf?rm?ti?n ?b?ut potential payoffs ?nd Airbu?’? l??k ?f ??liti??l ??w?r within th? specific country (it understands that th?r? is a close w?rking r?l?ti?n?hi? between th? l???l ?nd U.S. governments), it will r??liz? th?t Airbu? has a d?min?nt strategy t? ?ubmit a l?w ?ri??.B??ing ??rr????ndingl? will ?h???? a high priceâ€"the N??h equilibrium.Wh?n riv?l? kn?w littl? about th? setting ?r ???h ?th?r ?nd wh?n th?r? i? n?t a n?tur?l focal point, ?ut??m?? other than N??h equilibria (n?n-??uilibrium ?ut??m??) ?r? m?r? lik?l? t? ???ur.Str?t?g?It i? th? ?r?-d?t?rmin?d rul? b? whi?h ???h ?l???r decides hi? ??ur?? ?f action fr?m hi? li?t ?v?il?bl? t? him. How one course ?f action i? selected out of v?ri?u? ??ur??? ?v?il?bl? t? him i? known ?? ?tr?t?g? ?f the g?m?.T???? ?f Str?t?g?G?n?r?ll? tw? types ?f strategy ?r? ?m?l???d Pur? Str?t?g?: It i? th? predetermined ??ur?? ?f action to b? ?m?l???d by th? ?l???r. The ?l???r? kn?w it in ?dv?n??. It i? usually r??r???nt?d b? a numb?r with which the course ?f ??ti?n is ?????i?t?d.Mixed Str?t?g?: In mix?d ?tr?t?g? the ?l???r d??id?? hi? course ?f ??ti?n in accordance with some fix?d probability distribution. Pr?b?bilit? ?r? ?????i?t?d with ???h course ?f ??ti?n ?nd th? ??l??ti?n i? done ?? ??r th??? ?r?b?biliti??. In mix?d ?tr?t?g? th? ????n?nt ??nn?t be sure ?f th? ??ur?? ?f ??ti?n to be t?k?n ?n ?n? ??rti?ul?r ?????i?n.Decision ?f a G?m?In G?m? theory, best ?tr?t?g? for ???h ?l???r i? d?t?rmin?d ?n th? b??i? of ??m? rul?. Sin?? both th? ?l???r? ?r? ?x???t?d to b? rational in th?ir ???r???h this is known ?? th? ?rit?ri? ?f ??tim?lit?.Each player lists the ????ibl? ?ut??m?? fr?m hi? ??ti?n ?nd ??l??t? the b??t ??ti?n t? ??hi?v? hi? ?bj??tiv??.This criteria of ??tim?lit? is ?x?r????d ?? M?ximin f?r the m?ximi?ing ?l???r ?nd Minim?x f?r the minimi?ing player.Th? Prisoners Dil?mm? Th?r? ?r? m?n? situation in lif? wh?r? ??u ?h???? to do ??m?thing th?t is b??t f?r you, r?th?r than best f?r th? group, b???u?? ??u h?v? n? way ?f estimating h?w ??mmitt?d the ?th?r ????l? ?r? t?w?rd? th? gr?u? int?r??t?.Y?u kn?w that the ?ut??m? ?f being ??lfi?h can ??t?nti?ll? be b?d for ?v?r??n?, but ??u ?r?f?r th?t ?v?r??n? gets screwed r?th?r th?n b?ing the ?v?rl? ??n?id?r?t? gu? ?v?r??n? ??r?w?.F?r ?x?m?l?, if I h?v? no id?? if ??u are g?ing t? pay taxes, why w?uld i bother t? ??? t?x?? f?r th? new public swimming pool in whi?h you will di? your ?h????k?t? int??I would prefer th?t there b? n? swimming ???l ?t all th?n t? b? th? dumm? wh? pays f?r ?th?r ????l?? ?tuff.Suppose ?n th? ?th?r hand, th?r? ?r? ?l?nt? ?f l?w ?biding ?itiz?n? out th?r? ???ing t?x??, then why not avoid ???ing taxes so I dip my own ??? in th? swimming pool with?ut ???ing for it!   In ?th?r w?rd?, ??ting ?nti-???i?l m?k? ??n?? f?r me ??r??n?ll? r?g?rdl??? of h?w ??n?id?r?t? ?th?r people ? r?.The prisoners dil?mm? i? a v?r? popular example of a two-person game of strategic int?r??ti?n, ?nd its a common intr?du?t?r? ?x?m?l? in many g?m? th??r? textbooks. Th? l?gi? ?f th? g?m? i? ?im?l?:Th? tw? players in th? game have b??n ???u??d ?f a ?rim? and h?v? b??n placed in ????r?t? r??m? so that th?? cannot communicate with ?n? ?n?th?r. (In other words, th?? cant ??llud? ?r commit t? ?????r?ting.)Each player i? asked ind???nd?ntl? whether h? i? g?ing to ??nf??? t? th? ?rim? ?r r?m?in ?il?nt.B???u?? each of the tw? ?l???r? h?? tw? possible ??ti?n? (?tr?t?gi??), there ?r? f?ur possible ?ut??m?? t? th? g?m?.If both ?l???r? confess, they each get sent to j?il, but f?r f?w?r ???r? th?n if ?n? of th? ?l???r? g?t r?tt?d ?ut b? th? ?th?r.If one ?l???r confesses ?nd th? ?th?r remains ?il?nt, th? silent player g?t? punished severely whil? th? player who ??nf????d g?t? t? go fr??.If b?th players r?m?in ?il?nt, they ???h get a punishment th?t is l??? ??v?r? th?n if they b?th confess.In th ? g?m? itself, ?uni?hm?nt? (?nd r?w?rd?, where relevant) are r??r???nt?d b? utility numb?r?.Positive numb?r? represent g??d ?ut??m??, n?g?tiv? numbers r??r???nt b?d ?ut??m??, ?nd ?n? outcome i? b?tt?r th?n ?n?th?r if th? numb?r associated with it i? greater.Analysing the Pl???r? O?ti?n?On?? a game i? d?fin?d, the n?xt ?t?? in analysing th? game i? to ?????? th? ?l???r? ?tr?t?gi?? ?nd try t? und?r?t?nd h?w th? ?l???r? ?r? likely to b?h?v?. E??n?mi?t? m?k? a f?w assumptions when they ?n?l??? games: first, they assume th?t b?th ?l???r? are ?w?r? ?f the ????ff? b?th f?r th?m??lv?? and f?r th? ?th?r ?l???r, ?nd, ????nd, th?? ???um? th?t both ?l???r? ?r? l??king to rationally m?ximiz? their ?wn ????ff fr?m the g?m?.One ???? initi?l ???r???h i? t? l??k ?t their d?min?nt strategies- ?tr?t?gi?? that are best r?g?rdl??? ?f what ?tr?t?g? th? ?th?r ?l???r chooses. In the ?x?m?l? above, choosing t? ??nf??? i? a d?min?nt ?tr?t?g? f?r both ?l???r?:Confess i? b?tt?r for ?l???r 1 if ?l???r 2 ?h????? t? confess ?in??C?nf??? i? b?tt?r for player 1 if ?l???r 2 ?h????? to r?m?in ?il?ntC?nf??? is better f?r ?l???r 2 if ?l???r 1 ?h????? to ??nf???Confess is b?tt?r f?r ?l???r 2 if ?l???r 1 ?h????? to r?m?in ?il?ntW?rr?n Buff?tt ?r?vid?? ??m? illumin?ti?n ?? t? how the Prisoners Dilemma plays out in business in th? 1985 Berkshire Hathaway Annu?l r???rtTh? domestic t?xtil? indu?tr? operates in a commodity bu?in???, ??m??ting in a w?rld market in whi?h substantial ?x???? ?????it? ?xi?t?.Much ?f the trouble w? experienced w?? ?ttribut?bl?, b?th dir??tl? ?nd indir??tl?, t? ??m??titi?n fr?m f?r?ign ??untri?? wh??? w?rk?r? ?r? paid a small fr??ti?n of the U.S. minimum wage.But th?t in n? way m??n? that ?ur l?b?r f?r?? deserves any bl?m? f?r ?ur ?l??ing. In fact, in ??m??ri??n with employees ?f American indu?tr? generally, ?ur w?rk?r? w?r? ???rl? ??id, as h?? been th? ???? throughout th? t?xtil? bu?in???. In ??ntr??t n?g?ti?ti?n?, union l??d?r? and members w?r? sensitive t? ?ur di??dv?nt?g?? u? ???t ???iti?n and did n?t ?u?h f?r unrealistic w?g? in?r????? ?r un?r?du?tiv? work ?r??ti???.T? the contrary, they tri?d just ?? h?rd ?? w? did t? keep us competitive. Even during our li?uid?ti?n ??ri?d they ??rf?rm?d superbly. (Ir?ni??ll?, w? w?uld h?v? b??n b?tt?r off fin?n?i?ll? if ?ur uni?n h?d b?h?v?d unr????n?bl? some ???r? ?g?; we th?n w?uld h?v? recognized th? im????ibl? future th?t we faced, ?r?m?tl? closed down, ?nd ?v?id?d ?ignifi??nt futur? l?????.)Ov?r the ???r?, we h?d th? ??ti?n of m?king large capital expenditures in the t?xtil? operation th?t would h?v? allowed us t? ??m?wh?t reduce variable ???t?. E??h proposal to do ?? looked like an imm?di?t? winn?r.Measured b? ?t?nd?rd return-on-investment t??t?, in f??t, th??? ?r?????l? usually ?r?mi??d gr??t?r ???n?mi? benefits than w?uld have r??ult?d fr?m ??m??r?bl? expenditures in ?ur highly-profitable candy ?nd n?w?????r businesses.But th? promised b?n?fit? fr?m these t?xtil? investments were illusory. M?n? ?f ?ur compe titors, both d?m??ti? and foreign, were stepping u? t? th? same kind ?f expenditures ?nd, once enough companies did so, their reduced ???t? b???m? the b???lin? f?r r?du??d ?ri??? indu?tr?-wid?.Vi?w?d individually, each ??m??n?? capital investment d??i?i?n ?????r?d ???t-?ff??tiv? ?nd rational; vi?w?d collectively, the d??i?i?n? n?utr?liz?d each ?th?r ?nd w?r? irrational (ju?t ?? h????n? when each ??r??n watching a ??r?d? decides h? can ??? a littl? better if h? ?t?nd? ?n ti?t???). After ???h r?und of inv??tm?nt, ?ll th? ?l???r? had m?r? m?n?? in th? game ?nd returns r?m?in?d ?n?mi?.Thu?, w? f???d a mi??r?bl? ?h?i??: hug? capital inv??tm?nt would h?v? helped to k??? ?ur t?xtil? bu?in??? alive, but would h?v? l?ft u? with terrible returns on ?v?r-gr?wing amounts ?f ???it?l. Aft?r the investment, m?r??v?r, th? f?r?ign ??m??titi?n would ?till h?v? r?t?in?d a m?j?r, continuing ?dv?nt?g? in labor costs.A refusal to inv??t, h?w?v?r, would m?k? us in?r???ingl? n?n-??m??titiv?, ?v?n m???ur?d ?g?in?t d?m??ti? textile manufacturers. I ?lw??? thought m???lf in th? ???iti?n d???rib?d by W??d? All?n in ?n? of hi? m?vi??: “M?r? th?n any other tim? in hi?t?r?, mankind faces a crossroads. One ??th l??d? t? d????ir and utt?r h???l???n???, th? other t? t?t?l extinction. Let us ?r?? we h?v? th? wisdom to choose ??rr??tl?.”For an understanding of h?w th? t?-inv??t-?r-n?t-t?-inv??t dil?mm? ?l??? ?ut in a ??mm?dit? business, it i? instructive to l??k at Burlingt?n Industries, b? far the l?rg??t U.S. t?xtil? ??m??n? both 21 ???r? ago ?nd n?w. In 1964 Burlington h?d ??l?? ?f $1.2 billion against ?ur $50 milli?n.It had ?tr?ngth? in b?th di?tributi?n ?nd ?r?du?ti?n that we ??uld n?v?r h??? t? m?t?h ?nd ?l??, ?f ??ur??, had ?n earnings r???rd far ?u??ri?r t? ?ur?. It? stock sold ?t 60 ?t th? ?nd of 1964; ours w?? 13.Burlingt?n m?d? a decision t? ?ti?k t? th? t?xtil? business, and in 1985 had sales of about $2.8 billion. During th? 1964-85 ??ri?d, th? ??m??n? m?d? capital ?x??nditur?? of about $3 billion, f?r m?r? than any ?th?r U.S. t?xtil? company and m?r? th?n $200-per-share on th?t $60 ?t??k.A very l?rg? part ?f th? ?x??nditur??, I ?m ?ur?, w?? d?v?t?d to cost im?r?v?m?nt ?nd ?x??n?i?n. Given Burlingtons b??i? ??mmitm?nt t? stay in t?xtil??, I w?uld ?l?? surmise th?t th? companys ???it?l decisions were quite r?ti?n?l.N?v?rth?l???, Burlington has l??t ??l?? volume in r??l d?ll?r? ?nd h?? far l?w?r returns ?n ??l?? and ??uit? now th?n 20 years ago. S?lit 2-f?r-1 in 1965, th? ?t??k n?w ??ll? at 34 â€" on ?n ?dju?t?d b??i?, ju?t a littl? ?v?r it? $60 price in 1964. M??nwhil?, th? CPI h?? m?r? th?n tri?l?d.Th?r?f?r?, each share ??mm?nd? about ?n?-third the ?ur?h??ing ??w?r it did ?t th? end ?f 1964. Regular divid?nd? h?v? b??n paid but th??, t??, h?v? ?hrunk ?ignifi??ntl? in ?ur?h??ing ??w?r.This d?v??t?ting ?ut??m? for th? ?h?r?h?ld?r? indicates what can happen wh?n much brain ??w?r and ?n?rg? are ???li?d t? a f?ult? ?r?mi??. The ?itu?ti?n is suggestive ?f S?mu?l J?hn??n? h?r??: “A horse that ??n count t? ten is a r?m?rk?bl? horse â€" n?t a remarkable m?th?m?ti?i?n.” Lik?wi??, a t?xtil? ??m??n? that allocates ???it?l brilli?ntl? within it? indu?tr? is a r?m?rk?bl? t?xtil? company â€" but n?t a r?m?rk?bl? bu?in???.My ??n?lu?i?n from m? ?wn ?x??ri?n??? ?nd fr?m mu?h ?b??rv?ti?n ?f ?th?r bu?in????? i? th?t a good managerial record (m???ur?d b? economic r?turn?) i? far m?r? a function ?f wh?t business boat ??u g?t int? th?n it i? ?f h?w ?ff??tiv?l? ??u r?w (though int?llig?n?? ?nd ?ff?rt h?l? considerably, ?f ??ur??, in ?n? bu?in???, g??d ?r bad).S?m? ???r? ago I wrote: “When a m?n?g?m?nt with a r??ut?ti?n for brilli?n?? t??kl?? a bu?in??? with a r??ut?ti?n for ???r fund?m?nt?l ???n?mi??, it i? th? reputation ?f th? bu?in??? that r?m?in? int??t.” N?thing h?? since ?h?ng?d m? ??int ?f view ?n that matter. Sh?uld ??u find yourself in a chronically-leaking b??t, ?n?rg? d?v?t?d to changing v????l? i? likely to b? m?r? ?r?du?tiv? th?n ?n?rg? d?v?t?d t? ??t?hing l??k?.GAME THEORY STRATEGIESThe ?ri??n?r? dilemma l??? th? f?und?ti?n f?r advanced game th??r? ?tr?t?gi??, ?f whi?h th? ???ul?r ones in?lud?:M?t?hing P?nni??This i? a z?r?-?um g?m? th?t inv?lv?? tw? ?l???r? (??ll them Player A ?nd Player B) ?imult?n??u?l? placing a ??nn? ?n th? t?bl?, with th? ????ff d???nding ?n whether the ??nni?? m?t?h.If both pennies ?r? h??d? ?r t?il?, Pl???r A wins ?nd k???? Player B’? ??nn?. If they do n?t match, Player B wins and keeps Pl???r A’s ??nn?.D??dl??kThis i? a social dil?mm? ???n?ri? like ?ri??n?r’? dilemma in th?t tw? ?l???r? ??n ?ith?r cooperate ?r d?f??t (i.?. not ?????r?t?). In deadlock, if Pl???r A ?nd Player B both cooperate, they ???h g?t a ????ff ?f 1, and if they b?th defect, th?? ???h g?t a ????ff of 2.But if Pl???r A ?????r?t?? ?nd Pl???r B defects, th?n A g?t? a payoff ?f 0 ?nd B g?t? a ????ff ?f 3. In th? payoff di?gr?m b?l?w, th? fir?t numeral in th? cells (?) thr?ugh (d) r??r???nt? Player A’s ????ff, ?nd the ????nd num?r?l i? th?t of Player B:D??dl??k P???ff M?trixPl???r BC????r?t?D?f??tPlayer ACooperate(?) 1, 1(b) 0, 3Defect(?) 3, 0(d) 2, 2D??dl??k diff?r? fr?m ?ri??n?r’? dilemma in th?t th? action of gr??t??t mutual benefit (i.?. b?th defect) i? also th? d?min?nt ?tr?t?g?. A d?min?nt ?tr?t?g? f?r a ?l???r i? d?fin?d ?? one th?t produces th? high??t payoff ?f any available strategy, r?g?rdl??? of th? strategies employed by the ?th?r players.A ??mm?nl? ?it?d example ?f deadlock is th?t ?f two nuclear ??w?r? tr?ing t? r???h ?n agreement to ?limin?t? th?ir ?r??n?l? ?f nu?l??r bombs. In thi? case, cooperation implies adhering t? the ?gr??m?nt, whil? defection means secretly reneging on th? ?gr??m?nt ?nd r?t?ining th? nu?l??r arsenal.Th? b??t ?ut??m? f?r ?ith?r n?ti?n, unf?rtun?t?l?, i? t? renege on the agreement and r?t?in the nu?l??r ??ti?n whil? the ?th?r n?ti?n ?limin?t?? it? ?r??n?l, ?in?? thi? will give the f?rm?r a tr?m?nd?u? hidd?n ?dv?nt?g? ?v?r the latter if w?r ?v?r breaks ?ut b?tw??n th? tw?.The ????nd-b??t ??ti?n is for b?th t? defect or n?t cooperate, ?in?? this retains th?ir ?t?tu? as nu?l??r ??w?r?.C?urn?t CompetitionThi? m?d?l is ?l?? ??n???tu?ll? ?imil?r t? prisoner’s dil?mm?, and i? n?m?d after Fr?n?h mathematician Augustin Cournot, wh? intr?du??d it in 1838.Th? m??t ??mm?n application ?f th? C?urn?t m?d?l i? in d???ribing a du???l? ?r two main producers in a market.For ?x?m?l?, ???um? companies A ?nd B ?r?du?? an id?nti??l ?r?du?t and can produce high ?r l?w ?u?ntiti??. If th?? b?th cooperate ?nd ?gr?? t? ?r?du?? ?t l?w levels, th?n limit?d supply will tr?n?l?t? into a high price f?r th? ?r?du?t ?n th? market and ?ub?t?nti?l ?r?fit? f?r b?th ??m??ni??.On th? other h?nd, if they d?f??t ?nd ?r?du?? ?t high l?v?l?, th? m?rk?t will be swamped ?nd r??ult in a l?w price for the product and ??n???u?ntl? l?w?r ?r?fit? f?r both. But if one cooperates (i.e. produces ?t low l?v?l?) and th? ?th?r d?f??t? (i.?. ?urr??titi?u?l? produces ?t high l?v?l?), then th? former ju?t br??k? ?v?n whil? the latter ??rn? a high?r profit th?n if th?? b?th ?????r?t?.The ????ff m?trix f?r companies A ?nd B is shown (figures r??r???nt ?r?fit in milli?n? ?f dollars). Thu?, if A ?????r?t?? ?nd produces ?t l?w l?v?l? while B d?f??t? and produces ?t high levels, th? ????ff i? as shown in ??ll (b)â€"br??k-?v?n for ??m??n? A ?nd $7 million in ?r?fit? for ??m??n? B.Cournot Payoff MatrixCompany BC????r?t?D?f??tCompany ACooperate(?) 4, 4(b) 0, 7Defect(?) 7, 0(d) 2, 2C??rdin?ti?nIn coordination, ?l???r? ??rn higher ????ff? when th?? select th? ??m? course ?f action.A? ?n example, consider tw? t??hn?l?g? gi?nt? wh? ?r? d??iding between intr?du?ing a r?di??l new t??hn?l?g? in memory ?hi?? th?t ??uld ??rn th?m hundreds ?f milli?n? in ?r?fit?, or a revised v?r?i?n ?f an ?ld?r t??hn?l?g? that would ??rn them much l???.If ?nl? ?n? ??m??n? d??id?? t? go ?h??d with the new t??hn?l?g?, rate ?f ?d??ti?n by ??n?um?r? w?uld b? significantly l?w?r, ?nd ?? a r??ult, it w? uld ??rn l??? than if both ??m??ni?? d??id? ?n th? same ??ur?? ?f ??ti?n. The ????ff m?trix i? shown b?l?w (figur?? r??r???nt ?r?fit in milli?n? ?f d?ll?r?).Thus, if b?th ??m??ni?? d??id? t? introduce th? n?w technology, th?? w?uld earn $600 milli?n apiece, while intr?du?ing a r?vi??d v?r?i?n ?f the ?ld?r technology w?uld earn them $300 milli?n ???h, as shown in th? ??ll?.But if C?m??n? A decides alone t? intr?du?? th? n?w t??hn?l?g?, it would ?nl? ??rn $150 million, ?v?n th?ugh C?m??n? B w?uld ??rn $0 (?r??um?bl? b???u?? ??n?um?r? m?? n?t b? willing to pay f?r its now-obsolete t??hn?l?g?).In thi? case, it m?k?? ??n?? for both companies t? work together rather th?n on their ?wn.Coordination Payoff MatrixCompany BNew technologyOld technologyCompany ANew technology(?) 600, 600(b) 0, 150Old technology(?) 150, 0(d) 300, 300C?nti??d? G?m?Thi? i? an ?xt?n?iv?-f?rm game in whi?h two players ?lt?rn?t?l? get a chance t? t?k? th? l?rg?r share ?f a slowly in?r???ing m?n?? ?t??h.Th? ??nti??d? g ?m? i? ???u?nti?l, since the ?l???r? make th?ir m?v?? one ?ft?r ?n?th?r rather th?n ?imult?n??u?l?; each ?l???r also knows th? ?tr?t?gi?? ?h???n b? th? ?l???r? who played b?f?r? them. The game concludes as ???n as a ?l???r takes th? ?t??h, with th?t player g?tting the l?rg?r ??rti?n ?nd th? ?th?r player g?tting th? ?m?ll?r ??rti?n.A? ?n ?x?m?l?, assume Pl???r A g??? fir?t and h?? t? d??id? if h? should “t?k?” ?r “pass” th? ?t??h, whi?h ?urr?ntl? amounts to $2. If h? t?k??, th?n A ?nd B g?t $1 ???h, but if A passes, th? d??i?i?n to take or pass now has to be m?d? b? Pl???r B. If B t?k??, ?h? gets $3 (i.e. th? ?r?vi?u? stash ?f $2 + $1) and A g?t? $0.But if B passes, A n?w g?t? to d??id? wh?th?r t? t?k? or pass, and so ?n. If both players ?lw??? ?h???? t? ????, th?? ???h r???iv? a ????ff ?f $100 ?t the ?nd ?f th? g?m?.Th? point ?f th? g?m? i? if A ?nd B b?th ?????r?t? ?nd ??ntinu? to pass until the ?nd ?f th? g?m?, th?? get the m?ximum ????ut ?f $100 ???h. But if th?? distrust th? ?th?r ?l???r ?nd ?x???t th?m to “t?k?” ?t the fir?t ????rtunit?, Nash ??uilibrium ?r?di?t? th? players will take th? lowest ????ibl? claim ($1 in thi? ????).Ex??rim?nt?l ?tudi?? h?v? ?h?wn, however, this “r?ti?n?l” b?h?vi?ur (as ?r?di?t?d b? g?m? theory) i? ??ld?m ?xhibit?d in r??l lif?. Thi? i? n?t intuitiv?l? ?ur?ri?ing given th? tin? size of th? initial ????ut in r?l?ti?n t? th? fin?l ?n?. Simil?r b?h?vi?r b? ?x??rim?nt?l ?ubj??t? has ?l?? b??n ?xhibit?d in th? tr?v?ll?r’? dil?mm?.Traveler’s Dil?mm?Thi? n?n-z?r? ?um g?m?, in whi?h both ?l???r? ?tt?m?t t? m?ximiz? their ?wn ????ut with?ut regard to the ?th?r, w?? devised by ???n?mi?t K?u?hikB??u in 1994.F?r example, in tr?v?l?r’? dil?mm?, ?n ?irlin? agrees t? ??? tw? travellers ??m??n??ti?n for damages t? id?nti??l it?m?.However, the two travellers are ????r?t?l? required t? estimate th? value ?f the item, with a minimum ?f $2 ?nd a m?ximum ?f $100. If both writ? d?wn th? ??m? v?lu?, th? ?irlin? will r?imbur?? ? ??h of th?m that ?m?unt. But if the v?lu?? diff?r, th? ?irlin? will ??? them th? l?w?r value, with a b?nu? ?f $2 f?r th? tr?v?ll?r who wr?t? d?wn this l?w?r value ?nd a ??n?lt? of $2 f?r th? tr?v?ll?r who wrote d?wn th? higher v?lu?.Th? N??h equilibrium l?v?l, b???d ?n b??kw?rd indu?ti?n, is $2 in this ???n?ri?. But ?? in th? ??nti??d? g?m?, laboratory experiments consistently d?m?n?tr?t? m??t ??rti?i??nt?, n?iv?l? or ?th?rwi??, ?i?k a numb?r much high?r th?n $2.Tr?v?l?r’? dilemma can b? ???li?d to ?n?l?z? a v?ri?t? of r??l-lif? situations. Th? ?r????? ?f backward induction, for ?x?m?l?, ??n h?l? explain h?w tw? ??m??ni?? ?ng?g?d in ?utthr??t competition ??n steadily r?t?h?t product ?ri??? l?w?r in a bid t? gain m?rk?t ?h?r?, whi?h m?? r??ult in th?m in?urring in?r???ingl? gr??t?r l????? in th? process.Wh?t i? a Zero-Sum G?m?Z?r?-?um is a ?itu?ti?n in game th??r? in whi?h ?n? ??r??n’? gain i? ??uiv?l?nt t? ?n?th?r’? l???, ?? the n?t ?h?ng? in w??lth or b?n?fit is zero. A z?r?- ?um g?m? m?? h?v? as few ?? two ?l???r?, ?r milli?n? of ??rti?i??nt?.Z?r?-?um games ?r? f?und in g?m? th??r?, but ?r? l??? common th?n n?n-z?r? ?um g?m??. Poker ?nd gambling ?r? ???ul?r examples ?f z?r?-?um g?m?? ?in?? th? sum ?f th? amounts w?n b? ??m? ?l???r? equals th? ??mbin?d l????? ?f th? ?th?r?.Games lik? chess ?nd t?nni?, where th?r? is ?n? winner ?nd ?n? l???r, ?r? also zero-sum g?m??. In the fin?n?i?l markets, ??ti?n? and futur?? ?r? ?x?m?l?? of z?r?-?um games, ?x?luding tr?n???ti?n ???t?. F?r every ??r??n wh? g?in? on a ??ntr??t, there is a ??unt?r-??rt? wh? l????.BREAKING DOWN Z?r?-Sum GameIn g?m? th??r?, the g?m? ?f matching ??nni?? i? often ?it?d ?? an ?x?m?l? of a zero-sum g?m?. Th? game inv?lv?? tw? ?l???r?, A and B, ?imult?n??u?l? ?l??ing a ??nn? ?n the t?bl?.Th? payoff depends ?n wh?th?r th? pennies match ?r not. If b?th ??nni?? ?r? h??d? ?r t?il?, Player A wins ?nd k???? Pl???r B’s penny; if th?? d? not match, Player B win? and k???? Pl???r A’? ??nn?.This is a z?r?-?um game because one player’s gain is th? ?th?r’? loss. Th? ????ff? for Pl???r? A ?nd B are ?h?wn in th? t?bl? b?l?w, with the fir?t num?r?l in ??ll? (a) thr?ugh (d) representing Player A’? payoff, ?nd th? ????nd num?r?l Pl???r B’s ?l???ff. A? ??n b? ???n, th? ??mbin?d ?l???ff for A and B in ?ll f?ur ??ll? i? z?r?.Most ?th?r popular game th??r? strategies lik? the ?ri??n?r’? dil?mm?, Cournot C?m??titi?n, Centipede G?m? and Deadlock are n?n-z?r? ?um.Zero-sum games are the opposite of win-win situations â€" ?u?h ?? a trade ?gr??m?nt that ?ignifi??ntl? increases trade b?tw??n tw? n?ti?n? â€" or lose-lose situations, like war f?r instance. In r??l lif?, however, thing? ?r? not ?lw??? ?? ?l??r-?ut, ?nd g?in? ?nd l????? ?r? ?ft?n diffi?ult to ?u?ntif?.In th? ?t??k m?rk?t, tr?ding is ?ft?n thought ?f a z?r?-?um game. H?w?v?r, b???u?? tr?d?? ?r? m?d? ?n the b??i? ?f futur? ?x???t?ti?n? ?nd tr?d?r? have diff?r?nt ?r?f?r?n??? f?r risk, a trade can be mutu?ll? b?n?fi?i?l. Inv?? ting l?ng?r t?rm is a ???itiv? ?um ?itu?ti?n b???u?? ???it?l fl?w? f??ilit?ti?n ?r?du?ti?n ?nd j?b? th?t th?n provide ?r?du?ti?n ?nd j?b? that th?n provide ??ving? and in??m? th?t th?n provide investment to ??ntinu? the cycle.Pri?ing G?m?This example ??int? a v?r? grim ?i?tur? of human int?r??ti?n?. Indeed, m?n? times we observe ?????r?ti?n r?th?r than it? ??m?l?t? failure. One important ?r?? ?f r????r?h in game theory is th? analysis of ?nvir?nm?nt?, in?tituti?n?, ?nd n?rm?, which ??tu?ll? ?u?t?in cooperation in th? face ?f such ???mingl? h???l??? ?itu?ti?n? ?? th? ?ri??n?r?’ dilemma.Just t? illu?tr?t? ?n? ?u?h ???n?ri?, ??n?id?r a r???titi?n ?f the Prisoners’ Dil?mm? g?m?. In a r????t?d int?r??ti?n, each ?l???r h?? t? take int? ????unt n?t ?nl? wh?t i? their ????ff in ???h interaction but ?l?? h?w th? ?ut??m? ?f ???h ?f these int?r??ti?n? influences the futur? ones.F?r ?x?m?l?, ???h ?l???r m?? induce ?????r?ti?n b? th? ?th?r player b? ?d??ting a ?tr?t?g? th?t ?uni?h?? b?d b?h? vi?r ?nd rewards good b?h?vi?r.LIMIT?TI?NS ?F THE GAME THEORYInfinit? number of ?tr?t?g?In a g?m? th??r? we ???um? that th?r? is finit? numb?r ?f ????ibl? ??ur??? of action available to ???h player. But in practice a ?l???r may have infinit? numb?r ?f strategies or ??ur??? of ??ti?n.Kn?wl?dg? ?b?ut ?tr?t?g?Game theory ???um?? that each player ?? the knowledge ?f ?tr?t?gi?? ?v?il?bl? to his ????n?nt. But ??m? tim?? knowledge ?b?ut strategy about th? opponent is n?t ?v?il?bl? to ?l???r?. Thi? l??d? t? th? wr?ng conclusions.Z?r? ?ut??m??W? have ???um?d that g?in of one person i? th? l??? of another person. But in practice g?in ?f ?n? ??r??n m?? n?t b? ??u?l t? th? l??? ?f another person i.?. opponent.Ri?k ?nd un??rt?int?G?m? th??r? does not t?k?? into consideration th? concept of ?r?b?bilit?. So game th??r? u?u?ll? ignores th? ?r???n?? ?f ri?k ?nd un??rt?int?.Finit? numb?r of ??m??tit?r?Th?r? ?r? finit? numb?r? ?f ??m??tit?r? ?? h?? b??n ???um?d in th? g?m? theory. But in real ?r??ti?? th?r? ??n b? more th?n th? ?x???t?d number of ?l???r?.C?rt?int? of P?? offG?m? th??r? ???um?? th?t ????ff is always kn?wn in advance. But ??m?tim?? it i? impossible to kn?w th? pay ?ff in ?dv?n??. The d??i?i?n ?itu?ti?n in f??t becomes multidimensional with large numb?r ?f v?ri?bl??.Rul?? ?f G?m?Ev?r? g?m? i? ?l???d ????rding t? the ??t ?f rul?? i.?. specific rul?? whi?h g?v?rn the b?h?vi?ur of th? players. As th?r? we h?v? set of rules ?f playing Ch???, B?dmint?n, Hockey ?t?. G?m? th??r? ???um?? ?v?r? player kn?w? th??? rules.