Paper presented at Bulk Power Systems Dynamcs and Control IV -Restructurng, August 24-28, Santorn, Greece The Dynamcs of Customers Swtchng Supplers n Deregulated Power Markets Rchard E. Schuler Professor of Economcs and Cvl & Envronmental Engneerng Drector, Cornell Unversty Insttute for Publc Affars Ithaca, NY, USA Telephone: (607) 255-7579 E-mal: RES1@cornell.edu I. Introducton As the possblty of effectve competton s thought to arse n ndustres that were formerly characterzed as natural monopoles, pressure by some customers and /or potental entrants s brought to bear on poltcal and regulatory nsttutons to deregulate economcally certan aspects of these ndustres, and to allow market pressures to substtute for regulatory oversght as a means of restranng excessve prces. The further hope s that once freed of rate-of-return restrctons mposed by regulators, servceprovders wll seek to compete technologcally and to proft from cost cuttng nnovatons that ultmately may be translated through market pressures nto lower prces for customers. The ntal wave of deregulaton n the Unted States focused on ndustres where the captal was largely moble, but over the past twenty years the emphass has shfted to utltes wth substantal sunk captal (lterally and fguratvely), lke long dstance telephone servce, the generaton of electrcty, and now basc exchange telephone servce, and n the near future, retal purchases of electrcty from alternatve marketng agents. In the process, formerly vertcally ntegrated ndustres have been separated nto functonal components, snce n total, each ndustry s comprsed of complex networks that would be uneconomcal to duplcate n the whole. Thus the compettve aspects have been lmted, to a large extent, to those components of the ndustry that are most economcal to duplcate, gven the scale and locaton of customer demand. And n many nstances, lke electrcty transmsson and dstrbuton, the local feeder and dstrbuton cables porton of telephone servce, and the poles and conduts shared by both, t s both economcally and aesthetcally desrable to have all supplers share the same physcal facltes, whch means that a substantal regulatory presence wll reman to ensure that physcal access to and the subsequent user charge allocatons are assgned effcently and equtably to all supplers. These concerns about far and equal access to commonly used facltes, however, are not the focus of ths analyss whch presumes those dffcult regulatory ssues wll be managed. Rather the concern here s that n markets for bulk power supples, transmsson losses, costs and capacty constrants may solate customers from the effectve reach of many generators, so the remanng supplers may exercse market power and restrct prces from fallng to compettve levels. In a prevous statc equlbrum analyss, Hobbs and Schuler, 1985, showed that n olgopolstc power markets, equlbrum bulk power prces mght rse between 10 to 15 percent above regulated prces n the short run, but then fall to less than a 5 percent markup over a longer tme horzon when new compettors could complete addtonal generatng capacty. However, ths loss of allocatve effcency mght be tolerable f subsequent compettve pressures spur nnovatve advances n producton technologes that result n offsettng cost reductons. These prevous prce estmates were, however, predcated upon equlbrum condtons n olgopolstc markets; the addtonal ssue explored here s the lkely dynamc nterplay between customers and supplers n bulk power markets, and estmates are provded of the tme lags before buyers and supplers reach an equlbrum. Meanwhle, some customers may be exposed to monopoly-level prcng, and a methodology s llustrated for estmatng under what crcumstances and for how long that market power mght be exerted. By analogy, n the recently deregulated telephone ndustry n the U.S., a prolonged, slow transton to effectve competton has been observed among longdstance telephone carrers, despte substantal prce dfferences for smlar servces, followng the ncepton of
entry n 1984 1. Here the factors that are lkely to retard the onset of effectve competton n retal markets for compettve power supples are examned and projected, not as a functon of restrctve operatng and cost allocaton practces, but rather merely as a result of ntellgent prcng strateges by supplers n response to lagged customer behavor. The analyss begns wth the observaton that n many newly deregulated markets, and n markets where changng supplers mposes sgnfcant costs on customers and/or customers do not have adequate nformaton about the servce qualty and relablty of the new suppler, then when confronted wth a lower prce offered by an alternatve suppler, not all customers swtch nstantaneously. But, when faced wth a lag n customer response, what s the optmal prce response for the suppler chargng the hgher prce? In fact, the ntroducton of these market-clearng lags, or transactons costs, frequently stands neo-classcal mcro-economc prescrptons on ther head. 2 Thus the objectve of ths analyss s to estmate how retal supplers of electrcty mght prce over tme n response to the ntroducton of competton before market pressures begn to drve prces toward margnal cost, or at least a stable Nash equlbrum, as predcted by tradtonal theory and statc equlbrum analyss. II. Lagged Customer Response to Prce Dfferences Lags n customer response to prce dfferences may arse because of search or transactons costs. Search costs may be ncurred to learn about the avalablty of supplers chargng lower prces than the ncumbent and/or to seek out and verfy the satsfacton of other customers who have changed ther supplers recently. One example of transactons costs that may nhbt customers responses to prce dfferences s f they have substantal costs sunk n equpment that s necessary to use the servce whose prce has recently become unfavorable. In these crcumstances, even where search costs are modest as n fuel swtchng between electrc, ol, and gas heatng, as an example, market-share adjustments to a substantal prce spread mght be qute slow because of the threshold cost of change. Here the shfts n supplers 1 See Schuler, R. And Schuler, R. Jr (1996), as an example. 2 As an example, n the spatal economc lterature where transportaton costs cause the frcton, Martn Beckmann (1971) has shown that followng entry by compettors, ncumbent frms who are chargng mll prces can be expected to rase those prces. may follow very slowly over tme, dependng upon how customer equpment ages and warrants replacement. Search and transactons costs are frequently substantal n markets havng a sgnfcant spatal dmenson that must be brdged to reach geographcally dspersed customers. Examples nclude electrcty supply wth generaton (producton) located at fxed ponts and transmsson and dstrbuton lnes (transportaton) requred to reach far-flung customers, and basc exchange telephone servce where the swtch s located centrally and wre pars or fber optcs are the transportaton requred to reach a suffcent number of customers. Where transportaton costs provde a buffer between two separately located producers, customer adjustments to prce dfferences among them can lag apprecably because of both search and transactons costs. In certan crcumstances, t may actually be n the domnant frm s nterest to rase prces n response to spatal competton f all customers are not lost nstantaneously to the lower-prced frm. Regardless of the reasons for lagged customer response to prce dfferences for dentcal goods and servces from dfferent supplers, when these condtons exst and there are a lmted number of potental economc supplers, the frms can be expected to behave strategcally, and not all frms wll rush to match the prces of the lowest-prced suppler. The necessary condtons for such behavor exst n electrcty supply and varous aspects of telecommuncatons markets. In fact substantal delays have been observed by customers respondng to sgnfcant prce advantages n the markets for a number of goods and servces. 3 Furthermore, n the case of labor markets, consderable attenton s pad to the average duraton of unemployment n markets where numerous job opportuntes exst n order to estmate a structural rate. These estmates acknowledge that the quantty adjustments by ndvduals do not occur nstantaneously; the queston rased here s that n the face of those lags n markets wth few supplers, what s ther optmal prce response? Both n the labor market analyses 4 and n prevous work by Schuler 5 ths lagged quantty adjustment process s shown to be of the S-shaped, logstc functon form shown n Fgure 1. Labor economsts descrbe ths relatonshp as a hazard functon 6, and as appled to product markets, Schuler (1997) has descrbed the relatonshp as beng comprsed of two 3 See Schuler (1997), for examples. 4 See Kefer, N. (1998) 5 Op. Ct. (1997) 6 See Kefer, N. (1998)
phenomena. The frst s the tme requred to have all potental customers become aware of the alternatve opportuntes to acqure the product from some other suppler at a lower prce. The second step, whch s condtonal upon learnng about the possble lower-prced opportunty, s ganng confrmaton that the new suppler s n fact offerng the dentcal servce (n terms of locaton and qualty) at a lower prce, and n arrangng to swtch supplers. If customers are bombarded wth nformaton (advertsng and dnnertme phone calls) at a steady (constant) rate per unt tme, then the number (and proporton) of customers nformed about the new opportunty who were prevously not aware of t wll declne over tme. Thus a constant bombardment rate tmes a declnng base leads to a declnng rate of newly nformed customers, and so whle the number of customers who are aware of ths opportunty ncreases contnuously over tme so long as the nformaton campagn s sustaned, the rate of change declnes and faces a already experenced the new servce, then the rate of acceptance should be an acceleratng functon of the number (or proporton) of customers who have already accepted the new servce. The rate of converson to the lower prced suppler should therefore be the product of these two phenomena, whch results n the logstc functon of equaton (1). S t%1 & S t ' 8(pj t & p t ) S t Sj t where: S = Market share of suppler at tme t. t (1) p = Prce ncrement over margnal cost charged by t suppler at the tme t, normalzed by the spread between the monopoly prce and margnal cost. 8 = Speed of adjustment parameter saturaton effect as shown after tme t 3 n Fgure 1. By comparson, f once nformed, the rate at whch customers agree to accept the new opportunty s proportonal to both the potental gan (the prce spread) and the ablty to confrm the qualty of the alternatve servce, whch s proportonal to the number of customers who have S j t ' (1 & S ), where there are only two supplers. t One nce feature of ths logstc relatonshp s that t s symmetrc, so f at any tme, the relatve prces of the two supplers s swtched, the dentcal share adjustment
equaton holds. Furthermore, t has been shown elsewhere 7 that where there are more than two compettors, the same general relatonshp holds where p j s replaced by the share- t weghted prce of all other compettors and S j t ' (1 & S t ), the market share held by all other compettors. The tme adjustment parameter, 8, can be thought of as a dynamc prce elastcty (t has the dmensons of 1/tme), and attempts to relate t to conventonal notons of a prce elastcty are asssted by the manpulaton n equaton (2). 8 ' where: )S 1 S (1&S )(p j &p ) ' )S CQ S CQ P j & P P C ÆÉÉÉÉÉÈÉÉÉÉÉÇ 0 p P )S ' S t%1 & S t 1 ( P M & m )(1 & S ) Q = total quantty of servce n the market P,j = non-normalzed prce charged by supplers,j P M = monopoly prce m = margnal cost of producton 0 p = tradtonal prce elastcty of demand (2) As an llustraton, a frm servng about half of ts market who s chargng the monopoly prce and who has neglgble margnal producton costs, wll have 8 = 2, f ts tradtonal prce elastcty of demand s one. III. Potental Applcaton n Deregulated Electrcty Supples Dependng upon the reorganzed structure of the electrc ndustry, opportuntes for exertng market power may dffer, but so long as there are scale economes n producton that exceed the demand at several locatons and transportaton costs are apprecable, then some market power may arse. Partcularly f blateral contracts are reled upon to lnk wdely dstrbuted generators wth 7 See Schuler and Schuler (1996). dspersed large customers (ether ndustrals or muncpal companes), spatal olgopoly should be the expected market structure. If, however, as s proposed for most regons of the country, an ndependent system operator (ISO) s placed between generators and customers, and partcularly f separate enttes from the generators and large buyers act as the ISO and auctoneer, then f those auctons are effcently desgned (See the papers by Bernard, et. al., 1998, and Denton, et. al., 1998, that explore the desgn of effcent auctons), the generator may be solated from the lagged response of ndvdual customers snce all buyers and sellers n the aucton wll receve/pay the same marketclearng prce. Wth a lmted number of generators and/or buyers, these partes may be able to game the aucton, but that s not the market power problem beng emphaszed here. Instead, t s cases where buyers face dfferent prces, but are slow to react that are beng examned. One stuaton where ths may arse n electrcty markets wth a centralzed aucton s where all consumers do not buy drectly through the aucton, but rather purchase ther power through a lmted number of assemblers, as may be the case for many small resdental and commercal customers. In partcular, where the former vertcally ntegrated utlty spns off a seperate marketng entty wth a famlar name, many small customers may stck wth ther accustomed suppler relatonshp, ntally. A thrd crcumstance where ths customer-lag-nduced type of market power mght arse s f multple unregulated auctons were reled upon, n place of a sngle controlled area-wde, bulk power market-place. In ths crcumstance, nspred by proft opportuntes and the lkely emergence of very few compettve auctons n the regon, customers mght be slow to swtch from one aucton to another, partcularly f that swtch requred the constructon of new transmsson lnks and/or prces n all auctons were hghly varable. IV. Optmal Dynamc Prcng Strateges by Supplers Gven the lagged customer response to dfferent prces among dfferent supplers, wth a small number of vendors, the optmal prcng strategy for each frm can be deduced, gven ther assumptons about the prcng behavor of ther compettors. Furthermore, f each frm beleves the others are behavng n smlar ways, equlbrum solutons of dynamc prce patterns can be
explored, where each suppler s assumpton about ther compettors, and vce versa, are consstent wth ther own optmal behavor n those cases -- a Nash equlbrum. As an example, consder a fve perod tme horzon where each suppler seeks to maxmze the net present value of ther profts as n equaton (3). A ' S 1 B (p 1 ) % $S 2 B (p 2 ) % $2 S 3 B1 (p 3 ) % $ 3 S 4 B (p 4 ) % $4 S 5 [B (p 5 ) % V 5 ] where: (3) A = frm s net present value of profts. S t = frm s market share n perod t. B t = proft per customer earned by frm n perod t. $ = dscount factor = 1/(1+r); r = dscount rate. V t = resdual value at perod t. Each frm s problem s to maxmze equaton (3) wth respect to prces, subject to the share adjustment equaton (1), the prces charged by ts compettors and ts ntal market share, S 1. Ths s a dynamc programmng problem that can be solved recursvely startng wth perod fve and movng backward to today, and so the soluton to ths dynamc game s sub-game perfect. The outcome s dependent upon the prces selected by the compettor who faces a smlar optmzaton problem, so wth parameter values assgned to ths model, a pay-off matrx can be constructed to explore the exstence and nature of stable solutons to ths game. If the plannng horzon s fnte, V t can equal the salvage value of assets, or the resdual value that the current managers want to pass along to ther successors. Because economc profts equal zero when prces equal margnal cost and all assets are earnng a normal return commensurate wth other nvestments of smlar rsks, one way of defnng the tme horzon of ths game s at the tme when ntense competton s expected to ensue n ths ndustry. From that pont, T + 1, onward, p T+1 = 0 and B T+1 = 0, so V T = 0. Alternatvely, the beneft denal prncple developed by Langlos and Sachs (1993) could be employed whch suggests that after a ntal jostlng for poston, each frm recognzes that n a game of nfnte duraton, the best t can do s to charge the monopoly prce, the net effect of whch s mplct colluson. In that case, V T would be the net present value at tme T of pure monopoly profts over an nfnte tme horzon. Because, the ntenton of deregulaton s to encourage competton, the analyss employed here wll assume perfect competton after a specfc tme perod, T. The queston to be explored s how rapdly prces wll fall to that compettve level and how expectatons about T affect that dynamc prce pattern. For analytc convenence, all prces are normalzed by the dfference between the monopoly prce and margnal cost. Thus -1 # p j - p < +1, unless predatory prces that are below margnal cost are tolerated. Furthermore, snce f at margnal cost prces, economc profts equal zero, then wthout loss of generalty n the net present value calculaton of equaton (3), 0 # p # 1, where p = 0 represents margnal cost and p = 1 represents the monopoly prce. Further numercal smplfcatons can be made by explorng the last perod problem: Max. p T S T B (p T )%V T If ths s the end of the tme horzon, and wth the market share, S, already establshed by prces n prevous perods, then the optmal prce for ths last perod s the monopoly prce and p = 1 for all producers. In ths case, equaton (3) can be normalzed by the level of monopoly profts, the game reduces to one of settng prces n only the frst T-1 perods, and n each of these perods, normalzed profts range between zero and one. 8 Thus, 0 # S t, p t, B t # 1, and for perfect competton after T+1, V = 0. V. Numercal Estmates Analytcal solutons to ths out-of-equlbrum dynamc analyss are currently avalable only for the case where the ntal market shares are equal, and snce the focus of ths analyss s upon the early stages of deregulaton of a market that was formerly suppled by a monopoly, numercal llustratons are requred to explore the dynamc prce adjustment processes under a varety of parameter values. The ntal llustratons restrct supplers to offerng only two prces, the perfectly compettve margnal cost-based prce (p t = 0) and the monopoly prce (p t = 1). Two advantages arse from restrctng p t,[0;1]: frst, no assumptons must be made (4) 8 See Schuler (1997) and Schuler and Hobbs (1992), for detals on the analytcs of the game-theoretc soluton.
about the shape of the demand curve other than t results n a monotonc ncreasng, concave proft functon over the range of prces, 0 # p t # 1, and second, the number of possble pay-offs that must be explored n the search for a Nash equlbrum s reasonable for large T. 9 The remanng parameter value to be set before numercal llustratons can be provded s 8 whch reflects the speed of customer response to prce dfferences. Snce there has been lttle experence wth retal compettve response to dfferent electrcty prces, the parameter value selected s merely suggestve. As an example, n a prevous paper 10 a value of 8 =.32 s computed for electrcty, based upon hstorc estmates of tradtonal prce elastctes for varous classes of electrcty customers, wth an adjustment to reflect that n a compettve world customers would experence a much wder range of choces wth lower transfer costs. As an example, hstorc experence n long dstance telephone markets has been used to estmate 8 =.23 for that stuaton, and t s probable that transfers of electrcty supplers may become as easy for some of ther customers n the future. Furthermore, wth greater experence ganed by customers n the future, speeder responses mght be antcpated, and for ths reason, numercal results are presented for 8 =.25,.5 and 1.0 to explore the senstvty of the supplers prcng behavor to dfferent rates of customer response. In the case of 8 = 1, the mpled customer responsveness s approxmately a fve percent loss, per year n market share to a compettor chargng a ten percent lower prce. In the frst year, ths represents the equvalent of a farly nelastc equvalent of a statc prce elastcty (0 p =.5), but f the ten percent prce spread s mantaned over fve years, the longer term equvalent prce elastcty equals 2.26 11 a 9 The number of cells n a pay-off matrx that must be evaluated wth two compettors s: [c T-1 ] 2, where c s the number of alternatve prces consdered by each compettor. In a fve perod game, wth c=2, a 16 x 16 matrx of 256 alternatves must be explored. If however the range of prces consdered s expanded to fve, there are 625 possble prcng strateges for each frm rangng over the T-1=4 actve perods, and a matrx wth 390, 625 proft alternatves must be evaluated. 10 See Schuler (1998). 11 If.5 = 0 p = [)SCQ/SCQ] [)P/P], then the market share loss n the frst year due to a 10 percent prce dsadvantage s fve percent. In the second year, the remanng 95 percent market share s reduced by another fve percent so that n any subsequent perod, tme = T, S T = S 0 (1-0 p C )P) T. Thus, f S 0 =1, )P=.1 and 0 p =.5, S 5 =(1-.05) 5 =.774, a 22.6 percent loss n total market share n response to a ten percent prce dsadvantage. substantal response. An example of a payoff matrx for a four perod game (three actve perods snce both supplers choose the monopoly prce, p=1, n the fnal year) s shown n Table 1. Here, even wth a qute rapd rate of customer response (8=1.0) and wth the domnant suppler, frm 2, havng a 90 percent ntal market share, a unque set of prce strateges exst that represent a Nash equlbrum where the compettor charges margnal cost n the frst two years and then rases ts prce to the monopoly level n the thrd and fourth years. Meanwhle the domnant frm never fnds t proftable to budge from the monopoly prce, even n the face of ntense prce competton. In Table 2, the results for a fve perod game, wth p,[0;1], but wth a range of values for the customer adjustment speed parameter, emphasze how at the potentally low levels of 8 for compettve retal power markets, the supplers are lkely to be stubbornly strategc n ther behavor. For the majorty of cases explored, at least one of the supplers s estmated to charge the monopoly prce, and n many nstances, both wll prce at the monopoly level wthout any need for explct collusve actvty; the monopoly prce s seen by each frm to be n ts own best nterest. In the cases analyzed, the ntal market shares of the two supplers are vared from.1 and.9,.3 and.7 to.5 and.5, and the consumer adjustment speed parameter, 8, s set at.25,.5, and 1.0. The real dscount rate s set at.03 throughout 12. The results n Table 2 emphasze how crucal reasonable knowledge of 8 s n order to depct deregulated behavor. Near the prevously estmated rate of 8 for long dstance callng (8 =.23), both frms behave n an mplctly collusve fashon, regardless of ntal market shares. As the adjustment speed ncreases (8 =.5), the entrant begns to charge a compettve prce n the early years n order to mprove ts market share, but the ncumbent does not match ths compettve prce. Furthermore, f both frms begn wth half of the market, then nether fnds t proftable to compete. Only when 8 = 1, a value four tmes as fast as prevously estmated, does some modest competton begn to emerge n the frst three of the fve perods, but as the entrant s 12 A hgher, realstc dscount rate for compettve frms would result n even less compettve prcng behavor, snce the frm s tradeoff s between hgher profts now (p=1) versus larger market share n the future (p=0). However, f a growng market s antcpated, ths factor can also be ncorporated nto $, havng the equvalent effect of a lower dscount rate.
market share rses to the neghborhood of 50 percent both frms stop competng. Only n the case where both frms ntal shares are ffty percent, do the frms engage n prsoners -dlemma-type ntense competton n the frst two perods before settlng back to monopolstc behavor. However, n all of these cases, the frms manage to extract combned economc profts that are 58 percent or more of the maxmum possble monopoly profts. Comparng the results n Table 1 for 8=1 and S 12 =.1 wth those n Table 2, there s lttle effect on prcng strateges by extendng the tme horzon by one year. However, n Table 3, the tme horzon s extended to nne perods wth all other assumptons and parameter values held the same as n Table 2. Once agan, economc profts from perod ten onward are assumed to be zero, so n the tenth year, ether the managers retre or they expect perfect competton to ensue. Wth ths longer tme horzon, modest ncreases n compettve prcng are nduced. As examples, even wth extremely slow customer responses (8 =.25), the entrant wth ntal market shares less than one half s nduced to offer compettve prces n the early years snce they have a longer tme horzon to proft from future monopoly rewards. Note, however, t s always the promse of larger future monopoly profts that nduces compettve behavor n the present; by earnng lttle or no proft today, a larger market share may be obtaned n the future. Wth ths longer, nne year tme horzon, as the speed of adjustment parameter ncreases, the entrant s nduced to compete for many more perods (the frst fve years where 8 =.5 and the frst sx year where 8 = 1). But, only where 8 = 1, a value at the upper range of what mght be expected n power markets, s the ncumbent frm wth the domnant ntal market share nduced to meet the compettve prce so that ts market share does not fall below one half. In fact, n the nne perod game wth equal ntal market shares and 8 = 1, prsoner s-dlemmatype behavor does emerge over the frst sx years, and the compettors share only thrty percent of the maxmum possble level of monopoly profts (n net present value terms). However, three of the nne cases analyzed n ths nne perod game do not yeld Nash equlbra, probably because the prce s restrcted to two extreme values, the perfectly compettve and the monopoly prces. To explore the mpact of consderng a wder range of prce choces, the smulatons are repeated n Table 4 where p,[0,.25,.5,.75, 1], and an explct demand relatonshp must be assumed n order to estmate the per customer profts n the non-end-pont cases of p,[.25,.5,.75]. A lnear demand relatonshp s adopted for ths fve prce case, and the correspondng proft levels are B,[0;.44;.75;.94; 1]. Because of computatonal constrants, ths fve prce case s analyzed for only fve perods, and the results may be compared wth the two prce case n Table 2. The greater freedom of prce choce tends to move the compettors away from the extreme prces. In partcular, frms are less lkely to charge the monopoly prce (p = 1) f at p =.75, they can stll earn 94 percent of the monopoly proft ( a concave functon n prce) but reduce the possble rate of market share loss by at least 25 percent ( a lnear functon n prce). Thus, wth ths wder array of prces, the entrant s more lkely to compete prcewse n the early years, but t rarely offers prces as low as margnal cost. In fact, the entrant only sets ts prce at margnal cost for at most one perod, even wth 8 = 1, snce at a prce of.25 t earns 44 percent of monopoly profts. Smlarly, the ncumbent frm s more lkely to respond to the compettor s prce cuts early on n the game, when compared to the case where p,[0; 1], but those prce cuts are far more modest and never fall below p =.25. As a result, whle aggregate profts fall slghtly below 100 percent of the monopolst s maxmum for 8 =.25 (98.2 to 99.8 percent), even n the case wth farly rapd customer response (8 = 1), the compettors can be expected to be reapng 77 to 79% of the maxmum monopoly level profts. VI. Conclusons Ths analyss llustrates a useful technque for both regulators and compettve supplers for estmatng lkely prcng consequences n deregulated power markets. Gven the prevous observed lagged response by consumers n swtchng to lower prced supplers n deregulated telecommuncatons markets, and f the number of lkely supplers n any partcular deregulated power market turns out to be relatvely small, the gametheoretc analyss llustrated here may be a useful method to estmate realstc market outcomes of that deregulaton. The results n Table 4 may be most relevant to the regulator, and they emphasze the overwhelmng mportance of both massve nformaton campagns and the facltaton of customer transfers from one suppler to another (large 8) f substantal monopoly rents are not to be earned by the domnant suppler. If rapd customer adjustment rates are acheved, the onset of compettve prcng s also facltated by reallocatng ntal market shares so the domnant frm holds 70 percent or less of the market. Otherwse, the benefts to electrcty customers wll have to be derved largely from cost-cuttng technologcal advances nduced by the large potental profts; mmedate prce-cuttng ncentves cannot be
solely reled upon. Ths tool s also useful for compettors n these newly deregulated markets snce t llustrates ther best dynamc prcng strateges. Future analyses should focus on the consequences of longer tme horzons, snce wth lagged customer responses to prce cuts, a prmary reason for cuttng prces today s the hope of obtanng much greater rewards n the future. Those future benefts could arse because of a rapdly growng market, or the prospect that after some future date, mplct colluson may characterze the market (V T > 0). If, however, ntense prce competton s expected to break out at some future date (t = T+1) and to drve all supplers to prce at margnal cost, then ths dynamc game over a fnte tme horzon s the proper way to analyze the prce and market share adjustments followng deregulaton. The other worthwhle extensons of the model would be to nclude the entry decson explctly and to consder a game wth more than two compettors.
Table 1. Payoff table for four perod prcng game, two compettors (8 = 1, S 1 2 =.1, r=.03, p,[0,1]) Frm 1 s payoff n SW corner; 2 s payoff n NE corner p 2 000 001 010 100 011 101 110 111 p 1 000.092.095.11.11.11.11.11.11.820.83.91.91.92.91.92.92 001.17 1.5 010.17 1.6 100.17 1.6 011.31 2.2 101.29 2.6 110.31 2.3 111.52 2.7 * = Nash equlbrum 1.6 2.4 2.4 2.3.19.18.19.35.35.34 *.64 2.9 2.4 2.4 2.4 2.9.11.19.22.26.24.36.47 1.9 2.8 2.4 2.5 3.1.19.14.27.27.41 2.5 2.7 2.5 3.2.19.22.28.25.37.54 1.9 2.8 2.6 2.5 3.3.20.14.29.28.45 1.9 2.8 2.6 2.6 3.3.11.21.13.21.29.36 1.9 1.9 2.8 2.7 2.6 3.4.11.21.13.22.29.38
Market Adjustment Speed, 8 Table 2 Nash Equlbra Prcng Strateges and Profts n a Fve Perod Dynamc Game wth Two Compettors, (p, [0,1], r=.03).25.5 1.0 Compettor s Intal Share S12.1.3.5.1.3.5.1.3.5 Compettor s Behavor: Prce = p2 [1,1,1,1,1] [1,1,1,1,1] [1,1,1,1,1] [0,0,1,1,1] [0,1,1,1,1] [1,1,1,1,1] [0,0,0,1,1] [0,0,1,1,1] [0,0,1,1,1] Share = S2 [.16.4] [.3 6.3] [.5 6.5] [.1 6.2] [.3 6.4] [.5 6.5] [.1 6.57] [.3 6.52] [.5 6.5] NPV Proft = A2.47 1.42 2.36.57 1.51 2.36 1.03 1.40 1.37 Domnant Frm s Behavor: Prce = p1 [1,1,1,1,1] [1,1,1,1,1] [1,1,1,1,1] [1,1,1,1,1] [1,1,1,1,1] [1,1,1,1,1] [1,1,1,1,1] [1,0,1,1,1] [0,0,1,1,1] Share = S1 [.9 6.9] [.7 6.7] [.5 6.5] [.9 6.79] [.7 6.6] [.5 6.5] [.9 6.43] [.7 6.49] [.5 6.5] NVP Proft = A1 4.25 3.30 2.36 3.91 2.91 2.36 3.08 2.05 1.37 ------------ ------------- ------------ ----------- ------------ ------------ ------------ ------------ ------------ Combned Proft 4.72 4.72 4.72 4.48 4.42 4.72 4.11 3.45 2.74 Percent of Maxmum Profts (4.72) 100% 100% 100% 95% 93.7% 100% 87.1% 73.1% 58.1%
Market Adjustment Speed, 8 Table 3-Nash Equlbra Prcng Strateges and Profts n a Nne Perod Dynamc Game wth Two Compettors, (p,[0,1], r=.03).25.5 1.0 Compettor s Intal Share S12.1.3.5.1.3.5.1.3.5 Competor s Behavor: Prce = p2 [3-0 s; 6-1 s] [2-0 s; 7-1 s] [9-1 s] [5-0 s; 4-1 s] NO NO NO [6-0 s; 3-1 s] [6-0 s; 3-1 s] Share = S2 [.1 6.18] [.3 6.41] [.5 6.5] [.1 6.51] [.3 6.51] [.5 6.5] NPV Profts = A2.92 2.48 4.01 1.69 NASH NASH NASH 1.24 1.22 Domnant Frm s Behavor: Prce = p1 [9-1 s] [9-1 s] [9-1 s] [9-1 s] [1;5-0 s; 3-1 s] [6-0 s; 3-1 s] Share = S1 [.9 6.82] [.7 6.59] [.5 6.5] [.9 6.49] EQUIL. EQUIL. EQUIL. [.7 6.49] [.5 6.5] NPV Profts = A1 6.74 4.90 4.01 5.28 1.90 1.22 ------------ ------------ --------- ------------ --------- ---------- ---------- ------------ ------------ Combned Proft 7.66 7.38 8.02 6.97 3.14 2.44 Percent of Maxmum Profts (8.02) 95.5% 92.0% 100.0% 86.9% 39.2% 30.4%
Table 4-Nash Equlbra Prcng Strateges and Profts n a Fve Perod Dynamc Game wth Two Compettors, (p,[0,.25,.5,.75, 1], r=.03) Market Adjustment Speed,.25.5 1.0 8 Compettor s Intal Share S12.1.3.5.1.3.5.1.3.5 Compettor s Behavor: Prce = p2 [.5,.75,.75 [3-.75 s, [2-.75 s, [0,.5,.5, [.5,.5,.75, [.5,.75,.75,1, [0,0,.25, [0,.25,.5,.75,1] [.25,.25,.5,,1, 1] 2-1 s] 3-1 s].75,1].75,1] 1].75,1.75,1] Share = S2 [.1 6 ] [.3 6.33] [.5 6.5] [.1 6.23] [.3 6.38] [.5 6.5] [.1 6.37] [.3 6.47] [.5 6.5] NPV Profts = A2.50 1.42 2.30.62 1.42 2.17.76 1.31 1.66 Domnant Frm s Behavor: Prce = p1 [5-1 s] [.75,4-1 s] [2-.75 s, [5-1 s] [3-.75 s, [.5,.75,.75,1, [4-.75 s, [3-.5 s,.75,1] [.25,.25,.5, 3-1 s] 2-1 s] 1] 1].75,1] Share = S1 [.9 6.88] [.7 6.67] [.5 6.5] [.9 6.77] [.7 6.62] [.5 6.5] [.9 6.63] [.7 6.53] [.5 6.5] NPV Profts = A1 4.17 3.20 2.30 3.91 2.98 2.17 3.34 2.27 1.66 ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ Combned Proft 4.67 4.62 4.60 4.53 4.40 4.34 4.10 3.58 3.32 Percent of Maxmum Proft (4.72) 98.9% 97.9% 97.5% 96.0% 93.2% 91.9% 86.9% 75.8% 70.3%
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