Industry sunk costs and entry dynamics. Abstract

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1 Idustry suk costs ad etry dyamics Vladimir Smirov Uiversity of Sydey Adrew Wait Uiversity of Sydey Abstract We explore a ivestmet game where idustry suk costs provide aicetive for a firm to be a follower ito the market as opposedto a leader. For some parameter values, every firm could have adomiat strategy to wait, eve though immediate etry is sociallyoptimal this is a like prisoers' dilemma. I equilibrium, afirm is more likely to have a domiat strategy to wait with aicrease i the umber of potetial etrats. Fially, theequilibrium ca display a etry cascade. The authors would like to thak Sure Basov, Steve Dowrick, Simo Grat, Marti Osbore, Roha Pitchford, Matthew Rya, Rhema Vaithiaatha, Qua We ad a aoymous referee. Ay remaiig errors are the authors. Citatio: Smirov, Vladimir ad Adrew Wait, (2004) "Idustry suk costs ad etry dyamics." Ecoomics Bulleti, Vol. 12, No. 4 pp. 1 7 Submitted: March 25, Accepted: Jue 4, URL: 04L10008A.pdf

2 1 Itroductio Firm etry is a importat source of ew products ad, as a result, ca sigificatly ehace social welfare (Geroski 1995, p. 436). Whe makig the decisio about whe to eter a market a firm will cosider the beefits of eterig early ad facig less competitio, with waitig ad eterig the market at a later date, possibly after the techology or the market has bee developed. Empirically, secod-movers ofte do better tha the firms that eter a market first (Tellis ad Golder 1996). This paper examies the implicatios for the timig of firm etry ito a market i which there is a secod-mover advatage. A secod-mover advatage could arise i may differet situatios. I Hoppe (2000), a secod-mover advatage arises i a duopoly model of techology adoptio due to ucertaity ad decreasig adoptio costs over time. Here, o the other had, the secod-mover advatage is due to a free-rider effect. As a example, the developmet of a ew market ofte ivolves suk costs. Specifically, a firm may eed to ivest heavily i advertisig i order to geerate kowledge ad stimulate iterest i a ew product. Importatly, it ca be the case that a sigificat compoet of these costs are idustry suk costs, as opposed to firm-specific suk costs. Similarly, ivestmet i research ad developmet ca aid potetial competitors whe itellectual property rights are poorly protected (possibly iteratioally). 1 The same situatio could arise if a govermet implemets arrow (as opposed to broad) patet protectio, allowig secod-movers to imitate iovatios easily. As a modellig tool, this paper icorporates idustry suk costs ito a strategic model of ivestig as a leader or as a follower. The basics of the model are as follows. Before ay firm ca exploit a ew profitable market opportuity, a certai amout of resources eeds to be expeded o either advertisig, to iform the public of the ew product, or o o-pateted research. This cost is bore by firms that iitially eter the market, but this expediture is a public good for all potetial etrats i that, oce the ivestmet has bee suk, all firms ca beefit of this ivestmet if they choose to eter the market. The questio the arises for each firm as to whe they should eter the market: early etry allows them to beefit with fewer competitors but may mea they icur some of the idustry set-up costs; delayed etry may allow a firm to avoid the set-up costs but they also forgo some beefits by ot participatig i the market. Several iterestig results arise out of the model. First, cosider the case whe there are two potetial etry periods. This meas a firm ca eter immediately or it ca sit out of the market for oe period ad eter i the ext period. A firm caot eter the market if it decided ot to eter i both the first two periods. If suk costs are sufficietly high, each firm has a domiat strategy to wait ad ot eter the market util the secod potetial ivestmet period. This result is a type of prisoers dilemma; welfare is reduced by the delay i etry but o firm has a icetive to deviate. Give the free-rider problem here, a delay i ivestmet is more likely to occur with a icrease i the umber of potetial etrats. This is similar to the fidigs of Kapla et al (2003). 2 1 For example, see Stegema (2000), Ostergard (2000) ad Levy (2000) for a discussio of iteratioal protectio of itellectual property ad copyright. I aother cotext, Roberts (2000) argued that patets provided limited protectio to iteret compaies ad their techologies. 2 See Kapla et al (2003) Corollary 1. 1

3 Secod, as as future returs are discouted, if the umber of potetial ivestmet periods is icreased (from two periods), the beefit of waitig util the last opportuity to eter the market, evaluated at the start of the game, is reduced. Whe the potetial ivestmet horizo is sufficietly log, i the symmetric equilibrium the firms will adopt a mixed strategy betwee ivestig ad ot ivestig i this period - this is a coordiatio game. Note, this game differs from the usual coordiatio game somewhat; it is, istead, similar to what Bimore (1992) described as a Australia Battle of the Sexes. Third, oce oe firm has etered the market, all other potetial firms eter as soo as possible. This creates a etry cascade. A similar cascade occurs i Zhag (1997) whe firms have differig private iformatio regardig a ivestmet opportuity ad i Fudeberg ad Tirole (1985), for certai parameter values, whe the cost of adoptig a ew techology is decreasig over time. The model preseted geerates a ivestmet cascade without private iformatio ad decreasig ivestmet costs. Last, the applicatio cosidered here is a etry decisio with idustry suk costs. The model also applies to other scearios i which the firms must make a irreversible ivestmet (or decisio) ad there is a secod-mover advatage, icludig price-settig games (Hamilto ad Slutsky 1990). 2 -firm ivestmet game Cosider the followig set-up. There are 2 firms that are potetial etrats to some ew market. The et beefit from eterig is B per period, to be shared amogst all firms that have etered. 3 Oce etry has occurred there are a ifiite umber of productio periods; all firms discout future returs by δ per period. There are some costs C that are icurred i the first period i which etry occurs, where C is shared amog all the firms that eter B i that iitial period. Etry (by at least oe firm) is efficiet i that > 1 δ C.4 First, cosider the situatio whe there are oly two potetial etry periods, so that a firm ca eter i the first period, eter i the secod period, or decide to ot eter the market at all. 5 Note, i this model there is a exogeously determied deadlie for etry. This could come about if the profitable opportuity dissipates after a certai poit i time because, for example, of the ivetio of a substitute product or techology. 6 Let us show that it is always profitable for a firm to eter the market i the secod period, if it has ot already doe so. Cosider whe o firm etered the market i the first period. If m 1 firms eter i the secod period, the payoff to ay idividual firm from eterig, evaluated at the start of the game, is δ C. As B > C etry is profitable for every firm. If m(1 δ) m (1 δ) at least oe firm etered i the first period the payoff to a firm from eterig i the secod period, agai evaluated at the start of the two potetial ivestmet periods, is if a m(1 δ) 3 B could represet, for example, profits i the idustry that the firms share with perfect collusio. 4 Note that, give there are o firm specific suk costs, the welfare outcome i this model is the same regardless of the umber of firms producig, provided at least oe firm is i the market. 5 This two-period ivestmet game has a similar structure to the bak ru game aalyzed by Gibbos (1992, pp ) ad Diamod ad Dybvig (1983) ad Chamley s (2001) model of exchage rate speculatio. 6 Makig the deadlie (umber of potetial ivestmet periods) edogeous is beyod the scope of the paper ad is left for future research. 2

4 total of m firms etered over both periods. Clearly etry is profitable i this case. As a cosequece, if a firm has ot already doe so it will eter the market i the fial potetial ivestmet period. Secod, usig the result above, ow cosider a firm s decisio as to whether or ot to eter the market i the first period. To examie this issue we cosider: (a) the payoffs from etry whe the firm is the oly etrat; ad (b) whe they share etry i the first period. If 1 firms decide to wait, the beefit to the other firm from eterig i the first period is B C + (1 δ). (1) If the firm does ot eter i the first period, all of the firms will eter i the secod period, so the payoff to this firm is just discouted by oe period payoff of all firms eterig (1 δ) δc. (2) As a result, the payoff of waitig (ot ivestig i the first period) is bigger iff (1 δ )C > B. (3) Coversely, the firm will eter i the first period, give all the other firms do ot eter, if B > (1 δ )C. Now cosider the etry decisio of oe firm whe k of the other firms decide to eter i the first potetial ivestmet period, where 1 > k > 0, ad k 1 decide to wait. If the firm eters i the first period it will get the followig beefit B (1 δ) + ( 1 k ) B C k + 1. (4) O the other had, if it does ot eter it will eter i the secod period ad receive surplus of (1 δ). (5) Comparig these two equatios oe ca ifer that the beefit of waitig is bigger iff C > B. (6) From both these cases, the firm has a domiat strategy to ivest immediately if B > C. It is worth otig that this strategy is optimal i this case regardless of the umber of firms. Whe C > B > C(1 δ ), the firm are i a coordiatio game - each firm prefers to wait if k other firms eter but ivest if o other firms ivest, where > k > 0. I this coordiatio game there are may asymmetric equilibria. For example, firm 1 adopts the strategy to ivest immediately (ad to do so i ay period). All other firms will adopt the strategy to wait i every period util either aother firm has already ivested, or ivest if it is the last period of the game. Asymmetric equilibria have the disadvatage that they 3

5 do ot specify why oe firm eters ad the other firms wait. Our focus, i respose, is o symmetric equilibrium i which a firm will adopt a mixed strategy. If B < C(1 δ ), the firm has a domiat strategy to wait ad ot ivest i the first period. Now let us cosider whe B = C ad B = C(1 δ ). First, whe B = C, if a firm eters ad the other ( 1) firms wait i the first period, the eterig firm will receive a payoff of B C + =. If the firm waits i this case its payoff will be δc. (1 δ) (1 δ) (1 δ) Give that the payoff from eterig is greater tha the payoff from waitig, the firm will opt to eter immediately. If, o the other had, k firms eter i the first period, a firm will be idifferet betwee eterig ad waitig as the payoffs are the same -. Give this (1 δ) idifferece, may asymmetric equilibria exist i which at least oe firm eters, ad all the other firms ca either eter, wait or mix betwee both. However, whe B = C there is oly oe symmetric equilibrium; i the symmetric equilibrium all firms ivest immediately. Secod, cosider whe B = C(1 δ ). If all of the other ( 1) firms wait, a firm will be idifferet betwee eterig ad waitig as payoff i equatio 1 equals the payoff i equatio 2. If at least oe other firm eters immediately, a firm will have a domiat strategy to wait as the payoff give by equatio 4 is less tha the payoff give by equatio 5. I a similar maer to the case above, there are may asymmetric equilibria i which ( 1) firms wait ad the last firm ca either eter, wait or mix betwee both. There is, however, oly oe symmetric subgame perfect equilibrium i which all firms will wait i the first period. This discussio is summarized i Propositio 1. Propositio 1. Cosider the etry game with two potetial ivestmet (etry) periods. If B C all firms ivest immediately i the first period i the symmetric subgame perfect equilibrium (SPE). If C > B > C(1 δ ) each firm will mix betwee eterig immediately ad waitig to eter i the secod period i the symmetric SPE. Fially, if B C(1 δ ), i the symmetric SPE all firms will wait ad oly eter the market i the secod period. If B C(1 δ ) the firms are i a prisoers dilemma: the welfare of every firm would be improved if they all could commit to ivest immediately but each firm has a domiat strategy to wait, reducig total surplus. Now cosider the effect of a chage i. Note that C(1 δ ) is icreasig i ; this icreases the parameter rage for which B C(1 δ ). Thus a icrease i makes it more likely that every firm delays etry. This result arises because icreasig the umber of potetial etrats accetuates the free-rider problem. Corollary 1 summarizes this discussio. Corollary 1. A icrease i the umber of potetial etrats () icreases the iterval for which all firms have a domiat strategy to wait. For argumets sake, assume that B C(1 δ ), so that the firms are i a prisoers dilemma i the two-period ivestmet game. Now cosider the optimal strategies of the firms whe there are three potetial ivestmet periods. I this case, the payoff from waitig for a firm if o oe ivests i the first period is the two-period payoff discouted by a additioal δ - the extra period of delay reduces the beefit of waitig. Reducig the beefit from 4

6 waitig makes immediate etry more attractive. If this reductio i the beefit from waitig is sufficiet, a firm will o loger have a domiat strategy to wait. Istead they will adopt a mixed strategy betwee ivestig ad waitig. Propositio 2 summarizes this discussio. This poit is further illustrated i Example 1. Propositio 2. Assume B C(1 δ ), so that the firms are i a prisoers dilemma i the two-period game. As the umber of potetial ivestmet periods, j, is icreased, for some j > 2 the firms will o loger have a domiat strategy to wait. Proof. The outcome i the two-period game is as above - all firms have a domiat strategy to wait ad will receive a payoff of δ ( B C). If j = 3, the payoffs to the firms 1 δ are the same as i the two-period game, except for the payoff if all firms opted to wait. This payoff will be the two-period payoff, discouted by δ. Provided B + C < δ2 ( B C) (1 δ) 1 δ each firm will still have a domiat strategy to wait. There will be some j > 2 for which B + C > δ(j 1) ( B C); with this umber of periods, each firm o loger has a (1 δ) 1 δ domiat strategy to wait. The firms are the i a coordiatio game. Example 1. This example shows that whe B C(1 δ ) for two ivestmet periods, as the potetial ivestmet horizo is exteded the optimal strategy switches from a prisoers dilemma game to a coordiatio game whe there are a sufficiet umber of potetial ivestmet periods. Let C = 5, B = 3, δ = 0.9. Further, assume that there are three potetial firms. Figure 1 shows the ormal-form game whe there are two potetial ivestmet periods. I the figure, I refers to the strategy to ivest immediately ad W idicates that the firm does ot ivest i that period. The left-had payoff matrix refers to whe firm 3 ivests immediately ad the right-had pael relates to whe she does ot ivest i that immediate period (she plays W ). The payoffs are calculated usig equatios 1, 2, 4 ad 5. Firm 2 I W 25 I Firm 1, 25, 25 8, 9, W 9, 8, 8 9, 9, 7 Firm 3 - I Firm 2 I W I 8, 8, 9 7, 9, 9 Firm 1 W 9, 7, 9 7.5, 7.5, 7.5 Firm 3 - W Figure 1: A prisoers dilemma game for three firms ad two potetial ivestmet periods. As there are two periods, the choice for each firm is to ivest immediately or ivest i the secod ad fial ivestmet period. Each firm has a domiat strategy to wait ad oly ivest i the secod period, as i a prisoers dilemma game. This follows because B C(1 δ ) whe there are two potetial ivestmet periods. If the potetial ivestmet horizo is exteded so that there are three possible ivestmet periods, the oly payoff that is chaged from the above figure is whe all three firms opt to wait (W ) i the first period. I this case, the game proceeds to the ext period; give that there are just two potetial ivestmet periods left the game exactly resembles the twoperiod game. As a result, the payoff to each firm whe they all decide to wait i the first 5

7 period is that payoff from the two-period game (7.5) discouted by the additioal period, which i this case is The payoff for the three-period game are illustrated i Figure 2 below. Firm 2 I W 25 I Firm 1, 25, 25 8, 9, W 9, 8, 8 9, 9, 7 Firm 3 - I Firm 2 I W I 8, 8, 9 7, 9, 9 Firm 1 W 9, 7, , 6.75, 6.75 Firm 3 - W Figure 2: A prisoers dilemma game for three firms i a three-period ivestmet game. Here, due to the additioal discoutig, the payoff from waitig is ot as great as the payoff to ivestig for a firm if the other two firms do ot ivest immediately (7 > 6.75). Each firm o loger has a domiat strategy to wait, ad will adopt a mixed strategy i the symmetric equilibrium. I this mixed strategy equilibrium each firm ivests with a probability of approximately There are several further oteworthy poits that arise out of the model. Note that oce (at least) oe firm has etered ad bore the suk costs, all other firms will eter as soo as possible, creatig a etry cascade. A similar etry dyamic occurs whe firms have a domiat strategy to wait util the fial period. This suggests that etry cascades ca occur whe there are idustry suk costs or whe there is poor protectio of itellectual property, as well as i the presece of asymmetric iformatio (Zhag 1997) ad decreasig ivestmet costs (Fudeberg ad Tirole 1985). Refereces [1] Bimore, K. 1992, Fu ad Games: A Text o Game Theory, D.C. Heath ad Compay, Lexigto. [2] Diamod, D. ad P. Dybvig 1983, Bak Rus, Bak isurace, ad Liquidity, Joural of Political Ecoomy, 91(3), [3] Chamley, C. 2001, Dyamic Speculative Attacks, mimeo. [4] Fudeberg, D. ad J. Tirole 1985, Preemptio ad Ret Equalizatio i the Adoptio of New Techology, Review of Ecoomic Studies, 52(3), [5] Geroski, P. 1995, What do we kow about etry?, Iteratioal Joural of Idustrial Orgaizatio, 13, [6] Gibbos, R. 1992, A Primer i Game Theory, Havester Wheatsheaf, Hertfordshire. [7] Hamilto, J. ad S. Slutsky 1990, Edogeous Timig i Duopoly Games: Stackelberg or Courot Equilibria, Games ad Ecoomic Behavior, 2,

8 [8] Hoppe, H. 2000, Secod-mover advatages i the strategic adoptio of ew techology uder ucertaity, Iteratioal Joural of Idustrial Orgaizatio, 18(2), [9] Kapla, T., I. Luski, ad D. Wettstei 2003, Iovative activity ad suk cost, Iteratioal Joural of Idustrial Orgaizatio, 21(8), [10] Levy, C. 2000, Implemetig TRIPS - A Test of Political Will, Law ad Policy i Iteratioal Busiess, 31(3), [11] Ostergard, R. 2000, The Measuremet of Itellectual Property Rights Protectio, Joural of Iteratioal Busiess Studies, 31(2), [12] Roberts, B. 2000, The Truth About Patets, Iteret World, 6(8), [13] Stegema, K. 2000, The Itegratio of Itellectual Property Rights ito the WTO System, World Ecoomy, 23(9), [14] Tellis, G. ad P. Golder 1996, First to Market, First to Fail? The Real Causes of Edurig Market Leadership, Sloa Maagemet Review, 37(2), [15] Zhag, J. 1997, Strategic Delay ad the Oset of Ivestmet Cascades, RAND Joural of Ecoomics, 28(1),

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