Entry in foreign markets under asymmetric information and demand uncertainty.

Moner-Colonques, Rafael ; Orts, Vicente ; Sempere-Monerris, Jose J. 等

1. Introduction

Entry into foreign markets entails a number of difficulties. One such difficulty is a lack of knowledge of the market characteristics, which may persuade foreign firms to not enter the domestic market. This paper elaborates on the idea that domestic firms hold an informational advantage over foreign firms (see Hirsch 1976; Scherer 1999) in a two-period model of entry mode choice. We offer a complementary explanation for a foreign firm's choice between foreign direct investment (FDI) and exports when FDI is the entry mode that provides better knowledge of local demand. Then, our contribution focuses on a firm's incentive to become multinational and exploit the advantages of being close to the market (market-seeking FDI) rather than to exploit cost advantages in different locations (efficiency-seeking FDI).

The foreign expansion of firms, through exports and FDI, is very likely to involve uncertainty, since the environment in their home market is different from the one they will face in foreign markets. In fact, dissimilarities of any kind create obstacles to successful entry (Buckley and Ghauri 1999). Informational asymmetries between local and foreign brands that can eventually affect the mode of entry may be particularly significant in consumer goods industries, such as consumer electronics, pharmaceuticals, software, automobiles, household appliances, and personal computers. The hypothesis in our paper is reasonably intuitive; yet, to the best of our knowledge, it has not received much attention in the literature--a couple of notable exceptions are Horstmann and Markusen (1996) and Jain and Mirman (2001). In particular, we analyze the role of differential information in determining the foreign firm's entry mode decision.

The model that we examine assumes that (inverse) demand is linear and stochastic. Specifically, the demand intercept consists of an unknown recurrent term, which captures the idiosyncratic features of local economy, and an additive period-specific random shock. The host firm, which is only informed about the recurrent term, is the sole producer in the initial time period, and this generates a noisy market signal. (1) Then the foreign firm uses the information conveyed by the observation of the first-period output choice and price to update its prior beliefs about the stochastic demand in a Bayesian fashion. The second period unfolds in two stages. In the first stage, the foreign firm selects its mode of entry, which has some implications. If it enters as an investor then it incurs a fixed cost, whereas it incurs a variable unit cost if it enters as an exporter. Furthermore, if investment takes place then the foreign firm learns the recurrent term of the stochastic demand; otherwise, it employs its updated beliefs in the second-stage decisions. There is Cournot competition in the second stage, which amounts to either solving a duopoly under symmetric information and identical marginal costs when entry occurs through direct investment, or solving an asymmetric duopoly both in terms of information and marginal costs when entry is via exports.

We find that entry through FDI is favored by greater variability in demand and that it may occur even if variable export costs are zero. Interestingly enough, strategic behavior by the incumbent firm, which deviates from its first-period monopoly output, might be aimed at increasing the probability of foreign entry through FDI despite having to compete against an equally informed and efficient entrant; this never happens in a symmetric information environment. This is due to the strategic uncertainty entailed in the export mode when the foreign firm infers the state of demand based on the observation of the host firm's output and price. If the state of demand inferred were large enough and the uninformed firm entered as an exporter, then the cut into the host firm's output would be so significant that it would be better off facing an informed competitor. A comparison with the symmetric information environment reveals that FDI may be observed in more cases than under a symmetric information setting, either when the foreign firm thinks after observing the first-period price, that local demand is greater than what it actually is, or when there is sufficiently large variability in demand. Finally, the possibility that the foreign firm invests in the acquisition of information but services the market as an exporter is also considered. A condition on the size of the information purchasing cost for such an entry mode not to be an equilibrium is provided.

There is a widespread view that a firm must have some offsetting advantages relative to local firms for it to become a multinational firm that compensates for the inherent costs and risks of doing business abroad. Thus, recent models of the multinational corporation typically give the potential multinational firm a leading role as compared with domestically based firms. (2) Markusen (2002), in a simplified and reworked version of Horstmann and Markusen (1987), assumes that the multinational firm chooses between exports and FDI in a first period and, in a second period, the host firm takes its entry decision. Note, however, that the multinational firm's advantages can be lessened by letting the host firm enter in a later period when market size is larger. Basically, the incumbent multinational firm can often preempt local competition by building a plant in the host country. This result is also found in Smith (1987) and Motta (1992). (3) Our modeling assumes that the local firm is already established and plays before the multinational firm does. In contrast with Smith (1987) and Motta (1992), we introduce uncertainty and asymmetric information to explicitly model that local firms know the domestic market better than a foreign firm. These two features are aimed at placing the potential multinational firm at a disadvantage when entering a foreign market. There exist a few papers that examine FDI in a stochastic setting. Most of them rely on a supply-side view of the market; ours focuses on demand-side aspects. A number of papers have analyzed the behavior of multinational firms under cost and demand uncertainty (e.g., Das 1983; Itagaki 1991). However, this line of research takes the existence of a multinational firm as a given. Recently, Saggi (1998) has considered a monopolist's choice between FDI and exports in a two-period setting with demand uncertainty to examine the issue of timing of entry via FDI.

Very little theoretical work has considered that domestic firms know the market better than foreign firms in a dynamic model. Eaton and Mirman (1991) and Jain and Mirman (2001) analyze a two-period model of learning when a firm holds private information about the demand function in one of two markets. The former paper first examined the issue of dumping under asymmetric information. The latter paper assumes a multinational firm that is a monopolist in the home market and a Cournot duopolist in the foreign market. Outputs are not observable, and the multinational does not know the intercept of the foreign demand function. The elements of information manipulation coupled with increasing marginal costs give rise to deviation from the myopic analysis by both firms. We take this literature in a new direction by studying the effects of asymmetric information on the foreign firm's mode of entry. Some other theoretical works, such as Barros and Modesto (1995) and Horstmann and Markusen (1996), incorporate asymmetric information in the FDI versus export decision. (4) In contrast with these two papers, which deal with a game of mechanism design, we wish to put emphasis on oligopoly interaction in the presence of both uncertainty and informational asymmetry.

The next section begins by presenting the specifics of our model. Then, we characterize the Bayesian-Nash subgame perfect equilibrium of the above described multistage game with incomplete information. A robustness section discusses some extensions of the model. Two sections take up a comparison with the symmetric information setting and the consideration of an additional entry mode. The final section closes the paper.

2. A Duopoly Model with Uncertainty and Informational Asymmetry

The Model

We consider a host country h whose inverse demand for a homogenous good in period t is linear and stochastic in the following way,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where parameter [gamma] is market size, [Q.sub.t] is total output, and [[??].sub.t] is the stochastic price. There are two risk-neutral firms, a host and a foreign firm. There are two sources of uncertainty: (i) an unknown recurrent parameter [??] that reflects the idiosyncratic characteristics of the local economy and (ii) a time-dependent demand shock [[??].sub.t]. The second source of uncertainty makes total output a noisy signal of the demand in the host market. It is assumed that each of these two random variables has full support on R, and that they are independently and normally distributed. (5) In particular, [??] ~ N(m, v) and [[??].sub.t] ~ N(0, [mu]), where m is the mean of [??], v = 1/[[sigma].sup.2.sub.A] is [??]'s precision, and [mu] = 1/[[sigma].sup.2.sub.[epsilon]] is [[??]'s precision. It is convenient to define the expectation of [??] + [[??].sub .t] as the mean of the demand intercept, which in this case coincides with the mean of [??]. These distributions are the priors, which are known by both firms and are common knowledge.

The sequence of events is as follows. There is an initial period where nature selects the true value a of [??] according to the distribution N(m, v). This true value is not necessarily equal to m, but note that a is closer to m when v is large. This value a is exclusively revealed to the host firm, whereas it remains unknown for the foreign firm, so that when the host firm chooses output it is informed about a. In period t = 1, the host firm makes its output choice under uncertainty, and this produces a noisy market signal, [p.sub.1] + (1/[gamma])/[Q.sub.1], which is observed by both firms. Nature selects the time-dependent shock el according to N(0, [mu]), and no firm observes this realization. The prospective entrant observes [p.sub.1] and [Q.sub.1], where [p.sub.1] and [[epsilon].sub.1] stand for the realization of [[??].sub.t] and [[??].sub.t] in period t = 1, respectively; the host firm can, however, deduce the value of [[epsilon].sub.1] since it knows a and observes [p.sub.1]. The firm outside the market updates its knowledge about the stochastic demand after the observation of the signal. The posterior distribution of [??] for a foreign firm according to Bayesian updating is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The posterior mean [??] is a function of the priors and the signal observed; in particular, it is the weighted average according to the relative precisions of the prior mean and the signal. (6)

Then, the following two-stage game is played in period t = 2 using all the information available from period t = 1. In the first stage the foreign firm decides whether to invest or export, and in the second stage both the host and foreign firms compete in quantities, noting that the host firm has observed the foreign firm's entry mode. Before firms compete in quantities, nature chooses the time-dependent demand shock [[epsilon].sub.2] according to N(0, [mu]) and no firm observes its realization. The first-stage decision has an informational implication: (i) In the event of investing, the foreign firm will learn the true value a, that is, it will be an informed firm in the second stage, and (ii) if the foreign firm becomes an exporter then its output choice in the second stage is based on its updated beliefs, that is, the posterior distribution of A and [[??].sub.2] ~ N(0, [mu]). (7) There is then an informational asymmetry between these two ways of serving the host market. Just note that, whether investment or export occurs, there remains some residual uncertainty linked to the random variable [[??].sub.2]; this indicates that none of the firms are certain about inverse host demand. Otherwise the observation of the quantity produced in period t = 1 plus the market price would reveal the true value a to the foreign uninformed firm (see Figure 1). (8)

It is assumed that the marginal cost of output is constant and equal to c for all firms. If the foreign firm exports its output to h, then the firm incurs an additional per-unit export cost [tau]. It can be interpreted as due to natural (e.g., transportation costs) or artificial (e.g., tariffs) barriers to trade. If, alternatively, it establishes a plant in the host country, it incurs a setup cost of G [greater than or equal to] 0, which includes any possible cost associated with the gathering of information.

Equilibrium Analysis

We proceed to characterize the Bayesian-Nash subgame perfect equilibrium of the above multistage game with incomplete information. The game is solved in the standard backward way.

Analysis of Period t = 2

In the second stage of period t = 2, the foreign and the host firms compete a la Cournot, facing a stochastic inverse demand [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Two different scenarios can be reached that in fact are the two subgames that arise for every output choice made by the host firm in period t = 1.

[FIGURE 1 OMITTED]

(i) If the foreign firm decides to invest in stage one, it learns the true value a of, [??], so that there is a homogeneous duopoly with demand uncertainty and symmetric information; the host and the investor firms face the same marginal production costs. Note that for both firms [[??].sub.2] + (1/[gamma])[Q.sub.2] ~ N(a, [mu]), as a result of the residual uncertainty stemming from [[??].sub.2]. Duopolists maximize expected payoffs, and straightforward computations yield the following equilibrium quantities: [q.sup.*.sub.I] = [q.sup.*.sup.HI2] = [[gamma](a - c)]/3, where [q.sup.*.sub.I] denotes the second-period equilibrium output of the foreign firm when it invests and [q.sup.*.sub.HI2] denotes second-period equilibrium output of the host firm when it competes against an investor.

(ii) If the foreign firm enters as an exporter, then it employs its updated beliefs on [??] to make its output choice. There is a homogeneous duopoly with demand uncertainty and asymmetric information. In particular, firms hold different beliefs, that is, for the host firm [[??]sub.2] + (1/[gamma])[Q.sub.2] ~ N(a, [mu]), while for the exporter [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Besides, this setting entails a duopoly with different marginal production costs. Firms maximize the following expected profits where the expectations are taken with respect to all the information available to each firm. Thus

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where [q.sub.E] denotes the second-period output of the foreign firm when it exports and [q.sub.HE2] denotes the second-period output of the host firm when it competes against an exporter.

The first-order condition corresponding to the foreign uninformed firm is given by

[??] - c - [tau] - [2q.sub.E]/[gamma] - [E.sub.qHE2]/[gamma] = 0, (3)

and the one corresponding to the informed host firm and for all possible a is given by

a - c - [2.sub.qHE2](a)/[gamma] - [q.sub.E]/[gamma] = 0, (4)

where [q.sub.HE2](a) denotes that the output of the informed host firm is a function of the true value of a and [E.sub.qHE2] stands for the expectation the uninformed foreign firm has over the output of the informed host firm. The uninformed firm's expectation of [q.sub.HE2] coincides with the equilibrium output that the informed firm would set if it played a symmetric information game with the beliefs of an uniformed firm--see for instance the no information game in Ponssard (1979). (9) The equilibrium outputs are the following: [q.sup.*.sub.E] = [[gamma]([??] - c-2[tau])]/3 and [q.sup.*.sub.HE2](a) = [[gamma](a - c + [tau])]/3 + [[gamma](a - [??])]/6.

In fact, [q.sup.*.sub.E] can be rewritten as [[gamma](a - c - 2[tau])]/3 - [[gamma](a - [??])]/3 so that these output expressions contain two terms: The first one gathers the absence of uncertainty, while the second one captures the effect of demand uncertainty and informational asymmetry. (10) Note that [partial derivative][q.sup.*.sub.HE2]/[partial derivative][??] < 0, whereas [partial derivative][q.sup.*.sub.E]/[partial derivative][??] > 0. In fact, depending on the first-period realization of demand, the difference ([q.sup.*.sub.HE2] - [q.sup.*.sub.E]) might be negative. If this realization is low enough such that a > [??], then the informed host firm will always produce more than the uninformed exporter at equilibrium. In contrast, if the first-period realization of demand is high enough such that a < [??], the difference ([q.sup.*.sub.HE2] - [q.sup.*.sub.E]) shrinks and it might well become negative; this occurs when [??] > a + 2[tau]. Thus, if the uninformed foreign firm thinks after observing the noisy market signal that the market is better than what it actually is, it will produce more compared with a setting where all firms know the true value a of demand. Since the choice variables are strategic substitutes under Cournot competition, the rival informed firm responds with an output decrease. The opposite happens when the uninformed firm, after observing the noisy market signal, thinks that the market is worse than what it actually is. This strategic behavior leads to less variation in price adjustments. Graphically, an informed firm faces a downward sloping demand with an expected vertical intercept a, whereas an uninformed firm faces one with an expected intercept [??]. The distance between these vertical intercepts depends on how precise the observed signal is. To sum up, anything making demand more variable will benefit from the direct investment option.

At stage one in period t = 2, the foreign firm decides on the mode of entry by comparing the expected profits if it enters as an exporter or as an investor. Taking into account beliefs [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the expected payoffs of entry as an investor for all possible a, given that it will learn the true value a of [??], are obtained as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

If the foreign firm enters as an exporter, then its expected payoffs are given by

E[[PI].sub.E] = [gamma][([??] - c - 2[tau]).sup.2]]/9. (6)

A threshold value for [??], denoted by [??], is defined by E[[PI].sub.E] - E[[PI].sub.1] = 0, such that for [??] below (above) [??] the foreign firm will enter the host market as an exporter (investor). (11) Hence, the probability of [??] < [bar.m] is the probability of entry as an exporter. The threshold value is [bar.m] = c + [tau] + [(9G)l(4[tau][gamma])] - [[??].sup.2]/(4[tau])]. The next proposition shows period t = 2 Bayesian-Nash equilibrium.

PROPOSITION 1. Given ([??], [[??].sup.2]), period t = 2 Baycsian-Nash equilibrium is as follows:

(a) The foreign firm enters as an investor iff:

G/[gamma] < 4[tau]([??] - c - [tau]/9 + [[??].sup.2]/9,

with equilibrium outputs given by [q.sup.*.sub.I](a) = [q.sup.*.sub.HI2](a) = [[gamma](a - c)]/3.

(b) Otherwise, it enters as an exporter with the following equilibrium outputs:

[q.sup.*.sub.E] = [gamma]([??] - c - 2[tau])/3 [q.sup.*.sub.HE2](a) = [gamma](a - c + [tau])/3 + [gamma](a - [??])/6.

As usual, the decision about the mode of entry depends on the well-known tension between export variable costs, [tau], and G/[gamma], which is a normalized measure of the costs associated with establishing a subsidiary in the host market.

In the sequel, they will be referred to as adjusted setup costs. Additionally, in this model the entry mode decision is influenced by the updated beliefs (both [??] and [[??].sup.2]). Specifically, the comparative statistics are as follows. Lower adjusted setup cost and higher export variable costs encourage entry as an investor. Furthermore, more dispersion in posterior beliefs and a higher expected intercept for the foreign firm favor entry through FDI. Note that the relationship between [??] and the relevant parameters disclosed by Proposition 1 requires that export variable costs be strictly positive. If these costs were zero, then the entry mode decision would just rely on the expected incremental gains relative to the costs that are associated with entry through FDI rather than via exports. Consequently, it is possible to encounter entry through FDI for zero export variable costs. To fully understand the effect of [??] on the mode of entry, a comparison with a symmetric information environment is required and will be developed below.

Analysis of Period t = 1

Let V([??]) denote the expected value of second-period payoffs to the host firm as a function of the updated beliefs. Recalling that the updated beliefs are a function of first-period output, the expected value V([??]) is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where [[??].sub.1] = a - (1/[gamma])[q.sub.H1] + [[??].sub.1] is first-period price and [q.sub.H1] denotes the first-period output of the host firm, [[PI].sub.HE] ([??]([q.sub.H1])) stands for the host firm's payoffs when the foreign firm enters as an exporter, [[PI].sub.H1](x) is the host firm's payoffs when the foreign firm enters as an investor, and f is the density function of the random variable [[??].sub.i] + (1/[gamma])[q.sub.H1]. Note that in the event that the foreign firm invests the payoffs are not a function of [??] since both firms know a.

In period t = 1 the host firm is a monopolist and solves

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

The first and second terms in Equation 8 are the first-period and the second-period expected payoffs, respectively. We are interested in assessing whether [partial derivative]V[[??]([q.sub.H1])]/[partial derivative][q.sub.H1] is different from zero. In case it is zero, the output [q.sub.H1] that solves [partial derivative]E[[PI].sub.H]/[partial derivative][q.sub.H1] = 0 coincides with the monopoly output, which will be referred to as the myopic solution. On the other hand, if it differs from zero its sign will determine whether the host firm chooses an output above or below the myopic solution.

LEMMA 1. [partial derivative]V[[??]([q.sub.H1])]/[partial derivative][q.sub.H1] = (1/[gamma])f([bar.m])[[[PI].sub.HE]([bar.m]) - [[PI].sub.HI](x)].

PROOF. See the Appendix.

Therefore, the sign of [partial derivative]V[[??]([q.sub.H1])]/[partial derivative][q.sub.HI] is given by the sign of [[PI].sub.HE]([bar.m]) - [[PI].sub.H1](x). Since [partial derivative][q.sup.*.sub.HE2]/[partial derivative][??] is negative, [[PI].sub.HE]([bar.m]) are interpreted as the lowest payoffs the host firm will obtain provided the foreign firm enters as an exporter. A positive sign on the difference means that the host firm is better off with an exporter rival. It implies that the host firm will produce an output above the myopic solution. Such an output choice is intended to increase the probability mass that lies in the lower tail of f[[[??].sub.2] + (1/[gamma])[Q.sub.2]]. In other words, the host firm may influence in probabilistic terms the entry mode of the foreign firm at the beginning of period t = 2. Since [[PI].sub.HE]([bar.m]) = {[gamma][[2(a - c + [tau]) + a - [bar.m]].sup.2]]}/36 and [[PI].sub.H1] = [[gamma] [(a - C).sup.2]]/9, the difference is positive iff G/[gamma] < [4[tau](a - c + [tau]) + [[??].sup.2]/9, which allows us to characterize the first-period equilibrium. (12)

PROPOSITION 2. Period t = 1 Bayesian-Nash equilibrium for the host monopolist entails an equilibrium output above the myopic one iff

G/[gamma] < 4[tau](a - c + [tau]) + [[??].sup.2]/9;

the equilibrium output is set below the myopic one, otherwise.

Once competition takes place in period t = 2 it is known that, in a certainty context, the host firm definitely prefers to compete with a foreign exporter since the rival bears higher marginal costs. Nevertheless, this intuition is unclear in the presence of asymmetric information where the host firm is better informed about market demand since the host firm's profits are decreasing in [??] in case the foreign firm enters as an exporter. The export entry mode precisely entails strategic uncertainty when the foreign firm infers the state of demand based on the host firm's first-period output and price. As noted above, if the uninformed foreign exporter's revised beliefs are that the market is much better than what it actually is, then the host firm will enjoy a smaller market share since outputs are strategic substitutes. It is therefore natural that the host firm acts strategically by deviating from the myopic solution in order to modify, in probabilistic terms, the foreign firm's entry decision and the corresponding market equilibrium. Specifically, Lemma 1 states that the host firm does change its first period monopoly output, which means that it sacrifices first-period payoffs to later enjoy greater profits in the second period. Thus, Proposition 2 presents the direction of the deviation in the first-period output choice with respect to the myopic solution in order to try and induce either mode of entry. Note that overproduction, an equilibrium output choice in period t = 1 above the myopic solution, will rise for sufficiently low adjusted setup costs since the host firm will then prefer to compete against an exporter; that is, the host firm is better off coping with some strategic uncertainty rather than competing against a more efficient rival. Notice that small adjusted setup costs will imply the foreign firm's entry via FDI for a relatively low expected demand intercept, other things equal. This is not an attractive scenario for the host firm provided that condition G/[gamma] < [4[tau](a - c + [tau]) + [[??].sup.2]/9 is the same as condition [bar.m]] < a + 2[tau], and this means that the lowest second-period profits the host firm could expect in case of entry via exports are indeed higher than the corresponding ones in the case of entry via FDI (i.e., [[PI].sub.HE]([bar.m] > [[PI].sub.HI](x)). In such a setting, the host firm selects a first-period equilibrium output above the myopic one in order to decrease the rival's probability of entry as an investor, i.e., the probability that [??] > [bar.m]. Graphically, the host firm tries and shifts leftward the density function f[[??].sub.2] + (1/[gamma])[Q.sub.2]] for the foreign firm. Overproduction entails the host firm favoring its most preferred mode of entry while increasing its expected second-period payoffs in case of entry via exports. Besides, overproduction will imply a lower expected first-period price, which, since the monotone likelihood ratio property (MLRP) holds, is interpreted by the foreign firm as a worse host market. Then, in the case of entry via exports the foreign firm will produce less in equilibrium and, given that firms compete in quantities, the host firm will produce more in the second period. Therefore, the host firm would obtain greater payoffs had it produced the myopic output in the first period.

On the other hand, if adjusted setup costs are sufficiently high (i.e., [4[tau](a - c + [tau]) + [[??].sup.2]]/9 < G/[gamma]) then underproduction, an equilibrium output choice in period t = 1 below the myopic solution, appears in equilibrium. Underproduction is aimed at shifting rightward the density function f[[??].sub.2] + (1/[gamma])[Q.sub.2]] for the foreign firm to induce entry via FDI. The reason for this is that, since now a + 2[tau] < [bar.m], the strategic uncertainty borne by the host firm when entry occurs via exports is rather large since there are higher levels of [??] that will imply entry via exports, as compared with the case where [bar.m] < a + 2[tau]. Since the second-period host firm's profits are decreasing in [??], we will find situations where [[P].sub.HE]([??]) < [[PI].sub.HI](x). In such a case, the host firm finds it optimal to underproduce to encourage a change in the entry mode; this is better than choosing a first-period output above the myopic solution, and thereby a reduction of [??], despite increasing its second-stage profits in case it faced an exporter.

For further intuition, note that the worst situation for the host firm is to compete with an exporter that believes that the market is largely better than what it actually is, but not enough to change the foreign firm's entry choice to FDI. The reason is that the exporter will produce more at equilibrium and the host firm's best response is to accommodate by producing less. As a result, [[PI].sub.HE]([??]) are lower than those obtained if the host firm faced a foreign investor, that is, [[gamma][(a - c).sup.2]]/9. The host firm knows that when the foreign firm believes that the market is good enough then it will enter via FDI. Therefore, the departure from the myopic output is aimed at changing the foreign firm's expected mode of entry. With underproduction, a higher expected first-period price is realized, which, since the MLRP holds, is interpreted by the foreign firm as a good market. This thus reduces the likelihood of facing an exporter that incorrectly believes that the market is better than it is, but not enough to enter via FDI. Summarizing, over- or underproduction is a way for the host firm to exchange lower payoffs today for higher payoffs tomorrow in a profitable manner.

Therefore, the first-period output decision influences, in probabilistic terms, the foreign firm's mode of entry at the beginning of period two. Finally, note that, had we assumed symmetric information, then the host monopolist would have never deviated from the myopic equilibrium output since the choice of [q.sub.H1] would not have any commitment value given that both periods would not be linked anymore. Similarly, in case export variable costs were zero, then the foreign firm's entry mode decision would not depend on [??]; in such an eventuality it is pointless for the host firm to sacrifice profits in period t = 1 to affect the entry mode, and it chooses the myopic solution in the first period.

Figure 2 summarizes the direction of the deviations, above or below the first period myopic output, for the host firm, and the mode of entry, direct investment or exports, for the foreign firm. By Proposition 1, entry through direct investment (FDI) will rise if G/[gamma] < [4[tau]([??] - c - [tau]]/9 + ([[??].sup.2]/9), or equivalently if [bar.m] < [??], that is, above the 45[degrees] line; otherwise, there will be entry via exports (E). As indicated by Proposition 2, whenever G/[gamma] < [4[tau](a - c + [tau]) + [[??].sup.2]]/9, or equivalently for all [bar.m] < a + 2[tau], the informed host firm will deviate from the myopic solution and overproduce with the purpose of favoring entry via exports. This is more likely to happen for relatively low [bar.m], which will be observed when adjusted setup costs are rather low or when there is a greater variability in demand. However, as Figure 2 shows, we may find situations where the host firm overproduces, and there is entry via FDI; this is because the first-period realization of the demand shock is such that [??] is greater than [bar.m] There are other situations where the realization of the demand shock is such that [??] is lower than [bar.m]. Only in these latter cases is the host firm's goal achieved in the sense that its most preferred entry mode actually occurs. Similarly, underproduction by the host firm followed by entry via FDI (its preferred mode of entry) shows up when adjusted setup costs are relatively high (or [[??].sup.2] relatively low) and the realization of the demand shock is sufficiently large.

Robustness Analysis

We have just characterized the behavior of the host firm in the first period. This section elaborates on some extensions to assess how robust our result is.

Given that the host firm's output is crucial to the analysis and that it may not be empirically valid, it is interesting to discuss how the fact that the host firm's first-period output was not observed might alter the foregoing incentives that the informed host firm has to deviate from in the myopic solution. Put differently, we wish to elaborate on how the results will change when there is signal jamming. Since the uncertainty is assumed on the demand intercept, the host firm cannot affect the (noisy market) signal but it can modify the position of the density function of the stochastic price. In particular, it can be proved that the host firm will deviate by producing above the myopic solution in more situations as compared with the setting where signal jamming was not at stake. The change in the second-period host firm's expected profits now includes a new term, which is positive. (13) The change in the first-period price has an effect on the expected intercept [??], and the host firm's profits when facing an exporter vary as [??] varies. Since the host firm's second-period profits are decreasing in [??] when competing with an exporter, and it also happens that [??] increases with [p.sub.1], it follows that the host firm has a greater incentive to overproduce with the purpose of shifting leftward the density function of the stochastic price and consequently further favoring entry via exports.

[FIGURE 2 OMITTED]

Consider that in the first period there is already a duopoly where the informed host firm competes with an uninformed foreign exporter. If, as in the model, outputs are observable, then information from period one might make the foreign firm decide to switch to FDI in the second period. Concerning the host firm's behavior, note that the expected value of second-period payoffs would now be written in terms of the corresponding updated beliefs, but the same effects are at work. There is, however, an additional strategic effect since the host firm is not a monopolist anymore. Still, we should expect deviations from the myopic duopolistic output choice. If, on the other hand, outputs are not observable, then signal jamming occurs when firms have different information sets about the state of demand. The informed firm's incentives to manipulate information become increasingly complex, and the analysis is beyond the scope of the paper.

We next wish to discuss variations of the distribution functions of the key random variables. The proof of our results has assumed a Gaussian model approach; that is, both the state of nature and the private signals are the realizations of Gaussian random variables. Each of the two random variables has full support on R, and they are independently and normally distributed. One then wonders whether our conclusions might change under different assumptions. Before proceeding it is worth mentioning that in situations where Bayesian learning occurs, the Gaussian model approach is very often used because of the simplicity of this learning rule. Such simplicity relies on the following features. First, the normal distribution is summarized by the most intuitive parameters of a distribution, the mean and the variance (or the precision). Second, both the Bayesian updating rules for the mean and the variance are linear, which simplifies computations. Third, the signal contributes to the information on the state of nature in a way that is measured by the increase in the precision of the latter, which exactly coincides with the signal precision. Finally, and more importantly, the increase in the precision on the state of nature is independent of the realization of the signal and, therefore, can be computed ex ante. This is central since, when firms decide about some action that will have consequences on information acquisition, as in our setting, it is crucial to get an ex ante measurement of the information gain.

We argue that our results are not sensitive to the particular distribution functions of the random variables so long as any alternative distributions of the noise component of the signal satisfy both the strict MLRP and full support on the real line. The discussion that follows is focused on these features. The distribution of the noise component of the signal is very often assumed to satisfy the strict MLRP by the modeling methods employed in information economics, as is the case of the literature on experimentation and information manipulation. With this assumption, the agents' beliefs are affected by the signal in a regular way. In our model, the posterior mean of host inverse demand increases in the observation of a higher price. Thus, a high price is interpreted as a better state of demand since, by the MLRP, it is more likely to have come from a high demand curve. In this way, the host firm has an incentive to underproduce with the purpose of shifting rightward the density function of the stochastic price and consequently to favor entry through FDI, when it is the host firm's preferred entry mode; such an effect does not depend on the normality assumption. Among the families of density functions and probability mass functions that exhibit the MLRP are (apart from the normal with mean a, the true state of nature) the exponential and Poisson with mean a, the uniform under the interval [0, a], the chi-square (with noncentrality parameter a), and many others. It is more difficult to reach clearcut conclusions when the MLRP fails. For example, in the literature on experimentation, the direction of experimentation might change; here, underproduction might not be always undertaken when the host firm prefers facing an investor.

The support of the noise component of the signal is unbounded in the Gaussian model approach adopted. To examine the likely changes that a bounded support might bring about, consider the following modification and simplifications in our model. (14) Assume that host inverse demand is given by [p.sub.t] = [??] - [Q.sub.t] + [[??].sub.t] and that marginal cost of production c equals zero. There are two possible realizations of the state of nature [??] = {[a.bar], [bar.a]} with [bar.a] > [a.bar] > 0. The uninformed firm's prior probability that [??] - [bar.a] is denoted by [[rho].sup.0], and [rho]([p.sub.1], [q.sub.H1], [[rho.sup.0]) denotes the updated probability of the good state of nature. Further assume that the distribution of the random variable [[??].sub.t], the noise component of the signal, is characterized by a continuously differentiable density function f([[??].sub.t]) with zero mean and supp([[??].sub.t]) = (- s, s), for s [member of] [R.sup.+]. A direct implication of the boundedness of the support for [[??].sub.t] is that, depending on the first-period price, the uninformed firm might learn the true state of nature. To see this, note that two intervals of the conditional distribution of [[??].sub.1] can be constructed: In one, the observation of [p.sub.1] conditional on [??] = [a.bar] must satisfy that [p.sub.1] + [q.sub.H1] [member of] [[a.bar] - s, [a.bar] + s], and in the other, the observation of [p.sub.1] conditional on [??] = [bar.a] must satisfy that [p.sub.1] + [q.sub.H1] [member of] [[bar.a] - s, [bar.a] + s]. Hence, there are two possibilities:

(i) The everywhere fully revealing case (EFR), which occurs when the above two intervals do not overlap, that is, when [a.bar] + s < [bar.a] - s or s < ([bar.a] - [a.bar])/2. In this case, the uninformed foreign firm always learns the true state of nature and, therefore, if it observes [p.sub.1] such that [p.sub.1] + [q.sub.H1] [member of] [[a.bar] - s, [a.bar] + s], it updates its beliefs to [rho]([p.sub.1], [q.sub.H1], [[rho].sup.0]) = 0, whereas if it observes [p.sub.1] such that [p.sub.1] + [q.sub.H1] [member of] [[bar.a] - s, [bar.a] + s], then [rho]([p.sub.1], [q.sub.H1], [[rho].sup.0]) = 1.

(ii) The not everywhere fully revealing case (NEFR), which occurs when s > ([bar.a] - [a.bar])/2 and the intervals overlap. The updated beliefs of the good state of nature are then given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

so that there is full revelation of the true state of nature depending on the realization of [p.sub.1].

Considering the above, the conclusions of the paper have to be qualified. If in the EFR case asymmetric information is removed after period one, then the foreign firm's mode of entry will coincide with the one that would occur under symmetric information--which happens to be entry via exports when [??] = [a.bar] and entry via FDI when [??] = [bar.a]. Since the host firm is unable to affect the posterior beliefs of the foreign firm, it will produce the myopic output because there is nothing to gain in deviating from the first-period monopoly quantity. However, the NEFR case yields similar results to the analysis in the paper. When the observation of [p.sub.1] is such that we are in the middle branch of Equation 9 then the uninformed firm's posterior is nondegenerate. We may then compute its expected payoffs for each entry mode. The uninformed foreign firm reaches a decision rule in a way that, when [rho]([p.sub.1], [q.sub.H1], [[rho].sup.0]) is smaller than a threshold probability [[rho].sup.*], entry occurs via exports; if it is greater than [[rho].sup.*], then entry occurs via FDI. As to the host firm's behavior in period one, consider that the true state of nature is [a.bar]. Since this is known by the host firm, then it knows that any possible realization of [p.sub.1] implies that [p.sub.1] + [q.sub.H1] belongs to either the interval [[a.bar] - s, [bar.a] - s) or the interval [[bar.a] - s, [a.bar] + s]. The former interval fully reveals the state of nature and the latter one does not. Therefore, the corresponding second-period expected payoffs consist of two terms. The first term is equal to the probability that the market signal falls in the fully revealing interval multiplied by the payoffs of competing against an exporter who knows that [??] = [a.bar]. The second term is equal to the probability that the market signal falls in the other interval multiplied by the expected payoffs of facing an exporter (when [rho] < [[rho].sup.*]) plus the expected payoffs of facing an investor (when [rho] > [[rho].sup.*]). The latter term indeed captures the analysis in the model where the support is unbounded, given that with the Gaussian model approach there is no full revelation. The former term introduces the possibility that the host firm might deviate from the myopic output in order to reveal that the state of nature is bad. Consequently, the host firm's period one output choice internalizes that its decision affects the probability that the market signal may fall in the fully revealing interval.

A Comparison with the Symmetric Information Setting

To fully understand the role played by uncertain demand and informational asymmetry in the export versus direct investment decision, we proceed to establish a comparison with the symmetric information case. First, note that in the latter case, as indicated above, the host monopolist would not deviate from its monopoly output because its choice has no commitment value, and hence both periods would not be linked anymore. Therefore, the only interesting issue amounts to studying the mode of entry choice and comparing it with that of the previous section. The corresponding second-stage output expressions for period t = 2 can be easily obtained by taking a = [??] in part (b) of Proposition 1. Then, the next result immediately follows:

RESULT 1. If 0 < G/[gamma] [4[tau](a - c - [tau])]/9, then the foreign firm enters as an investor; otherwise, it enters as an exporter.

To be consistent with the analysis of the uncertain demand with informational asymmetry case, we assume that no entry is not allowed. This is implied by the following restriction on the parameters: a > max{c + 2[tau], c + 3 [square root of (G/[gamma]]}. The comparison of Proposition 1 with the above result yields the following Proposition.

PROPOSITION 3. The range of G/[gamma] that induces entry by the foreign firm as an investor does not necessarily shrink when demand uncertainty with informational asymmetry is introduced.

The proof easily follows by comparing expressions [4[tau](a - c - [tau])]/9 and [4[tau]([??] - c - [tau]) + [[??].sup.2]]/9. For the case ([??] - a > 0), the latter expression is always greater than the former; therefore, the range of G/[gamma] that induces entry as an investor is greater under demand uncertainty and informational asymmetry. On the contrary, if a - [??] > 0, the range of G/[gamma] that induces entry as an investor is greater under demand uncertainty and informational asymmetry if the updated variance is sufficiently large, that is a - [??] < ([[??].sup.2]/4[tau]); the opposite holds otherwise. Note that, while it might be expected that direct investment will occur in more cases under a certainty environment, we have found that uncertainty and informational asymmetry need not go against the direct investment decision.

An Additional Entry Mode

The foregoing analysis has considered that the informational aspect and the cost aspect of each entry mode are nonseparable. One wonders how the entry mode choice would be affected by letting the foreign firm invest in that acquisition of information about the permanent characteristics of the local economy and serve the host market as an exporter. Thus, there is a third scenario in the second stage of period t = 2 where both the host and foreign firms are informed about the true value a of [??], but duopolists are asymmetric in marginal costs since the foreign firm bears an additional per-unit export cost [tau]. The amount paid for the acquisition of the information is denoted by [beta]G. It is assumed that [beta] belongs to the interval (0, 1); values of [beta] greater than one imply that this entry mode is never employed at equilibrium. The parameter [beta] is interpreted as the proportion of the setup costs devoted to purchasing the information. The second-stage equilibrium quantities are the following: [q.sup.*.sub.M] = [[gamma](a - c - 2[tau])]/3 and [q.sup.*.sub.HM2] = [[gamma](a - c + [tau])]/3, where subscript M stands for the entry mode that mixes investing in information and exporting.

At stage one in period t = 2 the foreign firm's expected payoffs corresponding to this additional mode of entry are obtained as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)

Comparing the three entry modes leads to the following result:

RESULT 2. Investing in information and exporting will not be an equilibrium entry mode as long as

[beta] > 1/(G/[gamma]) min {G/[gamma] - 4[tau]([??] - c - [tua])/9, [[??].sup.2]/9}.

Subtracting Equation 10 from Equation 6 yields the first term in the above condition. It gathers the opportunity cost of tariff jumping provided that both entry modes suppose knowledge about a. Therefore, the sign of this difference is the result of the tradeoff between the adjusted setup costs of FDI versus the export variable costs. Similarly, the second term is obtained by subtracting Equation 10 from Equation 7, which measures the opportunity cost of acquiring the information about a provided both entry modes entail the same export variable costs. Note that the condition that establishes which of the two terms is the minimum coincides with the one that determines the FDI versus export choice in Proposition 1. Thus, the above condition discloses that the proportion of the setup costs devoted to purchasing the information must be sufficiently large for the entry mode through investing in information and exporting not to appear at equilibrium. Hence, the previous results would remain valid to the consideration of this additional mode of entry.

3. Concluding Remarks

This paper has moved one step further in the study of entry and information acquisition with an application to the internationalization decisions of firms. While the entry mode decision has been extensively explored, the impact of uncertainty for all firms along with the fact that potential entrants hold less information on domestic demand characteristics has thus far been ignored. We have argued that a foreign firm may engage in direct investment in order to acquire knowledge about foreign markets rather than exploit advantages of any type. We have considered a two-period model with one host firm and one foreign firm; the host firm produces in both periods but the foreign firm produces only in the second period. The foreign firm decides, before second-period production, whether to serve the host market via exports or FDI. The analysis offers some interesting insights that remain valid as long as either entry mode has both cost and informational implications. There are no structural linkages between the two periods, yet the host firm's first-period decision provides a noisy signal that conveys statistical information about market size; the incumbent host firm will typically deviate from its first-period monopoly output to influence, in probabilistic terms, the foreign firm's entry mode. The consideration of several modes of entry together with the fact that there is not a uniquely preferred mode for the incumbent results in output choices below or above the myopic solution. Interestingly enough, the informed host firm may produce below the myopic solution in equilibrium to favor entry via FDI. This occurs when strategic uncertainty is important since otherwise entry via exports of the uninformed foreign firm would imply a large reduction in the second-period expected profits so that the host firm indeed prefers to compete against an informed and equally efficient entrant. A fruitful line of future research would be to deepen into the combination of entry in foreign markets and information gathering. One such possibility could contemplate a dynamic model where the timing of investment is thoroughly analyzed in order to better understand some observed behavior by multinational firms.

Appendix

PROOF OF LEMMA 1. Recall that [[??].sub.1] + (1/[gamma])qH1 ~ N(a, [mu]), with density function

F([[??].sub.1] + 1/[gamma][q.sub.H1]) = [square root of [mu]/2[pi][e.sup.-1/2[mu]([[??].sub.1] + 1/[gamma][q.sub.H1] - a).

The partial derivative of the expected value of second-period payoffs is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(a) Integration of the second term by parts, noting that {[partial derivative]f[p.sub.1] + (1/[gamma])[q.sub.H1]]}/[partial derivative]f[p.sub.1] + (1/[gamma])[q.sub.H1]]}/[partial derivative][p.sub.1], yields

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(b) Integration of the third term reads

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Rearranging,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Noting that [partial derivative][??]/[partial derivative][q.sub.H1] = [partial derivative][??]/[partial derivative][p.sub.1] x 1/[gamma] gives the expression in Lemma 1

[partial derivative]V([??]([q.sub.H1]))/[partial derivative][q.sub.H1] = 1/[gamma] f([bar.m]) [[[PI].sub.HE]([bar.m]) - [[PI].sub.HI](x)].

We would like to thank Christos Constantatos, Amparo Urbano, the editor Laura Razzolini, and two referees for their useful comments and suggestions. We gratefully acknowledge the financial support from Spanish Ministerio de Educacion y Ciencia and FEDER projects SEJ2004-07554/ECON and SEJ2005-08764/ECON.

Received April 2006; accepted January 2007.

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(1) A portion of the literature on entry deterrence has examined the role of prices as signals that convey information about determinants of postentry profitability (see the preeminent paper by Milgrom and Roberts 1982). Both private information and uncertainty are assumed in Matthews and Mirman (1983) so that price is a noisy signal that only delivers statistical information.

(2) Specifically, oligopolistic settings that formally address the strategic role of FDI by making use of a game-theoretic approach include Smith (1987), Horstmann and Markusen (1987, 1992), and Motta (1992, 1994), among many others.

(3) Both these papers consider a change in the sequentiality of decisions so that the host firm makes its entry decision before the foreign firm's choice about how to serve the host market. In particular, Motta (1992) suggests that if the host firm is the first mover then it may happen that the foreign firm does not enter at all the no entry strategy is not contemplated by Smith (1987).

(4) Specifically, these authors compare entry by a foreign firm via FD1 with entry via a contractual arrangement with a local agent, who has private information about market characteristics. This creates agency problems, and the multinational firm must weigh the gains from information gathering--and thus avoid costly mistakes if direct investment occurs--against the surplus the agent can extract because she has superior (private) information about the market.

(5) The distributional assumption of normality of the random variable makes a closed-form solution possible. However, this assumption is by no means essential since the results in the paper will continue to hold as long as the probability distribution function satisfies the monotone likelihood ratio property (MLRP) and the support is unbounded. A robustness discussion of variations of the distribution functions, as well as of the support of the random variables, is given later.

(6) These formulae can be found in DeGroot (1970). Further, note that the sign of ([??] - m) is ambiguous since it is given by the sign of (a + [[epsilon].sub.1] - m) and, therefore, it can be either positive or negative regardless of a being above or below m. This is because of the influence of the time-dependent demand shock. Also, the posterior precision increases with the mere fact of observing the signal.

(7) This assumption relating the information about a and the way of serving the host market is made for the sake of exposition. There are no qualitative changes in the results as long as the investment strategy implies learning about a in a faster way than the exporting strategy.

(8) There is an extensive literature devoted to the analysis of information acquisition and manipulation. Finns facing stochastic demand have an incentive to gather information by engaging in experimentation; this is achieved by adjusting their myopic decisions in order to affect their own information flow. Firms will find it optimal to experiment depending on the nature of the strategic variables and whether uncertainty is on the intercept or the slope of demand (see, e.g., Mirman, Samuelson, and Urbano 1993b; Harrington 1995; Alepuz and Urbano 1999). If, in addition, the actions of firms are not observable by rivals, then there arises an informational interaction even when the opportunity to experiment is not present. This interaction leads firms to adjust their unobserved actions to manipulate the beliefs of rivals; this conduct is known as signal jamming (see Mirman, Samuelson, and Urbano 1993a; Urbano 1993). Neither experimentation nor signal jamming are an issue here given the structure of information; also, the incumbent cannot affect the precision of the noisy signal by altering its first-period output since uncertainty is assumed on the intercept and not on the slope of demand. The incumbent can nevertheless manipulate its output to modify the foreign firm's mode of entry in probabilistic terms since, by doing so, it conveys statistical information about its private information.

(9) This is equivalent to taking the expected value with respect to the information available to the uninformed firm for all possible a in the informed firm's first-order condition, which yields [Eq.sub.HE2] = [[gamma]([??] - c) - [q.sub.E]/2. Substituting this in the uninformed firm's first-order condition and solving for [q.sub.E] and [q.sub.HE2](a) yields the equilibrium quantities in the text.

(10) Note that given the normality assumptions on the random variables, their realizations may take on negative values. Since firms are constrained to choose positive quantities, this possibility can be disregarded by appropriately choosing the variances in the model.

(11) Note that we are disregarding the case of no entry. No entry will not happen if [??] is sufficiently large, that is, if and only if [??] > max{c + 2[tau], c + [square root of (9G/[gamma]) + [??]]}.

(12) The Bayesian learning rule from a Gaussian model implies, among other things, that [[??].sup.2] can be computed by the host firm ex ante since it is obtained directly from the priors.

(13) This term is -(1/[gamma])[[partial derivative][[PI].sub.HE](m)/[partial derivative][bar.m]]([partial derivative][[bar.m]/[partial derivative][p.sub.1]) [[integral].sup.m.sub.-[infinity]] f[p.sub.1] + (1/[gamma])[q.sub.H1]][dp.sub.1] > 0.

(14) The computations are available from the authors upon request.

Rafael Moner-Colonques, * Vicente Orts, ([dagger]) and Jose J. Sempere-Monerris ([double dagger])

* Department of Economic Analysis and ERI-CES, University of Valencia, Campus dels Tarongers, Avda, dels Tarongers s/n, 46022-Valencia, Spain; E-mail Rafael.Moner@uv.es; corresponding author.

([dagger]) Department of Economics and International Economics Institute, University Jaume I, Castellon, Campus Riu Sec, Avda. Sos Baynat, s/n, 12006-Castellon, Spain; E-mail orts@eco.uji.es.

([double dagger]) Department of Economic Analysis and ERI-CES, University of Valencia, Campus dels Tarongers, Avda, dels Tarongers s/n, 46022-Valencia, Spain; E-mail Jose.J.Sempere@uv.es.