Higher the bribe (ie more is the 'height' of the barrier to entry), lower will be the fairness. In the … first stage, the incumbent (…rm 1) decides on a level of bribery, b ('height' of the entry barrier). We show that if the bribe (the 'height' of the entry barrier) chosen by …rm 1 in the …first stage is below a threshold value (b), then all types of …rm 2 enter.
If the bribe (the "height" of the barrier to entry) is between b and b (where b > b), then some types enter ...rm 2. If the market sizes are large enough, then the optimal bribe (the optimal "height" of the barrier to entry) is in the interval b; b. When the good is a complement (ie <0), we show that the optimal bribe (the optimal 'height' of the entry barrier) is always zero (free entry is guaranteed in equilibrium).
Does an increase in uncertainty lead to an increase in the equilibrium bribe (the "height" of the entry barrier) and a decrease in market quality. Note that the …m task always chooses zero bribes in the …first stage when the goods are complementary.
Related Literature
In Dixit (1980), the original firm's irrevocable investment ... allows the firm to change its own marginal cost curve and thus the post-entry equilibrium. The role of such an irrevocable investment in entry deterrence is to change the initial conditions of the post-entry game in favor of the incumbent ... rm. However, unlike Dixit (1980), in our model such a bribe changes the marginal cost of the potential market entrant and not the marginal cost of the incumbent firm.
Note that there is a business-stealing effect if the equilibrium output per …rm decreases as the number of …rms grows. Note that if an additional competitor reduces output per income in a homogeneous Cournot oligopoly (there is corporate theft), market entry will be excessive (from a welfare perspective). Maskin (1999) analyzes a model in which capacity installation by an incumbent firm deters others from entering the industry.
However, the incumbent may increase the operating costs of …rm 2 by paying a bribe (sayb) to a politician, which may in turn harm a potential entrant. In the second stage, the entrant (...rm 2) observes its own marginal costs and then decides whether to enter or not.
Notations and Assumptions
Note that when is unity then the products are homogeneous (perfect substitutes) and when is zero the products are independent.
Third stage equilibrium
Given the equilibrium outcome in the third phase, we then proceed to analyze the game in the second phase. In the second phase…rm 2 makes a move and chooses to enter or not. We analyze the relationship between the bribes paid (height of the nerdy barrier) in the…first stage and the entry decision of…rm 2 in the second stage.
… We first analyze the behavior of … rm 2 when its type = 0 (ie, the lowest possible type). We then show that even the lowest possible species ( = 0) will receive a strictly positive payoff¤ if it enters. This means that if b = 0 (...rm 1 does nothing), all types (even the type with the lowest efficiency) will choose to enter.
Remark Note that …rm 2 enters i¤ it expects strictly positive pro…t in the post-entry game. This will help us derive the most important results about optimal bribes (optimal entry barrier height) in the next section.
First stage equilibrium
Optimal bribe (height of entry barrier)
Remark Other things remaining the same, the market size, A, and the differentiation parameter, play a decisive role in determining the optimal bribe,b (optimal height of entry barrier). If A and is small enough, then the optimal bribe (optimal height) is zero (for small A and the inequality in Proposition 4(i) is likely to be satisfied...). On the other hand, if A and is large enough, a positive b (or even the highest possible bribery level, b) can be observed in equilibrium (Proposition 4 - (ii) and (iii)).
It states that if there is an equilibrium with strictly positive bribery, then the level of such a bribe will be at least b. Therefore, in equilibrium we will observe either a "zero" bribe or a bribe that is at least b. Therefore, it is at least possible bribes (height of the entry barrier) higher if the market size, A, is larger.
Remark When goods are complemented, regardless of the level of fairness index (or market quality), we observe no bribe (zero height of entry barrier) in equilibrium. With complements, however, it is better for the incumbent …rm to allow entry, as it boosts its demand and therefore its pro…t. In emerging economies like India, where market quality is poor, it is better for the government to promote competition in complementary goods.
Since competition in substitutes tends to eat away benefits, the incumbent finds it beneficial to use bribes and discourage entry.
Optimal bribe (optimal height) with no uncertainty
Remark Note that if is small enough, then the optimal bribe (optimal height of entry barrier) is ,b = 0. However, if is large enough and market size,A, is above a critical level, then b = ^b and we have completely blocked entry. Note that when there is uncertainty (>0) and there is a positive bribe in equilibrium (i.e. b >0), it is at least b (see statement 5).
Without uncertainty (= 0), the equilibrium bribe amount (the height of the entry barrier), when positive, is b = ^b. That is, the equilibrium bribe, when positive, is greater under imperfect information than under perfect information (because^b < b). This means that the bribe (i.e. the level of the entry barrier) is higher under uncertainty than under perfect information.
Remark When goods are complementary, with no uncertainty ( = 0) the optimal bribe (optimal height of entry barrier), b = 0.
Total social surplus
Market quality
An illustrative example
More uncertainty leads to an increase in the height of the entry barrier (the bribe amount) and a decrease in market quality. Zero bribery (which implies zero height of the entry barrier and thus safe entry) always maximizes total profit and market quality. But when goods are complementary, then zero bribery always maximizes total profit and market quality.
Proposition 9 When goods are substitutes (>0), zero bribery (no entry barrier) may not maximize surplus or market quality. Note As noted in the introduction, this result is somewhat related to Mankiw and Whinston (1986). In our example, both total surplus and market quality are maximized at b = b (maximum possible height and no access at all).
Proposition 10 When goods are complementary ( <0), if A k then zero bribe (zero height of entry barrier) maximizes both total surplus and market quality. Note For supplement 2 [ 1;0). In Proposition 10, we showed that if the market size is large enough, zero bribes maximize both total surplus and market quality when goods complement. Will the results change if instead of Cournot competition we have Bertrand competition in the third phase.
Yano (2014) “Market Quality and Market Infrastructure in the South and Technology Di¤usion”, International Journal of Economic Theory. In the appendix we provide the equilibrium calculations and proofs of all results mentioned in the article. If …rm 2 chooses to participate in the second phase, then in the third phase the …rms play an incomplete information court game and earn duopoly profits.
If …rm 2 had chosen not to enter the second stage, then …rm 1 chooses monopoly production. Note that in the second stage 2 will enter i¤ is e¢ science ( ) is higher than a critical type. We analyze the relationship between the bribe paid in the …first stage and the decision of …rm 2 to enter the second stage.
Proof of Proposition 3 Note that it is clear from the discussion in the main part of our paper that. In the …first stage …rm 1 chooses the optimal bribe level to maximize the expected wage¤ (anticipating the equilibrium outcomes in stages 2 and 3).
Optimal bribe when goods are substitutes ( > 0)
Proof of Theorem 4(iii) Since > 0 implies that q1(b) is strictly increasing in all b2 b; b we must have. Proof of theorem 5 Note that from theorem 4 we get sufficient conditions under which b = 0 orb 2 b; b.
Optimal bribe when goods are complements ( < 0)
Case of No uncertainty ( = 0)
Case of substitutes ( > 0)
Case of complements ( < 0)
