C

S

,

R’_{I},

C

, 0

,

We will assume that, which means that when the weaker foreign supplier takes away all this country’s business due to her cooperation with the domestic supplier, she makes an improvement. It is easy to see that “C” is a dominant strategy for the weaker foreign supplier, and is thus always played by her. The decision of the stronger foreign supplier, however, is slightly more complicated. There are two cases: 1) when R’_{I} >, the NE is ~~; and 2) when R’~~_{I} <, the NE is

Proposition 2. If the weaker foreign supplier has its major business in China such that cooperation with the domestic entrant becomes her dominant strategy, then the domestic supplier will be successful. On the other hand, the stronger foreign supplier may or may not choose to cooperate, dependent how seriously his businesses with the other countries are affected.

We will now ignore government’s intervention in the following discussion. Let us consider the coalitional game among the domestic user (Y), the foreign supplier (W) and the new domestic supplier (N). Ignoring the empty coalition and those coalitions not containing Y, there are three coalitions should be examined in details: {Y, W}, {Y, N}, and {Y, W, N}. We will denote the coalition values as follows:

(1)

Here we assume that 0 < V_{YN} < V_{YW} < V_{YWN}. The main reason that the grand coalition {Y, W, N} has the biggest value is because it combines both of the more advanced technology advantage of the foreign supplier and the cost advantage of the domestic supplier. And for all other coalitions S we define v (S) = 0.

We will consider the existence of a core solution. We are looking for (x_{Y}, x_{W}, x_{N}) ≥ (0, 0, 0) such that

(2)

Proposition 3. Under our assumption 0 < V_{YN} < V_{YW} < V_{YWN}, the core is always nonempty.

Proof. In fact for any ε > 0 sufficiently small, define x_{Y} = V_{YW} – ε, x_{W} = ε, x_{N} = V_{YWN} – V_{YW}. Then it is easy to verify: x_{Y} + x_{W} = V_{YW}, x_{Y} + x_{N} = V_{YWN} – ε > V_{YN} (for ε > 0 small), x_{Y} + x_{W} + x_{N} = V_{YWN.}

Q.E.D.

In view of Proposition 3, the core in general contains infinitely many outcomes, and which outcome in the core will be realized as the solution of the cooperative game actually depends on the bargaining power of the foreign supplier as one side and {Y, N}-coalition as the other side.

At the beginning when the domestic supplier is completely ignorant to the technology, i.e. V_{YN} = 0, the foreign supplier may regard (M, 0) as the status quo, where M is its monopoly profit. As a result the solution looks like

(3)

In a dynamic process, V_{YN} and V_{YWN} may increase together with time. At each instant τ, the foreign supplier may regard (M, V_{YN} (τ)) as the status quo, and only accept a solution as least as good as

(4)

In particular, in case the foreign supplier is able to control the technology leakage, it will try to keep its core technology secret in order to make sure that V_{YN }(τ) is never so big, maintaining

(5)

Summing up briefly we have Proposition 4. In the dynamic process of the cooperation of the foreign supplier, the domestic supplier and the domestic user, while the domestic supplier can acquire some of the advanced production technology to strengthen its bargaining position, the foreign supplier will try to keep the core technology under private control so that its net profit will not be reduced in the long-run.

Now we consider the role of the government. It could introduce policies encouraging technology transfer from foreign suppliers to domestic suppliers. For example it could give priorities of entering the domestic market to those foreign suppliers who agree to transfer technology to and cooperate with their domestic counter-parts.

Based on the idea in Proposition 4, in the cooperation with the domestic supplier, the foreign supplier has a tradeoff in technology transferring. On the one hand, more advanced technology is transferred to the domestic supplier means larger part of the production task will be

Figure 4. Maximum level of technology transfer.

given to the domestic supplier, lowering the production costs and increasing the “size of the pie” V_{YWN} shared by the three parties involved. In this sense, if we use t to represent the percentage of technology transferred, V_{YWN}(t) could be regarded as an increasing function in t. On the other hand, the higher level of advanced technology has been transferred to the domestic supplier, the stronger bargaining position for the coalition {Y, N}, which implies that V_{YN }(t) is also increasing in t. We may assume that V_{YWN}(t) and V_{YN}(t) are continuous functions defined on the interval [0, 1]. When government encourages the cooperation between the domestic supplier and the foreign suppliers, it at the same time triggers the competition among the potential foreign suppliers in entering this market. A foreign supplier who completely refuses technology transfer will be unlikely accepted as a cooperator. This implies both of M = 0 and V_{YWN}(0) = 0.

As t increases, it is reasonable to assume that V_{YWN}(t) increases in a decreasing speed, i.e. V_{YWN}(t) being a concave function. On the other hand, for the increasing function V_{YN }(t), obviously we have V_{YN }(0) = 0; and if technology were completely transferred to the domestic supplier, then the participation of the foreign supplier is no longer significant, which implies V_{YN}(1) = V_{YWN}(1).

From the result in the last subsection, we now have:

(6)

Note that x_{W}(t) is continuous on [0, 1], there must exists a t* at which x_{W} is maximized. It is reasonable to assume that the process of technology is from less advanced level to more advanced level. Our above argument leads to:

Proposition 5. Under the intervention of the government, the foreign supplier will eventually agree to cooperate with the domestic supplier, agreeing to transfer the production technology up to a level of t*.

The result of Proposition 5 can be interpreted by Figure 4.

5. Conclusions

We have studied the bi-oligopoly markets of high-tech equipments in developing countries. The most important result is probably that the government can play a very important role in these markets to accelerate the structure evolution and improve the welfare outcomes.

While we present Proposition 5 in the last section, it is just a conclusion in the not-very-long long run. In a bigger time scale, every type of technologies will eventually become out-of-date unless it is being improved by R & D. Any developing country, while on the one hand should introduce open-door policy, encouraging technology transfer from the developed countries, on the other hand, must also invest in R & D, trying to catch up with the developed countries in every field.

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