現(xiàn)實生活中的卡特爾組織

摘要：卡特爾組織是由競爭企業(yè)所構(gòu)成的共謀聯(lián)盟。企業(yè)通過在商品價格、產(chǎn)量和市場份額等方面訂立協(xié)定而形成的同盟。本文將先闡述卡特爾組織的優(yōu)點及其不穩(wěn)定性，并運用保潔與聯(lián)合利華的例子來分析卡特爾組織在現(xiàn)實生活中的穩(wěn)定性。

關(guān)鍵詞：卡特爾組織 博弈論 納什平衡 囚徒困境

Abstract：Cartel is a collusive agreement among competing firms， within which cartel members agree on such matters as price fixing， total industry output， market shares. This essay will first elaborate the benefits of making a cartel and its instability， and then analysis the reason why this cartel works significantly stable using real world example.

Keywords: Cartel Formation Game Theory Nash-Equilibrium Prisoners’Dilemma

Economic Model

The game of prisoners’ dilemma is of important relevance to the oligopoly and cartel theory. The incentive to cheat by a member of cartel， and eventual collapse of cartel agreement is better explained with the model of prisoners’ dilemma (Ahuja， 2010). A washing powder price example would be used to illustrate the prisoner’s dilemma.Consider the prisoners’ dilemma in Figure 1 from PG’s view， PG has to think about what Unilever will choose. Assume that， PG thinks Unilever will cheat in the game. Then the best response for PG is cheating. But if PG thinks Unilever will cooperate and set an agreement， in order to make a bigger profit， PG also will choose cheat. It is quite similar from Unilever’s view. Therefore， (cheat， cheat) will be the Nash equilibrium for the game. Although this choice is the worst situation in the game， their selfish behavior leads them to cheat others.

Real World Performance

However， in the real world， PG and Unilever will not set the price and quantity discretely. When deal with a continuous choice， Cournot model is helpful to illustrate the benefit of cooperate or set cartel and the strong incentive to cheat on the part of cartel members. As that the products are differentiated， hence some customers receive different utilities from different products (KopalleShumsky， 2010). Specially， let PG be company 1 and Unilever be company2， then (million) be the demand for product1， and the price is p1 and p2 . The total cost is fixed， which equal $40 million. To make the calculation simple， the demand function will be defined as:

d1(p1，p2) = 24-4p1+2p2 d2(p1，p2)= 24-4p2+2p1 (1)

Then the profits will become:

π1=p1×d1(p1，p2)=24p1-4p12 +2p1p2-40 (3)

π2=p2×d2(p1，p2)=24p2-4p22 +2p1p2-40 (4)

Then first order condition will be used to find the best response function of each company， and the result will be showed in Figure 2.

P1=3+p2/4 (6) P2=3+p1/4 (5)

These two best response functions intersect at point (4， 4)， and there is no sense for these two companies change any more. Hence this is the Nash equilibrium. The point (4， 4) is the Nash equilibrium for both of these companies， however， this is not the point which will make the maximize profits for them. Arthur and Sheffrin (2003) point out that， in microeconomic theory， one firm can maximize its profits when it reach the monopoly quantity level， in this case π=π1+π2=48p-4p2-80 (8)， which means each company produce 12 million washing powders with a price of $6. Therefore， these two companies cooperate and abide by the agreement， and share the joint monopoly profits of $32million.

But this situation is instable and it will be broken up by these two companies trying to produce and sell more at the agreed price. In Figure 3， MC is the marginal cost curves of one company. OP and OQ are the price and output of the company， which are fixed by the collusive agreement. Hence， under the agreement each company’s profit is also fixed. However， if company cheats in the game， and increase its output to OQ1without any changing in the fixed price. Then it can increase its profits by the shaded area ABC. Once the other company finds its rival cheating in the game， the collusive agreement will not exist anymore.

In one-shot equilibrium， the members have an incentive to deviate from the collusive agreement， since it will get more profits if it increases its output. However， it hardly happens in a repeated game or long-time equilibrium. Paha (2010) has elaborated that， cartel-firms can jointly deviate from a cartel with m members. This gives rise to potentially new equilibrium. However， such joint deviations are difficult in practice. Allowing for the joint deviations may create internally stable cartels. In the case of PG and Unilever， if these two companies both refuse the collusive agreement and reduce price at same level at the same time. But this action will not help each company gains more profits， because of the unchanged market share. Hence， these two companies will not deviate but stay in the internally stable cartels.

Conclusion

Cartel is a good commercial collusion， within which the cartelists own a monopoly market and share significantly high profits. However， each company would like to gain extra more profits by decreasing the price or increasing the output under the agreement of fixed price and output. But， this situation will only happen in one-shot equilibrium. In long-term situation， companies have full knowledge of their rivals’ action， and clearly notice the drawbacks of getting rider of cartel. Therefore， none of the companies will easily choose to cheat in the game， and it is the most important reason， which is widely agreed， that PG and Unilever set up a stable cartel for three years or even longer.

Reference:

[1]Arthur. S.， Sheffrin. S. M. (2003). Economics: Principles in action. pp. 171 Pearson Prentice Hall.

[2]Dixit. A.， Skeath. S.， Reiley. D. (2009). Games of Strategy. Norton.

[3]Kopalle. P.， Shumsky. R. A. (2010). Game Theory Models of Pricing. Oxford University Press.

[4]Nowaihi. A. Al.， Levine. P. L. (1985). The Stability of the Cournot Oligopoly

[5]Model: A Reassessment. Journal of Economics Theory 35， 307-321， 1985.

[6]Paha. J. (2010). Endogenous Cartel Formation with Heterogeneous Firms and Differentiated Products. Justus-Liebig-University Giessen.