现实生活中的卡特尔组织 卡特尔组织

　　摘要：卡特尔组织是由竞争企业所构成的共谋联盟。企业通过在商品价格、产量和市场份额等方面订立协定而形成的同盟。本文将先阐述卡特尔组织的优点及其不稳定性，并运用保洁与联合利华的例子来分析卡特尔组织在现实生活中的稳定性。
　　关键词：卡特尔组织 博弈论 纳什平衡 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 P&G’s view, P&G has to think about what Unilever will choose. Assume that, P&G thinks Unilever will cheat in the game. Then the best response for P&G is cheating. But if P&G thinks Unilever will cooperate and set an agreement, in order to make a bigger profit, P&G 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, P&G 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 (Kopalle&Shumsky, 2010). Specially, let P&G 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.