Research On The Stability About Tacit Collusion Of Corporations In The Course Of Output Competition

The collusion is usually divided into two types :One type is cooperative collusion ,Another type is tacit collusion。The former is defined that there are some compulsive contracts among all participations of the cooperative collusion;The latter is defined that there are no compulsive contracts among all participations of the cooperative collusion.In the economic domain the tacit collusion is popular. Especially the tacit collusion is more popular than the cooperative collusion on the condition that the compulsive contracts among all participations of the collusion are forbidden by law .Howere,wo know that the alliance in the cooperative collusion is voluntary and abandoned, so every participation of the cooperative collusion offen deviates the contracts on impulse of advantage. Therefore, in order to research questions of collusion it is extraordinary essential to research the stability about the tacit collusion. Stephen Martin researched the stability about the tacit collusion from the angles of inner stability and exterior stability about competition of output in advanced industrial economics.However this paper researched the stability about the tacit collusion from the angles of the participations of the tacit collusion in the course of competition of output.The model assumes all corporations face the same inverse demand function: p = a-bQ, the same cost function: C ( q)=cq.( p delegates market price; Q delegates general market supply; a ,b and c is coefficient.) First of all ,this paper upbuilt a static game model of complete information in order to depict questions of the tacit collusion of v enterprises in the course of competition of output.The model assumes that there are k enterprises to participate the tacit collusion and the residuary f enterprises are independent enterprises.According to game theory, if all the enterprises to participate the tacit collusion abide by the contracts,the profit of every enterprise to participate the tacit collusion can be expressed.The expression is as below: If some enterprise to participate the tacit collusion betrayed the contracts while the other enterprises to participate the tacit collusion abide by the contracts, the profit of the treacherous enterprise can be expressed.The expression is as below: ( )( )2 2*221m16 1v bsπ= k +f+ If πm* < πk*,wo know the tacit collusion as strict stability;If πm* ≤πk*, wo know the tacit collusion as weak stability;If πm* > πk*, wo know the tacit collusion as instability.Obviously,if f ? k+1 =0, the tacit collusion is weak stability;if f ? k+1 ≠0, the tacit collusion is instability.In order to research the questions of collusion deeply,wo introduce the difference factor of production.wo can find similar results. The expression is as below: If 2 ( 1)2k = + θv?, the tacit collusion is weak stability; If 2 ( 1)2k ≠+ θv?, the tacit collusion is instability. In the second chapter, this paper upbuilt a finitely repeated games model of complete information in order to depict questions of the tacit collusion of v enterprises in the course of competition of output. The model assumes that every enterprise to participate the tacit collusion abide by grim strategies in the course of finitely repeated games. According to game theory, if all the enterprises to participate the tacit collusion abide by the contracts in the course of finitely repeated games,the total profit of every enterprise to participate the tacit collusion can be expressed.The expression is as below: ( )1*1nkEπ= δ??δδπ,δis discount here , 0 < δ< 1. If some enterprise to participate the tacit collusion betrayed the contracts in the t th game ,the total profit of the treacherous enterprise can be expressed.The expression is as below: * * *n 1 ** * k1 1 1 1t kE mπ= δ??? π? π? δ+ δ?π古δ???+ δ?πδ?δ?+πδ古According to the definitions of stabilities,wo know that if f ? k+1 =0, the tacit collusion is weak stability;if f ? k+1 ≠0, the tacit collusion is instability.In order to research the questions of collusion deeply,wo introduce the difference factor of production.wo can find similar results. The expression is as below: If 2 ( 1)2k = + θv?, the tacit collusion is weak stability; If 2 ( 1)2k ≠+ θv?, the tacit collusion is instability. In the third chapter, this paper upbuilt a infinitely repeated game model of complete information in order to depict questions of the tacit collusion of v enterprises in the course of competition of output. The model assumes that every enterprise to participate the tacit collusion abide by grim strategies in the course of infinitely repeated game. According to game theory, if all the enterprises to participate the tacit collusion abide by the contracts in the course of infinitely repeated game,the total profit of every enterprise to participate the tacit collusion can be expressed.The expression is as below: ( )1* *lim1 1nk kE nπ= →+∞δ??δδπ=δ?πδ,δis discount here , 0 < δ< 1. If some enterprise to participate the tacit collusion betrayed the contracts in the t th game ,the total profit of the treacherous enterprise can be expressed.The expression is as below: * *** * k1 1 1t kE mπ= δ??? π? π? δ+ δ?π古δ???+δ?πδAccording to the definitions of stabilities,wo know that if f ? k+1 =0or f ? k+1 ≠0and ( )( )( )2211 4 1vδ= v + ++ k f+ , the tacit collusion is weak stability;If f ? k+1 ≠0 and ( )( )( )22011 4 1v< δ< v + ++ k f+ , the tacit collusion isinstability;If f ? k+1 ≠0 and ( )( )( )2211 4 1vδ> v + ++ k f+ , the tacit collusion is strict stability. In order to research the questions of collusion deeply,wo introduce the difference factor of production.wo can find similar results. The expression is as below: if 2 ( 1)2k = + θv? or 2 ( 1)2k ≠+ θv?and ( )* *2* *2 2m km mq qδ= ??? q + + vsθ? θ??????? q?+ vsθ?θ??? , the tacit collusion is weak stability; If 2 ( 1)2k ≠+ θv? and ( )* *2* *02 2m km mq q< δ< ??? q + + vsθ? θ??????? q?+ vsθ?θ??? , the tacit collusion is instability; If 2 ( 1)2k ≠+ θv? and ( )* *2* *12 2m km mq q??? q + + vsθ? θ??????? q?+ vsθ?θ??? < δ<, the tacit collusion is strict stability. In conclusion, on the condition that all corporations face the same inverse demand function ,cost function and the different extent of production,if all corporations process static game of complete information or finitely repeated games l of complete information, quantitative connection of k and f fix on the stability of collusion: if 2 ( 1)2k = + θv?, the tacit collusion is weak stability;if...