Conditions Where the Ruled Class Unites for the Revolution:Applicability of a Game Theory on Social Dilemmas
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摘要
Revolutions,typical cases of crucial social transformations,cannot be realized successfully without a large number of activists. Therefore,creating conditions favorable for acquiring enough participants should be an important topic of Marxist social science. In particular,this problem includes the "free-ride,"because the benefits of revolutionaries' activities are gained not only by the activists but also by all other members. The paper analyzes problems such as this one,applying non-cooperative game theory to social dilemma problems. This leads to some interesting results. In this research,the problem of the workers' choice between unity or freeride is first defined using numerical examples of the gain structure. It is defined again in a more generalized form using other parameters. In so doing,we express both the cost of participating in the movement and the gains from the concession of the ruling class. Because this analysis focuses on the importance of the number of participants,the concession of the ruling class is framed as a function of the number of participants. The results of this analysis revealed that the economic base and superstructure accurately correspond in some game structures but not in others. In other words,the social dilemma presents either as a case of prisoners' dilemma or as a chicken game. Furthermore,this paper analyzes the influence of group size,and it was revealed that groups with a large number of members,such as a ruled class,find it particularly difficult to unite. This phenomenon is called the "large group dilemma. "In these ways,this research shows that the aforementioned type of game theory can be used to analyze the difficulties and possibilities of social movements.
Revolutions,typical cases of crucial social transformations,cannot be realized successfully without a large number of activists. Therefore,creating conditions favorable for acquiring enough participants should be an important topic of Marxist social science. In particular,this problem includes the "free-ride,"because the benefits of revolutionaries' activities are gained not only by the activists but also by all other members. The paper analyzes problems such as this one,applying non-cooperative game theory to social dilemma problems. This leads to some interesting results. In this research,the problem of the workers' choice between unity or freeride is first defined using numerical examples of the gain structure. It is defined again in a more generalized form using other parameters. In so doing,we express both the cost of participating in the movement and the gains from the concession of the ruling class. Because this analysis focuses on the importance of the number of participants,the concession of the ruling class is framed as a function of the number of participants. The results of this analysis revealed that the economic base and superstructure accurately correspond in some game structures but not in others. In other words,the social dilemma presents either as a case of prisoners' dilemma or as a chicken game. Furthermore,this paper analyzes the influence of group size,and it was revealed that groups with a large number of members,such as a ruled class,find it particularly difficult to unite. This phenomenon is called the "large group dilemma. "In these ways,this research shows that the aforementioned type of game theory can be used to analyze the difficulties and possibilities of social movements.
Revolutions,typical cases of crucial social transformations,cannot be realized successfully without a large number of activists. Therefore,creating conditions favorable for acquiring enough participants should be an important topic of Marxist social science. In particular,this problem includes the "free-ride,"because the benefits of revolutionaries' activities are gained not only by the activists but also by all other members. The paper analyzes problems such as this one,applying non-cooperative game theory to social dilemma problems. This leads to some interesting results. In this research,the problem of the workers' choice between unity or freeride is first defined using numerical examples of the gain structure. It is defined again in a more generalized form using other parameters. In so doing,we express both the cost of participating in the movement and the gains from the concession of the ruling class. Because this analysis focuses on the importance of the number of participants,the concession of the ruling class is framed as a function of the number of participants. The results of this analysis revealed that the economic base and superstructure accurately correspond in some game structures but not in others. In other words,the social dilemma presents either as a case of prisoners' dilemma or as a chicken game. Furthermore,this paper analyzes the influence of group size,and it was revealed that groups with a large number of members,such as a ruled class,find it particularly difficult to unite. This phenomenon is called the "large group dilemma. "In these ways,this research shows that the aforementioned type of game theory can be used to analyze the difficulties and possibilities of social movements.
引文
[1]Ohbayashi,Shinya,Voluntary supply of collective goods through expansion of group-introduction of group reputation effect,Sociological Theory and methods,2015,Vol.30,No.1,in Japanese.
[2]Kimura,Kimihiro,Dilemma of Large Groups:Collective Behavior and Collective Scale Mathematics,Minerva Shobo,in Japanese,2002.
[3]Muto,Masayoshi,“Social dilemmas and environmental problems”in Seiyama,Kazuo eds.Mathematical Analysis of Social Dilemma and Inequality,Yuhikaku,in Japanese,2015.
[4]Olson,Mancur,The Logic of Collective Action:Public Goods and the Theory of Groups,Harvard University Press,1965.
[1]C(m)>C(m+1)and D(m)>D(m+1)also hold here since the increase of free riders is supposed to increase social loss.This is said to be a co-benefit condition.
[2]In a chicken game,a certain number“unites”and a certain number“free ride”,so we calculated the equilibrium number of the freeriders(m*=N-the rational number of participants to the movement).Its first condition is D(m*+1)≤C(m*)indicating that to unite is beneficial for the m*+1th member of the ruled class,and the second condition is D(m*)≧C(m*)indicating that free-ride is beneficial for the m*th member,and both conditions make the next inequality;SF+N-11-hm*SF+N-h1-h.This result shows that the number of free-riders m*increases when the current situation(S)and the number of whole members(N)rise and decreases as the additional gain(F)of the result of the participation and the cost(1-h)of the participation increase.Although participants tend to be irritated at times with a small number of followers,they could be a little calm if they understand that the number of followers(N-m*)is also determined by these objective situations.
[2]Kimura,Kimihiro,Dilemma of Large Groups:Collective Behavior and Collective Scale Mathematics,Minerva Shobo,in Japanese,2002.
[3]Muto,Masayoshi,“Social dilemmas and environmental problems”in Seiyama,Kazuo eds.Mathematical Analysis of Social Dilemma and Inequality,Yuhikaku,in Japanese,2015.
[4]Olson,Mancur,The Logic of Collective Action:Public Goods and the Theory of Groups,Harvard University Press,1965.
[1]C(m)>C(m+1)and D(m)>D(m+1)also hold here since the increase of free riders is supposed to increase social loss.This is said to be a co-benefit condition.
[2]In a chicken game,a certain number“unites”and a certain number“free ride”,so we calculated the equilibrium number of the freeriders(m*=N-the rational number of participants to the movement).Its first condition is D(m*+1)≤C(m*)indicating that to unite is beneficial for the m*+1th member of the ruled class,and the second condition is D(m*)≧C(m*)indicating that free-ride is beneficial for the m*th member,and both conditions make the next inequality;SF+N-11-hm*SF+N-h1-h.This result shows that the number of free-riders m*increases when the current situation(S)and the number of whole members(N)rise and decreases as the additional gain(F)of the result of the participation and the cost(1-h)of the participation increase.Although participants tend to be irritated at times with a small number of followers,they could be a little calm if they understand that the number of followers(N-m*)is also determined by these objective situations.