Abstract: After obtaining the basic yield v(i), the fair and reasonable distribution of the surplus value generated by cooperation has become the focus for all players. DRIESSEN and FUNAKI (1991) proposed the ED value based on the idea of egalitarianism, which evenly distributed the surplus value of the grand coalition to all players; considering the differences in individual abilities among players, ORTMANN (2000) allocated the surplus value of the grand coalition using the ratio of individual value to the total individual value. Based on this idea, the PD value proposed belongs to a typical utilitarian solution. Afterwards, many scholars conducted extensive research on the fairness and rationality of these two solutions. Fortunately, PD value compensates for the shortcomings of ED value in completely ignoring individual differences among players in the allocation scheme of surplus value of the grand coalition, but overly relying on the individual abilities of players and neglecting their collaborative abilities. The problem of insufficient use of countermeasure information in profit distribution scheme is exposed.
TIJS (1981) adopted the ideal income vector b^v for income distribution, but there was a situation where the grand coalition’s value was not enough distributed (i.e.,v(N)b^v(N)). By defining concession vector to determine the concession values that each participant should undertake when successfully obtaining ideal values b^v_i, TIJS innovatively proposes the τ-value of the quasi-equilibrium game based on the idea of concession. We consider the selfish nature exhibited by cooperative participants in real life, especially in economic issues, when faced with the distribution of benefits. Inspired by the ideas of TIJS, this paper proposes an egoistic approach to the distribution of surplus value in the grand coalition after giving each participant individual value. This article defines the egoistic vector of cooperative games based on egoistic thinking, and proposes the Monopolize Surplus Division value (MSD value) of cooperative games based on the ratio of the egoistic demand of each player to the total egoistic demands of all players. This effectively overcomes the disadvantage of insufficient use of game information in PD value distribution of benefits, and realizes the “distribution according to work” of surplus value in grand coalition. By studying the properties of MSD value, this paper gives the first axiomatic description of MSD value by using the proportionality of egoistic income, efficiency and invariance.
CHOUDHURY et al. (2020) used algebraic theory to uniquely describe the solution of cooperative game. Inspired by the idea, this paper first presents a set of direct sum decomposition conclusions for weakly essential cooperative game spaces. Secondly, with the direct sum decomposition theory of Euclidean space, it has been proven that MSD values can also be uniquely characterized by inessential game property and individual covariance combined with the proportionality of egoistic income. Finally, by redefining the weight coefficient used to present the importance of each player in game and constructing an optimization model, the MSD value is proven to be the only optimal solution of the optimization model. Taking the issue of revenue distribution for tourism pass as an example, a comparative analysis is conducted between MSD values and other values, and the application significance of MSD value is discussed.

Key words: surplus function, basic yield, egoistic income vector, decomposition, proportionality

摘要： 考虑到对策中的参与者在分配收益时的自私心理。本文定义了参与者的利己值,在此基础上提出了合作对策新的分配规则——联盟盈余独占值(MSD值)。该值先将基本收益值(即v(i))分配给各参与者,采用利己思想,以各参与者的利己值占所有参与者利己值总和之比对大联盟盈余值公式进行比例分配。首先,本文研究了MSD值的公理性质并利用欧式空间的直和分解理论给出该值的两组唯一性刻画方法。其次,利用优化理论证明了MSD值是一优化模型的唯一最优解。最后,以旅游通票的收益分配问题为例,对MSD值和其它值进行了对比分析,讨论了MSD值的应用价值。

关键词: 盈余函数, 基本收益, 利己向量, 直和分解, 成比例性