In this paper, we firstly provide an axiom for solutions of TU games, called the coalitional gap desirability (CGD), by adapting the recent coalitional surplus desirability (Hu, 2019). It is verified that no solution satisfies both the CGD and the classical efficiency except for the trivial situation where there are no more than two players in a cooperative game. We then introduce an adapted axiom by averaging coalitions’ gap, namely the average coalitional gap desirability. The equal allocation of nonseparable contributions value (ENSC value) is axiomatized by this averaged version together with the efficiency and additivity axioms. Finally, the axiomatic results are extended to the weighted ENSC value (Hou, et al., 2019).

This paper studies cooperative games and provides a new solution concept called proportional split-off solution based on proportional rule and the forming procedure for a coalition. By applying a given weighted vector and based on decrease of profits, a suitable distributed partition of the grand coalition is obtained. And then, depending on coalitions’ ordering in partition, the marginal contribution of the coalitions is determined by using proportional rule. Later on, three axiomatizations of the proportional split-off solution are proposed by adopting consistency. Finally, application of the new solution is studied on the regional economic situation. By building a synergy game, we analyze the contributions and program of the regional economic synergistic development in Yangtze River Delta.

The difficulty of medical insurance risk decision-making in practical applications is that the insured person’s illness is uncertain. For this reason, we try to use machine learning coupled with reservoir sampling to establish a dynamic prediction model to assist medical insurance companies in making intelligent risk decisions. Three aspects were specifically made. First, we build a medical insurance risk decision model, and theoretically we obtain optimal decision rules; then, based on historical data with a fixed sample size, we build a framework for intelligent medical insurance static risk decision-making; finally, to improve static intelligent prediction regarding the lag of risk decision-making guidance, the idea of using machine learning coupled with reservoir algorithm to carry out intelligent dynamic risk decision-making is proposed, dynamic sampling is performed on continuously updated data sets, and a predictive model that is dynamically updated over time is established. Take diabetes as an example of the insured disease, the 2017 Tianchi Precision Medicine Competition-Artificial Intelligence-Assisted Diabetes Risk Prediction Data. In view of the high dimensionality and complex types of data feature variables, the machine learning algorithm selected is random forest. Experiments and comparisons on the training set with the same sample size and the same test set show that the effect of the decision model based on dynamic prediction is better than the static prediction model.

In order to improve the green supply chain performance, the government gives retailers green product subsidies, and manufacturers give retailers green promotion subsidies. Based on the Stackelberg game analysis of the secondary supply chain composed of manufacturers and retailers, we explore the impact of green product subsidies and green promotion subsidies on the supply chain performance considering consumers’ green preference. It is found that subsidies have a positive effect on product greenness and profit. When consumer preference is not high or product greenness coefficient is low, green product subsidies are more suitable; When consumers have high preference or green promotion efficiency, green promotion subsidies are more suitable. As an external subsidy of the supply chain, the regulation ability of green product subsidy is limited; As an internal subsidy of supply chain, green promotion subsidy can produce higher performance.

There exist a risk of breakdown in the real bargaining games. Muthoo developed an alternating-offer bargaining with a risk of breakdown under the assumption that players are rational. Lots of works on psychology show that decision makers are loss averse. To investigate the impact of loss aversion for players on bargaining game with a risk of breakdown, Muthoo’s alternating offers bargaining game is reconsidered. First, the highest rejected offer in the past is regarded as reference points, which makes the payoffs and equilibrium strategies depend on the history of bargaining. Then, a subgame perfect equilibrium is constructed, which depends on the history of bargaining through the current reference points. And its uniqueness is shown under assumptions: Strategies depending only on the current reference points, immediate acceptance of equilibrium offers and indifference between acceptance and rejection of such offers. Finally, a comparative statics of loss aversion coefficients is performed, and the convergence of the subgame perfect equilibrium for the probability of breakdown tending to zero is analyze. It is shown that a player benefits from loss aversion of the opponent and is hurt by loss aversion of himself.

In this work, the index system of the information technology industry in private enterprises is established, which includes six aspects: Profitability, operation ability, solvency, expansion ability, innovation ability, and company scale. Then, the GA-BP algorithm combining genetic algorithm and neural network is introduced to analyze and predict the growth of the enterprise. After preprocessing the data gained from Wind dataset, the model is trained and the coefficient of determination R2 on the test set is 0.9997, showing its outperformance than other five machine learning algorithms. Through the correlation coefficient analysis between the growth rate of market value and the growth value predicted, the validity of the established model is tested. Finally, the index system is simplified by ranking the importance of the features via Random Forest Algorithm. The coefficient of determination R2 on the test set is 0.8929 when eight features are selected, proving the rationality of the initial index selection again.