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Normally entrepreneur would raise fund from angel investors during the initial round. If the venture program was by then successful, the entrepreneur would then continue the fund-raising process from venture capitalist. By adopting the convertible preferred stock, we managed to construct the two-stage angel investment decision process. This research reveals the following: (1) The probability of the first stage’s success has negative relationships with levels of priority dividend in both first and second stages, as well as with the venture capitalist’s proportion of shares. (2) The probability of the second stage’s success has negative relationships with the venture capitalist’s proportion of shares and the dividend level of both first and second stage funding. (3) There has been a threshold of dividend distribution, which belongs to angel investor. While the level of angel investor’s shares is higher than the threshold, AN would decide to join the second phase of the program; otherwise, AN would exit the project at the end of the first stage.

When venture capital has been invested into venture companies, venture capitalists and venture entrepreneurs form a principal-agent relationship. Take into account the fact that the venture entrepreneur’s effort is a long process, because the effort is not the same at different stage. Therefore, efforts variables are seen as the multistage dynamic variable, and venture investment principal-agent model with venture entrepreneurs having multistage efforts is constructed on the basis of the classic principal-agent theory in the paper. Further, in the later stage effort of venture entrepreneurs is affected by the size of prestage benefit with venture capitalists and venture entrepreneurs; thus the fairness preference model is improved, and venture investment principal-agent model with venture entrepreneurs having multistage efforts is constructed on the basis of fairness preference theory. Both theoretical derivation and simulation have demonstrated that, under the condition of information asymmetry, if the fairness preference of venture entrepreneurs holds, then(1)venture capitalists provide venture entrepreneurs with level higher than that without fairness preference,(2)in every single stage venture entrepreneurs make efforts higher than those without fairness preference, and(3)in two periods both venture investors and venture entrepreneurs gain total real gains higher than those in two periods without fair preference.

The infinity period dynamic control problem of distribution channel was studied with differential game approach. Four differential dynamic control models of coordinated channel game, uncoordinated static game, Stackelberg game with manufacture controlled, and Stackelberg game withnretailers controlled were constructed. Some results applied dynamic optimization theory made with Hamilton function. The conclusions are as follows. (1) Optimization brand investment controlled by manufacture has nothing to do with time. (2) Retail price was the most minimum when channel was integrated. (3) Manufacture’s profits of uncoordinated static game and Stackelberg game with manufacture controlled were more than Stackelberg game withnretailers controlled. (4) Retailer’s profits of Stackelberg game withnretailers controlled were less than Stackelberg game with manufacture controlled. (5) Channel’s total profits of Stackelberg game withnretailers controlled were the most minimum.

In a distribution channel, channel members are not always self-interested, but altruistic in some conditions. Based on this assumption, this paper adopts a behavior game method to analyze and forecast channel members’ decision behavior based on result fairness preference and reciprocal fairness preference by embedding a fair preference theory in channel research of coordination. The behavior game forecasts that a channel can achieve coordination if channel members consider behavior elements. Using the behavior game theory model we established, we can prove that if retailers only consider the result fairness preference and they are not jealous of manufacturers’ benefit, manufacturers will be more friendly to retailers. In such case, the total utility of the channel is higher compared with that of self-interest channel, and the utility of channel members is Pareto improved. If both manufactures and retailers consider reciprocal fairness preference, the manufacturers will give a lower wholesale price to the retailers. In return, the retailers will also reduce retail prices. Therefore, the total utility of the channels will not be less than the total utility of the channel coordination, as long as the reciprocity wholesale prices meet certain conditions.

An existence result for the solution set of symmetric vector quasi-equilibrium problems that allows for discontinuities is obtained. Moreover, sufficient conditions for the generalized Levitin-Polyak well-posedness of symmetric vector quasi-equilibrium problems are established.

This paper studies channel consisting of a manufacturer and two retailers. As a basis for comparison, the first, multiagent Stackelberg model has been structured based on perfect rationality. Further, fairness preference theory will be embedded in marketing channel multiagent Stackelberg model, and the results show that if the retailers have a jealous fairness preference, the manufacturer will reduce the wholesale price, retailers will increase the effort level, product sales will be increased, and the total channel utility and manufacturers’ utility will be pareto improvement, but the pareto improvement of retailers’ utility is associated with the interval of jealousy fairness preference coefficient. If the retailers have a sympathetic fairness preference, the manufacturer increases wholesale price, retailers reduce the effort level, and the total channel utility, manufacturer’s utility, and retailers’ utility are less than that of the no fairness preference utility.