Research On Prize Distribution Strategy Of China Sports Lottery Under Uncertainty

Different from general consumer goods,lottery has special product characteristics, consumer groups and market structure. How to analyze the prize distribution of lottery as a special product and help lottery providers to design the best odds of winning and prizes to improve the scientific development of lottery industry is an important subject to study.In this study, general equilibrium model of lottery market was built under the condition of uncertainty with the objective of studying the decision-making problem of prize distribution policy of China sports lottery. On the one hand, the major premise of lottery market behavior is that lottery prize is uncertain. Uncertainty involves in both risk and ambiguity (Knightian Uncertainty). Risk refers to the uncertainty under deterministic condition of probability measure, while ambiguity is the uncertainty under non-deterministic condition of probability measure. In the framework of the general equilibrium,this study considered consumers' attitude toward the two kinds of uncertainty and has depicted more profoundly their motivation to buy lottery tickets as well as its influence on the equilibrium results. In addition, from the perspective of evolutionary game, it has also discussed how the choices of sports lottery prize distribution policy will evolve when there is uncertainty in lottery ticket providers' behaviors. On the other hand, there are only two lottery providers in Chinese market—Sports Lottery and Welfare Lottery. For most lottery products,it is a duo-oligopoly market,whereas for a few special products,such as"Toto" and "Traditional soccer betting" of sports lottery,due to the significant differences between the rules of the game and the fact that there is only one product provider—sport lottery,it may be regarded as a perfect monopoly market. Based on the background of practical market structure,this study considered both the situation of perfect monopoly and that of duo-oligopoly when building model.With a general equilibrium model that takes a full account of the uncertainty environment and the special structure of lottery market in China, this study discussed the decision-making problems of sports lottery prize distribution policy. Based on the analysis of theoretical model derivation and real parameter simulation, this study drew conclusions as follows:First, under the condition of monopoly, with the increase of consumers'preference for risk, it is feasible to make use of their pursuit of risk to continuously reduce the payout of sports lottery products so that more profits can be gained. In addition, as lottery consumers with particularly risk preference prefer the products of high uncertainty, lottery providers can increase he variance and the uncertainty of products without changing the rate of return by means of reducing the odds of winning and at the same time increasing the prize payout so as to motivate the consumers'purchase intention.Second, in the context of double oligopoly, as there are two lottery providers competing with each other, the sensitivity of consumers to the expected return and variance changes of lottery products increases with the increase of their risk preference, which will lead to more ferocious market competition and a sharp reduction in welfare for the ticket providers as compared with the case in perfect monopoly. This is the biggest difference between duopoly market and monopoly market. Moreover, the greater the elasticity of substitution between the two kinds of lottery products, the more prizes are needed to be set to attract consumers, and accordingly the less profit the providers will get. In other words, under the conditions of duopoly, in order to obtain excess profit, differentiation strategy such as brand differentiation, service differentiation, and product differentiation must be taken to seek the "blue ocean" of lottery field and meet the differentiation needs of consumers.Third, under the conditions of duopoly, when there are differences in prize distribution between the two competing lottery products, consumers are more likely to choose the one with larger variance to win the potential revenue out of uncertainty if the return rates of the two are the same. In this case, the product with smaller variance needs to set a higher prize, that is to say, higher return rate is needed as "reverse risk compensation"? for consumers. In practice, taking sports lottery "5 out of 11 numbers in any order" game (return rate 59.09%) and welfare lottery "5 out of 20 numbers in exact order" game (return rate 57.50%) for example,although the two products have the same positioning and similar game play, the former provides a higher expected return as "reverse risk compensation" for consumers as it has better odds of winning but smaller variance.Fourth, if consumers are ambiguity averse, it will reduce the welfare of sports lottery provider,and with the expanding of consumer ambiguity aversion interval, its profitability will be gradually reduced. At this point, the optimal policy is to explicitly inform consumers of the odds of winning, thereby eliminating the ambiguity effect.By contrast, if consumers are ambiguity preferred, it will enhance the welfare of the provider, and with the expanding of consumer ambiguity preference interval, its profit capacity will be gradually enhanced. That way, the optimal policy is to obscure the odds of winning of existing products. In addition, when designing new products, the calculation of the odds of winning should be as complicated as possible, which can maximize consumers' preference for uncertainty, increase the effectiveness of ambiguity incentives, and raise more public funds for society. Finally, the action mechanisms of both risk and ambiguity are independent of each other. Therefore, at the same level of risk aversion (preference), consumer ambiguity aversion (preference)behavior will increase (decrease) balanced winning prizes, and if the ambiguity aversion (preference) behavior is ignored, the providers will miscalculate the balanced winning prizes.Fifth, in case that the lottery providers are bounded rationality and players'choice of prize distribution policy is uncertain, the equilibrium of market game is not the result of one-time choice but the one after trial-and-error learning and imitation of all the stakeholders in a medium- or long-term evolution, also can be regarded as a process of survival of the fittest and gradual evolution. In this way, the optimal policy depends on a combination of change returns, change costs and competitor's policies.In particular, when the change return in the game is much bigger than the change cost,the evolutionary equilibrium policy is that both sides choose "change" policy; on the contrary, when the change return is smaller than the change cost, the evolutionary equilibrium policy is that both sides choose "non-change" policy; further,when the change cost falls in between the change return of the stakeholders, the choice of the policy depends on the factors like additional market sales and cost change .The conclusions of this study have great practical significance for the operation and management of sports lottery. First, when developing sports lottery prize distribution policy, we need consider both the characteristics of risk preference and ambiguity preference of various consumers and carry out differentiation pricing. In the case of risk preference, the ticket provider can only passively measure the relative risk aversion coefficient of consumers, and then formulate the optimal policy;whereas for the ambiguity preference, the providers, by means of deliberately blurring the odds of winning and increasing the publicity of "ticket buyers hitting jackpot",can make consumers more confident in lottery winning and thus increase the sales of lottery products. Second, if there is no special demand, there is no need for the design of lottery products with too many prize levels, because when considering consumers'preference to first-order moment and second-order moment of lottery products only and on condition that ticket providers possess enough freedom to control the odds of winning and prize payout, single-prize grade lottery products can cover all the consumer preferences for uncertainty; Additionally, design and promotion of lottery games with multiple prize levels will increase operating costs, which is not conducive to profit gain. Third, under the condition of fixed rate of return, the odds of winning should be lowered and prizes should be increased in order to cater to consumer preference for uncertainty. Fourth, in the duo-oligopoly market, the differentiation strategy should be implemented to reduce the substitution elasticity between the lottery products and avoid the malignant price war through heterogeneity competition.Fifth, the higher degree of consumer preference for risk and ambiguity, the greater the profits of ticket providers and the smaller of consumers' welfare will be. Consequently,lottery tickets may become the tax revenue of the poor, which will weaken the redistribution function of lottery. The government should balance the relationship between various stakeholders by means of government pricing, tax system and public welfare fund to make social welfare reach Pareto optimality.