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Function fields, their places and valuations
Published in Jürgen Bierbrauer, Introduction to Coding Theory, 2016
20.7 Definition. Adiscrete valuationis a mapping v : F → ℤ ∪ {∞} such that the following hold:v(x) = ∞ if and only if x = 0.v(xy) = v(x) + v(y) for all x, y ∈ F.v(x + y) ≥ min{v(x), v(y)} for all x, y ∈ F.There exists t ∈ F such that v(t) = 1.v(K) = 0.
Keep it or give back? Optimal pricing strategy of reward-based crowdfunding with a hybrid mechanism in the sharing economy
Published in International Journal of Production Research, 2020
Lei Guan, Yongxue Mu, Xiaolin Xu, Lianmin Zhang, Jun Zhuang
To understand how the hybrid mechanism affects the pricing strategy of the creators, this research is organised from two aspects. First, we consider two cases on the valuation of investors, since we think that the discrete valuation and the continuous valuation represent different kinds of products. For the discrete valuation, we investigate the two-point distribution which is the same as that in Hu, Li, and Shi (2015). Under this case, we find that AON is the best choice under most situations. For the continuous valuation, we study two specific distributions, i.e. the uniform distribution and the normal distribution. We find that the hybrid mechanism now is the best choice for the creator. These results indicate that different types of investors’ valuation will force the creator to choose different crowdfunding mechanisms. Second, we consider the two-stage problem as the basic model setting, while using the three-stage problem to check the robustness of our conclusions. For the discrete valuation of investors, the main insights can carry over except that under the menu pricing strategy, the creator may adopt the hybrid mechanism. For the continuous valuation of investors, all conclusions hold, and we get some additional insights, e.g. the optimal prices increase at late stages.