有兩部分如下。1.我們研究Cournot-Bertrand 競爭。Cournot公司用產量來決定它的最大獲利。Bertrand公司則用產品價格來決定它的最大獲利。假設全部公司數量不變，我們使用replicator dynamics來調整Cournot公司與Bertrand公司的比率。目標是此比率的極限行為。2. 兩個物種競爭的極限行為已於2004年完全解決。我們打算繼續研究兩種以上物種的競爭。另外我們打算研究 predator–prey 系統裡合作獵捕問題。 ;There are two parts in the proposal.1. We investigate the evolution of Cournot and Bertrand firms in replicator dynamics. Assume the total number of firms is fixed. At each time period, each firm is randomly matched with a Bertrand or a Cournot counterpart to play a duopoly game, and then a firm’s populations evolve according to replicator dynamics. The goal is to find out the long-rum behavior. In particular, whether all firms choose either price or quantity competition as the unique and globally stable limit.2. We will continue our study on population sizes of species that could compete or cooperate with each other. Difference systems are used to model the population sizes of species. In Cushing et al. J. Differential Equation Application 10 (2004), the behavior of two competing species is completely solved. We consider some special cases for species more than two. We also consider cooperative hunting in a discrete predator–prey system.
