As two special types of the general n-dimension fuzzy numbers, fuzzy n-cell numbers and fuzzy n-ellipsoid numbers play an important role in the representations of imprecise multichannel digital information. Denote the families of all n-dimension fuzzy numbers, fuzzy n-cell numbers and fuzzy n-ellipsoid numbers, by K(Rn), L(Rn) and E(Rn), respectively. In this paper, we study the topological structures of the sets L(Rn) and E(Rn) with the topology induced by the supremum metric D∞. Our main result is as follows: for every n>1, there exist homeomorphisms H1,H2:(K(Rn),D∞)→[0,+∞)×ℓ2(c) such that H1(L(Rn),D∞)=H2(E(Rn),D∞)={0}×ℓ2(c), where ℓ2(c) is a non-separable Hilbert space whose weight is the cardinality of the set of all real numbers. As a consequence, the spaces (L(Rn),D∞) and (E(Rn),D∞) are homeomorphic to the Hilbert space ℓ2(c), and hence do not have the fixed point property.
We obtain a complete classification of the structure of finite groups in which every self-centralizing subgroup of non-prime-power order is a TI-subgroup or a subnormal subgroup.
Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants. The recent discovery of the powerful class of zero-determinant strategies in the iterated prisoner's dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents. However, strategies in the prisoner's dilemma game are only two strategies. Are there these results for general multi-strategy games? To address this question, the paper develops a theory for zero-determinant strategies for multi-strategy games, with any number of strategies. The analytical results exhibit a similar yet different scenario to the case of two-strategy games. Zero-determinant strategies in iterated prisoner's dilemma can be seen as degenerate case of our results. The results are also applied to the snowdrift game, the hawk-dove game and the chicken game.
By empirical evidences, it is difficult to find a trading strategy with consistently good performance over a long period, and strategies' profitability seem to be varying through time in a cycle fashion. Under the price formation mechanism based on a market-maker with risk aversion to inventory, this paper elaborately detects the crucial factors that affect strategy' profitability with two common trading strategies, i.e. trend following strategy and value investing strategy. We find that the capitals invested in strategies play an important role in limiting self's profits and affecting each other's interactions. Also the market maker's risk aversion to inventory could make positive or negative influences on strategies' profitability. Consistent with empirical evidences, the inverted parabola response of strategy' payoffs to self's capitals is found. This pattern implies the profits that the strategy could bring to its users are limited and originates from the balance between the increasing capitals invested and the decreasing payoffs per capital. Based on the cross influences of the variations in one strategy's capitals on the other's payoffs, the interactions between the two strategies could be prey-predator, symbiosis or competition. In the long time horizon with the two strategies' payoffs reinvestment, the market can spontaneously evolve to the equilibrium where each strategy gains even.
对一类拥有风险资产完美信息的两个内部人在连续时间内竞争的市场模型,引入了半强有效性定价下的信息协议古诺均衡.利用滤波理论和极大值原理,探讨了不同协议下的古诺均衡的存在性,给出了所存在均衡的闭式解,以及相应的期望利润,剩余信息,市场流动参数等市场特征,并证明了最优信息协议古诺均衡的存在唯一性.研究表明,双方在选择交易策略时只能释放部分信息,才能达到古诺均衡以实现正的最大化收益;否则,如果不释放信息或完全释放共同的私有信息,则都不存在这种均衡.
