Real R&;D options with time-to-learn and learning-by-doing

We model R&D efforts to enhance the value of a product or technology before final development. Such efforts may be directed towards improving quality, adding new features, or adopting technological innovations. They are implemented as optional, costly and interacting control actions expected to enhance value but with uncertain outcome. We examine the interesting issues of the optimal timing of R&D, the impact of lags in the realization of the R&D outcome, and the choice between accelerated versus staged (sequential) R&D. These issues are also especially interesting since the history of decisions affects future decisions and the distributions of asset prices and induces path-dependency. We show that the existence of optional R&D efforts enhances the investment option value significantly. The impact of a dividend-like payout rate or of project volatility on optimal R&D decisions may be different with R&D timing flexibility than without. The attractiveness of sequential strategies is enhanced in the presence of learning-by-doing and decreasing marginal reversibility of capital effects.     

On the reduced game property for and the axiomatization of theT-value of TU-games

Summary The τ-value is a one-point solution concept for transferable utility (TU-) games. The paper introduces a particular type of a reduced game. It is established that the τ-value possesses the reduced game property with respect to the reduced game presented. That is, there is no inconsistency in what the players of the reduced game receive-either in the original game or in the reduced game-according to the τ-value concept. In addition, the paper provides an axiomatic characterization of the τ-value in terms of the relevant reduced game property and standardness for two-person games.     

Evaluation of firm’s loss due to incomplete information in real investment decision

We investigate the effect of incomplete information in a model where a start-up with a unique idea and technology pioneers a new market but will eventually be expelled from the market by a large firm’s subsequent entry. We evaluate the start-up’s loss due to incomplete information about the large firm’s behavior. We clarify conditions under which the start-up needs more information about the large firm. The proposed method of evaluating the loss due to incomplete information could also be applied to other real options models involving incomplete information.     

CEV下有交易费用的回望期权的定价研究

本文在研究服从CEV过程且无交易费用的回望期权定价模型的基础上,推导出CEV下有交易费用的回望期权定价模型,并利用变量转换和二叉树方法求解,最终给出了CEV下有交易费用的回望期权的近似解。     

Evolutionary games

This paper deals with a mathematical game. As the name implies, the game concept is formulated with biological evolution in mind. An evolutionary game differs from the usual game concepts in that the players cannot choose their strategies. Rather, the strategies used by the players are handed down from generation to generation. It is the survival characteristics of a strategy that determine the outcome of the evolutionary game. Players interact and receive payoffs according to the strategies they are using. These interactions, in turn, determine the fitness of players using a given strategy. The survival characteristics of strategy are determined directly from the fitness functions. Necessary conditions for determining an evolutionarily stable strategy are developed here for a continuous game. Results are illustrated with an example.Dedicated to G. LeitmannThis work was supported by NSF Grant No. INT-82-10803 and The University of Western Australia (Visiting Fellowship, Department of Mathematics, 1983).     

Games with vector payoffs

Two-person games are defined in which the payoffs are vectors. Necessary and sufficient conditions for optimal mixed strategies are developed, and examples are presented.     

An evasion game with a destination

This paper solves an aiming and evasion game in which a gunner with a number of shots attempts to hit an evader moving along the positivex-axis. The gunner's aiming of the evader is complicated by the fact that there is a delay due to the time taken for the shot to reach the evader from the gunner.     

Social systems analysis

We present a model of social systems as special types of games in extensive form in which perception and learned strategies play an important role. We discuss personality, emotions, and the relation of utility to Maslow's hierarchy of values. We also formulate a new class of games, partially cooperative games, and attempt to define a solution concept for these.     

Adjacency on polymatroids

This paper characterizes adjacency for extreme points of a polymatroid. Two extreme points of a polymatroid are adjacent if and only if they either differ in exactly one component or differ in exactly two components with the two components satisfying a certain ordering relation. A polynomial algorithm generates and lists all extreme points adjacent to a given extreme point of a polymatroid. Similar results hold for the core of a convex game.     

税企博弈模型──防止出口骗税的一个对策

本文初步探讨了现行出口骗税行为处罚所产生的负效应，进而建立了税企博弈模型．在国家税收期望损失为零的情况下，首次提出了出口骗税罚款系数公式（L）．该公式揭示了罚款系数与检查概率之间的关系，为税务决策部门制定罚款系数及税务操作部门安排检查力量提供了理论依据．公式（L）可操作性强，具有一定的实用价值．