The Influence of Information Acquisition on the Complex Dynamics of Market Competition

In this paper, we build a dynamical game model with three bounded rational players (firms) to study the influence of information on the complex dynamics of market competition, where useful information is about rival’s real decision. In this dynamical game model, one information-sharing team is composed of two firms, they acquire and share the information about their common competitor, however, they make their own decisions separately, where the amount of information acquired by this information-sharing team will determine the estimation accuracy about the rival’s real decision. Based on this dynamical game model and some creative 3D diagrams, the influence of the amount of information on the complex dynamics of market competition such as local dynamics, global dynamics and profits is studied. These results have significant theoretical and practical values to realize the influence of information.

ROBUST ASYMPTOTIC CONTROLLABILITY UNDER TIME-VARYING PERTURBATIONS

We investigate the effect of time-varying perturbations on the dynamical behavior of nonlinear control systems. More specifically, we study the effect of such perturbations on the controlled equivalent of asymptotically stable sets, i.e. asymptotically controllable sets. In the first part of this paper we illustrate by a simple example how different types of perturbations affect this dynamical behavior and use concepts from dynamical game theory in order to identify classes of perturbations which allow to model the effects of numerical discretization errors both in time and space. In the second part we introduce appropriate robustness properties and prove that these are inherent properties for asymptotically controllable sets under these classes of perturbations.

VIABLE CAPTURE BASIN FOR STUDYING DIFFERENTIAL AND HYBRID GAMES: APPLICATION TO FINANCE

Viability theory can be applied for determining viable capture basin for control problem in presence of uncertainty. We first recall the concepts of viability theory which allow to develop numerical methods for computing viable capture basin for control problems and guaranteed control problems. Recent developments of option pricing in the framework of dynamical games with constraints lead to the formulation of guaranteed valuation in terms of guaranteed viable-capture basin of a dynamical game. As an application we show how the viability/capturability algorithm evaluates and manages portfolios. Regarding viability/capturability issues, stochastic control is a particular use of tychastic control. We replace the standard translation of uncertainty by stochastic control problem by tychastic ones and the concept of stochastic viability by the one of guaranteed viability kernel. Considering the Cox–Rubinstein model, we extend algorithms for hedging portfolios in the presence of transaction costs and dividends using recent developments on hybrid calculus.