Narrow Results

Differential games with additive payoffs are considered. A new approach to constructing the characteristic function for such games is defined. Properties of optimality principles such as the core and the Shapley value constructed by applying the new characteristic function are studied. The solutions obtained are demonstrated by means of an example.

The issue of regulation of cross-border data flows is one of the difficulties in digital trade negotiations among countries. This paper considers three cross-border data flow regulation scenarios under technological progress: namely, unilateral, bilateral and trilateral cross-border data flow regulation. By constructing a differential game model, the game equilibrium strategies under the three scenarios are solved and analyzed. The results show that in the unilateral scenario, the higher the digital technology level of the data importing country, the lower the actual cross-border data restriction index of the data exporting country. In the bilateral scenario, when a country’s digital technology is relatively low, its government regulation is high and it tends to adopt a “defensive” cross-border data flow policy. In the trilateral case, due to the existence of double digital trade barriers and other effects, the actual cross-border data restriction index of a country in the middle of the digital technology level is much higher than that of a country at the bottom of the digital technology level; a country at the bottom of the digital technology level is more restrictive than a country in the middle of the digital technology level than a country at the top of the digital technology level.

We study a differential game of one pursuer and one evader described by infinite systems of second order ordinary differential equations. Controls of players are subjected to geometric constraints. Differential game is considered in Hilbert spaces. We proved one theorem on evasion. Moreover, we constructed explicitly a control of the evader.

In this paper, we address the problem of groundwater exploitation by heterogeneous farmers for irrigation purposes. In particular, we study the possible inefficiencies that can arise in this type of common resource problem by considering the dynamic and strategic interactions between groundwater users. To this end, we build a two-player differential game in which two types of farmers (or many farmers grouped into two types, with a representative farmer for each group) display different characteristics related to their agricultural activity. More precisely, they can have different water demand functions, extraction costs, crop productivity, land types and time-preferences. Conditions are studied for the existence and uniqueness of the cooperative and non-cooperative solutions asymptotically converging to a steady state. The model is then applied to the case study of the Western La Mancha aquifer. Effects of the different heterogeneities on the degree of inefficiency of non-cooperative solutions with respect to cooperative solutions are analyzed. Numerical results show that cooperation is always beneficial for the environment and for the agents: It results in higher levels of groundwater stock and total welfare. Moreover, considering heterogeneous time preferences is crucial for reducing the inefficiency of non-cooperation with respect to cooperation, regardless of the other asymmetries between farmers.

The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for target enclosing task with all constraints above, by integrating the collision threat and maneuver boundaries into a novel nonlinear cost functional, the studied target enclosing problem is described as a nonlinear nonzero-sum differential game. Further, to avoid iterative calculations caused by traditional nonlinear-game-solving methods, an approximate solution which can be constructed directly is designed. Then the approximate Nash equilibrium strategies can be educed by the constructive approximate solution for the proposed nonzero-sum game. Analysis shows that the proposed control strategies can asymptotically approach the exact one and can ensure a zero-error tracking of the enclosing configuration. Simulation results illustrate lower time costs and better enclosing accuracy while the collision avoidance and maneuver amplitude constraints are satisfied simultaneously.