A path-following version of the Todd-Burrell procedure for linear programming

We propose a path-following version of the Todd-Burrell procedure to solve linear programming problems with an unknown optimal value. The path-following scheme is not restricted to Karmarkar's primal step; it can also be implemented with a dual Newton step or with a primal-dual step.This work has been completed with the support from the Fonds National Suisse de la Recherche Scientifique, grant 12-34002.92.     

On stochastic games with additive reward and transition structure

In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player.For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.     

State transformations and the derivation of Nash closed-loop equilibria for non-zero-sum differential games

In this paper the usefulness of state transformations in differential games is demonstrated. It is shown that different (admissible) state transformations give rise to different closed-loop Nash equilibrium candidates, which may all be found by solving systems of ordinary differential equations. A linear-quadratic duopoly differential game is solved to illustrate the results.     

二人零和连续对策上的判断与最优策略间的关系

引进了二人零和连续对策上的判断，判断块以及在判断下的最优策略等概念．研究了判断下的最优策略集与经典最优策略集之间的关系，得到了一些在理论上有趣而且有用的结果．     

The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games

In 1951, Dvoretzky, Wald and Wolfowitz (henceforth DWW) showed that corresponding to any mixed strategy into a finite action space, there exists a pure-strategy with an identical integral with respect to a finite set of atomless measures. DWW used their theorem for purification: the elimination of randomness in statistical decision procedures and in zero-sum two-person games. In this short essay, we apply a consequence of their theorem to a finite-action setting of finite games with incomplete and private information, as well as to that of large games. In addition to simplified proofs and conceptual clarifications, the unification of results offered here re-emphasizes the close connection between statistical decision theory and the theory of games.A first draft of this paper was completed when Khan and Rath were visiting the Institute for Mathematical Sciences at the National University of Singapore in August 2003; they thank the Institute for supporting their visit. A preliminary version was presented at the Midwest Economic Theory Conference held at Indiana University, Bloomington in October 2003; the authors are grateful to Eric Balder, Robert Becker, William Thomson and Myrna Wooders for questions and helpful suggestions.     

Stationary and nonstationary strategies in Hotelling's model of spatial competition with repeated pricing decisions

This paper examines Hotelling's model of location with linear transportation cost. Existence of pure strategy subgame perfect equilibria in the infinitely repeated price game with fixed locations is proved. These subgame perfect equilibria have a stick and carrot structure. Given firm locations, there are discount factors sufficiently high that there is a subgame perfect equilibrium with a two-phase structure. Given the discount factors, there are stationary subgame perfect equilibria for a wide range of locations. However, for some pairs of location, no symmetric simple penal code exists, all subgame perfect profiles are nonstationary, and there is only one seller in the market in infinitely many periods. Received July 1996/Final version May 1998     

A Non-Interior Path Following Method for Convex Quadratic Programming Problems with Bound Constraints

We propose a non-interior path following algorithm for convex quadratic programming problems with bound constraints based on Chen-Harker-Kanzow-Smale smoothing technique. Conditions are given under which the algorithm is globally convergent or globally linearly convergent. Preliminary numerical experiments indicate that the method is promising.     

Successive Pursuit with a Bounded Detection Domain

We study a coplanar model of the successive pursuit of two evaders with unlimited turn rates of the players and a bounded detection domain of a pursuer. Involved in catching the first evader, the pursuer may lose sight of the other. In this case, it must search later for the lost evader in the plane. We describe two guaranteed pursuit strategies obtained as solutions of differential games. Both strategies include a two-stage strategy to shorten to a specified quantity the distance to the nearer evader, and a two-stage strategy to search and capture the other.The strategies are distinguished by their search plans. First, coalition is pursued as a whole. Then, to minimize an uncertainty index, the pursuer approaches the first evader using the strategy of successive pursuit with the unmoved second evader at its last observed position. Subsequently, the pursuer moves directly to that position of the second evader, or according to the more complex plan, alternates between traversing a straight line and arcs of logarithmic spirals. After detection, the remaining evader is captured with the use of a simple pursuit strategy.The barriers fit the strategies. We call them approximate, since they bound the states where the pursuer succeeds with the guaranteed (but not optimal as in the case of ordinary barriers) strategies. These barriers are surfaces of constant values of a special game of degree. The more complex search plan secures a wider winning area.Geometrical interpretations and some numerical results for a set of parameters of the game are provided.     

A dynamical characterization of evolutionarily stable states

Evolutionary stability, the central solution concept in evolutionary game theory, is closely related to local asymptotic stability in a certain nonlinear dynamical system operating on the state space, the so-called "replicator dynamics". However, a purely dynamical characterization of evolutionary stability is not available in an elementary manner. This characterization can be achieved by investigating so-called "derived games" which consist of mixed strategies corresponding to successful states in the original game. Using well-known facts, several characterization results are obtained within this context. These also may shed light on the extremality properties of evolutionary stability.     

Recent Strategies and Applications for l-Asparaginase Confinement

l-asparaginase (ASNase, EC 3.5.1.1) is an aminohydrolase enzyme with important uses in the therapeutic/pharmaceutical and food industries. Its main applications are as an anticancer drug, mostly for acute lymphoblastic leukaemia (ALL) treatment, and in acrylamide reduction when starch-rich foods are cooked at temperatures above 100 °C. Its use as a biosensor for asparagine in both industries has also been reported. However, there are certain challenges associated with ASNase applications. Depending on the ASNase source, the major challenges of its pharmaceutical application are the hypersensitivity reactions that it causes in ALL patients and its short half-life and fast plasma clearance in the blood system by native proteases. In addition, ASNase is generally unstable and it is a thermolabile enzyme, which also hinders its application in the food sector. These drawbacks have been overcome by the ASNase confinement in different (nano)materials through distinct techniques, such as physical adsorption, covalent attachment and entrapment. Overall, this review describes the most recent strategies reported for ASNase confinement in numerous (nano)materials, highlighting its improved properties, especially specificity, half-life enhancement and thermal and operational stability improvement, allowing its reuse, increased proteolysis resistance and immunogenicity elimination. The most recent applications of confined ASNase in nanomaterials are reviewed for the first time, simultaneously providing prospects in the described fields of application.