Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.

Determination of rational strategies for players in two-target games

This paper addresses some of the basic issues involved in the determination of rational strategies for players in two-target games. We show that unlike single-target games where the task of role assignment and selection of strategies is conceptually straightforward, in two-target games, many factors like the preference ordering of outcomes by players, the relative configuration of the target sets and secured outcome regions, the uncertainty about the parameters of the game, etc., also influence the rational selection of strategies by players. The importance of these issues is illustrated through appropriate examples.

Effect of microstructure and hardness on the grinding abrasive wear resistance of a ball bearing steel

Grinding media wear appears to be non-linear with the time of grinding in a laboratory-scale ball mill. The kinetics of wear can be expressed as a power law of the type w=atb, where the numerical constant a represents wear of a particular microstructure at time t = 1 min and b is the wear exponent which is independent of the particle size prevailing inside a ball mill at any instant of time of grinding. The wear exponent appears to be an indicator of the cutting wear mechanism in dry grinding: a plot of the inverse of the normalised wear exponent (Image ) versusHs (where Hs is the worn surface hardness of the media) yields a curve similar to that of a wear resistance plot obtained in the case of two-body sliding abrasive wear. This method of evaluating the cutting wear resistance of media is demonstrated by employing 15 different microstructures of AISI-SAE 52100 steel balls in dry grinding of quartz in a laboratory-scale ball mill.

Ball wear mechanisms and control in the grinding of sulfide and phosphate ores

Marked ball grinding tests were carried out in the laboratory using high carbon low alloy steel (cast and forged) and high chrome cast iron balls. Relative ball wear as a function of grinding period and milling conditions was evaluated for the different type of ball materials in the grinding of lead-zinc sulphide and phosphate ores. Results indicated that ball wear increased with time and showed a sharp increase for wet grinding over dry grinding. Ball wear under wet grinding conditions was also influenced by the gaseous atmosphere in the mill. The influence of oxygen on the corrosive wear of grinding balls was increasingly felt in case of sulphide ore grinding. The grinding ball materials could be arranged in the following order with respect to their overall wear resistance:

Combined Cryo and Room-Temperature Ball Milling to Produce Ultrafine Halide Crystallites

The combined milling at cryogenic temperature as well as room temperature (RT) has been carried out to prepare ultrafine NaCl crystallites. The milling has been done in evacuated tungsten carbide vials backfilled with high-purity Ar. The results indicate the effect duration of cryomilling prior to RT milling has a strong effect on the final crystallite size. The deformation aided sintering of NaCl crystallites during RT milling and leads to the formation of bimodal distribution of crystallites. The cuboidal-shaped NaCl crystallite undergoes a roughening transition due to plastic deformation. The experimental results are explained using the temperature-dependent mechanical properties of NaCl single crystals and plastic-deformation-induced roughening.

Laboratory studies on ball wear in the grinding of a chalcopyrite ore

Wear of high carbon low alloy (HCLA) cast steel balls during the grinding of a chalcopyrite ore was evaluated under different experimental conditions. The role of oxygen in enhancing ball wear during wet finding is brought out. The influence of pH on ball wear was also examined from the view point of acid production during grinding and reactivity of sulphides. Contributions from corrosion and abrasion towards ball wear are quantified in terms of ball wear rates as a function of time, particle size and gaseous atmosphere in the mill.

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Provider-Customer Coalitional Games

Efficacy of commercial wireless networks can be substantially enhanced through large-scale cooperation among involved entities such as providers and customers. The success of such cooperation is contingent upon the design of judicious resource allocation strategies that ensure that the individuals' payoffs are commensurate to the resources they offer to the coalition. The resource allocation strategies depend on which entities are decision-makers and whether and how they share their aggregate payoffs. Initially, we consider the scenario where the providers are the only decision-makers and they do not share their payoffs. We formulate the resource allocation problem as a nontransferable payoff coalitional game and show that there exists a cooperation strategy that leaves no incentive for any subset of providers to split from the grand coalition, i.e., the core of the game is nonempty. To compute this cooperation strategy and the corresponding payoffs, we subsequently relate this game and its core to an exchange market setting and its equilibrium, which can be computed by several efficient algorithms. Next, we investigate cooperation when customers are also decision-makers and decide which provider to subscribe to based on whether there is cooperation. We formulate a coalitional game in this setting and show that it has a nonempty core. Finally, we extend the formulations and results to the cases where the payoffs are vectors and can be shared selectively.

Preparation of ultrafine CsCl crystallites by combined cryogenic and room temperature ball milling

The present investigation reports the preparation and microstructural characterization of ultrafine CsCl crystallites using combined cryogenic and room temperature (RT) mechanical milling. The milling has been performed in evacuated WC vials under high purity argon atmosphere. The low temperature milling has been utilized as an effective means of rapid fracturing of the CsCl crystallites. This was followed by RT milling for different time durations. The final crystallite size obtained is 10 +/- 6 nm for sample cryo-milled for 11 h and subsequently RT milled for 35 h. The experimental findings indicate the strong effect of duration of cryo-milling on the final size of the crystallites. The prolonged room temperature milling leads to increase of the crystallite size due to deformation-induced sintering. The results have been discussed in the light of currently available literature. (C) 2011 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Friction between a Steel Ball and a Steel Flat Lubricated by MoS2 Particles Suspended in Hexadecane at 150 degrees C

A steel ball was slid on a steel flat lubricated by molybdenum disulfide (MoS2) particles suspended in hexadecane oil at 150 degrees C. The friction data is compared with that obtained when the ball was slid on the flat sprayed apriori with nominally dry MoS2 particles. The friction in the dry experiment was found to increase with temperature while the friction in wet condition was found to decrease with increasing temperature. Micro-Raman and Fourier transform IR spectroscopy are used to explore the roles of environmental moisture and chemical degradation of oil on the formation of antifriction film on the steel substrate.

General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.