Analytical solution for a class of linear quadratic open-loop Nash game with multiple players

In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrix can be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure.     

An efficient game for vehicle-to-grid coordination problems in smart grids

Emerging plug-in electric vehicles (PEVs), as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grids, like frequency and voltage regulations, by coordinating their active and reactive power rates. However, due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviours among these units in a distributed way. In this paper, we formulate the underlying coordination problems as a novel class of Vickrey–Clarke–Groves style (VCG-style) auction games where players, power grids and PEVs do not report a full cost or valuation function but only a multidimensional bid signal: the maximum active and reactive power quantities that a power grid wants and the maximum per unit prices it is willing to pay, and the maximum active and reactive power quantities that a PEV can provide and the minimum per unit prices it asks for. We show the existence of the efficient Nash equilibrium (NE) for the underlying auction games, though there may exist other inefficient NEs. In order to deal with large-scale PEVs, we design games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extend the so-called quantised-progressive second price mechanism to the underlying auction games to implement the efficient NE.     

Analytic numerical solution of coupled semi-infinite diffusion problems

In this paper, we consider coupled semi-infinite diffusion problems of the form u_t(x, t)− A² u_xx(x,t) = 0, x> 0, t> 0, subject to u(0,t)=B and u(x,0)=0, where A is a matrix in , and u(x,t), and B are vectors in . Using the Fourier sine transform, an explicit exact solution of the problem is proposed. Given an admissible error and a domain D(x₀,t₀)={(x,t);0≤x≤x₀, t≥t₀ > 0, an analytic approximate solution is constructed so that the error with respect to the exact solution is uniformly upper bounded by in D(x₀, t₀).     

An approach to the solution of nonlinear unconstrained optimization problems

An approach to reducing a constrained convex programming problem to an unconstrained optimization problem is considered. An initial internal feasible point is supposed to be specified. An equivalent unconstrained optimization problem is formulated in such a way that the calculated values of gradients (subgradients) of original functions do not violate the initial constraints. Properties of introduced functions are investigated. Convexity conditions are formulated for the unconstrained optimization problem. The results may by useful for the development of algorithms for solving constrained optimization problems.     

An approximate dynamic programming approach to convex quadratic knapsack problems

Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic programming relaxation (CQPR), and (b) the integral parts of the solutions to CQPR. We propose a new heuristic which adaptively fixes the variables according to the solution of CQPR. We report computational results for QKPs with up to 200 integer variables. Our numerical results illustrate that the new heuristic produces high-quality solutions to large-scale QKPs fast and robustly.     

Deforestation and foreign transfers: a Stackelberg differential game approach

In this paper, our concern is with deforestation as a global environmental issue. Foreign transfers from developed or Northern countries to developing or Southern countries have been proposed to deal with that issue. We use a Stackelberg differential game approach where the two players are: a donor community (the leader) and a recipient country (the follower). We study the impact of different specifications for the transfer function, related to the different information structures the players can consider when playing the Stackelberg game. The different scenarios are compared both from the environmental and economic points of view.     

Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients

In this paper, a class of fuzzy random differential equations with non-Lipschitz coefficients is studied. The existence and uniqueness of solutions for fuzzy random differential equations with non-Lipschitz coefficients is first proved. Then the dependence of fuzzy random differential equations on initial values is discussed. Finally the non-confluence property of the solution for fuzzy random differential equation is investigated. Our main tool is the Gronwall lemma.     

On uniqueness of solution to the multi-peg towers of hanoi

The multi-peg Towers of Hanoi problem is still open. No provably optimal constructive algorithm to solve the problem is known. The minimum number of moves required is also unknown. Though optimal solutions are observed to be non-unique, the exact uniqueness criteria of an optimal solution are little known to the literature. This paper revisits a deterministic algorithm conjectured to optimally solve the problem and addresses the uniqueness characteristics of an optimal solution.     

A narrative metaphor to facilitate educational game authoring

In this paper we present WEEV (Writing Environment for Educational Video games), a methodology for educational point-and-click adventure game authoring. Our approach aims to allow educators to actively collaborate in the educational game development process, using a narrative-based representation. WEEV is based on a pragmatic reinterpretation of previous works on narrativity and video games, enhanced by the use of a novel visual language to represent the flow of the story or narrative. The WEEV methodology has been implemented into an actual tool based on the already established <e-Adventure> platform for educational games. This tool was improved with feedback gathered from formative evaluation, end-users testing (i.e. educators), and actual use in the development of an educational game. The system, still under development, presents some user-interaction problems along with a need for the educational effectiveness of the resulting games to be further analyzed. However, this paper highlights that, according to the qualitative results of evaluations, WEEV can indeed be successfully applied to simplify the game creation process and that by using representations of games that educators can understand, WEEV can help provide educational value to games.     

Higher order dispersive and dissipative hybrid method for the numerical solution of oscillatory problems

In this paper, an improved explicit two-step hybrid method with fifth algebraic order is derived. The new method possesses dispersion of order 10 and dissipation of order seven, which is first of its kind in the literature. Numerical experiment reveals the superiority of the new method for solving oscillatory or periodic problems over several methods of the same algebraic order.     

Ordinal optimization approach to rare event probability problems

In this paper we introduce a new approach to rare event simulation. Because of the extensive simulation required for precise estimation of performance criterion dependent on rare event occurrences, obstacles such as computing budget/time constraints and pseudo-random number generator limitations can become prohibitive, particularly if comparative study of different system designs is involved. Existing methods for rare events simulation have focused on simulation budget reduction while attempting to generate accurate performance estimates. In this paper we propose a new approach for rare events system analysis in which we relax the simulation goal to the isolation of a set of good enough designs with high probability. Given this relaxation, referred to as ordinal optimization and advanced by Ho et al. (1992), this paper's approach calls instead for the consideration of an appropriate surrogate design problem This surrogate problem is characterized by its approximate ordinal equivalence to the original problem and its performance criterion's dependence not on rare event occurrences, but on more frequent events. Evaluation of such a surrogate problem under the relaxed goals of ordinal optimization has experimentally resulted in orders of magnitude reduction in simulation burden.     

An online game approach for improving students’ learning performance in web-based problem-solving activities

In this paper, an online game was developed in the form of a competitive board game for conducting web-based problem-solving activities. The participants of the game determined their move by throwing a dice. Each location of the game board corresponds to a gaming task, which could be a web-based information-searching question or a mini-game; the former was used to guide the participants to search for information to answer a series of questions related to the target learning issue, while the latter was used to provide supplementary materials during the gaming process. To evaluate the performance of the proposed approach, an experiment was conducted on an elementary school natural science course. The experimental results showed that the proposed approach not only significantly promoted the flow experience, learning attitudes, learning interest and technology acceptance degree of the students, but also improved their learning achievements in the web-based problem-solving activity.     

Simple reinforcement learning agents: Pareto beats Nash in an algorithmic game theory study

Repeated play in games by simple adaptive agents is investigated. The agents use Q-learning, a special form of reinforcement learning, to direct learning of behavioral strategies in a number of 2×2 games. The agents are able effectively to maximize the total wealth extracted. This often leads to Pareto optimal outcomes. When the rewards signals are sufficiently clear, Pareto optimal outcomes will largely be achieved. The effect can select Pareto outcomes that are not Nash equilibria and it can select Pareto optimal outcomes among Nash equilibria.Acknowledgement This material is based upon work supported by, or in part by, NSF grant number SES-9709548. We wish to thank an anonymous referee for a number of very helpful suggestions.     

On the Existence and Uniqueness of Equilibrium Situations in Markovian Games with Discounting

Markovian (stochastic) two-person games with discounting are considered. It is proved that if the set of states of such a game and the set of decisions of the players are finite, then the game has values and both players have optimal stationary strategies. The proof, which is based on the principle of contracting mappings, is constructive and leads to a recurrent algorithm of finding solutions of the game. The question of uniqueness of an equilibrium situation in the game considered is also discussed. In addition to the Markovian game with discounting in the context of the principle of contracting mappings, its subgame, namely, a Markovian decision process with discounting is also studied.     

An approach to solving discrete vector optimization problems over a combinatorial set of permutations

Complex discrete multicriteria problems over a combinatorial set of permutations are analyzed. Some properties of an admissible domain for a combinatorial multicriteria problem embedded into an arithmetic Euclidian space are considered. Optimality conditions are obtained for different types of effective solutions. A new approach to solving the problems formulated is constructed and substantiated. This work was supported by the Fundamental Research Fund of Ukraine (project Φ251/094). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 158–172, May–June 2008.     

An evolutionary game approach to IoT task offloading in fog-cloud computing

The Journal of Supercomputing - Developing the edge and fog computing has been the result of the fast growth of cloud-based IoT applications. These new paradigms define new resource management...