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Relevant bibliographies by topics / Differential games

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Academic literature on the topic 'Differential games'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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Journal articles on the topic "Differential games"

1

Platzer, André. "Differential Hybrid Games." ACM Transactions on Computational Logic 18, no. 3 (August 21, 2017): 1–44. http://dx.doi.org/10.1145/3091123.

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Quincampoix, Marc. "Playable differential games." Journal of Mathematical Analysis and Applications 161, no. 1 (October 1991): 194–211. http://dx.doi.org/10.1016/0022-247x(91)90369-b.

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Smolyakov, É. R. "Multicriterion differential games." Cybernetics and Systems Analysis 30, no. 1 (January 1994): 10–17. http://dx.doi.org/10.1007/bf02366357.

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Bressan, Alberto. "Noncooperative Differential Games." Milan Journal of Mathematics 79, no. 2 (August 28, 2011): 357–427. http://dx.doi.org/10.1007/s00032-011-0163-6.

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Pei, Hai-Long, and Ming-An Tong. "Team Differential Games." IFAC Proceedings Volumes 23, no. 8 (August 1990): 433–37. http://dx.doi.org/10.1016/s1474-6670(17)51954-0.

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Serea, Oana-Silvia. "Reflected Differential Games." SIAM Journal on Control and Optimization 48, no. 4 (January 2009): 2516–32. http://dx.doi.org/10.1137/080739215.

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Fonseca-Morales, Alejandra, and Onésimo Hernández-Lerma. "Potential Differential Games." Dynamic Games and Applications 8, no. 2 (April 3, 2017): 254–79. http://dx.doi.org/10.1007/s13235-017-0218-6.

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Yong, Jiongmin. "On Differential Evasion Games." SIAM Journal on Control and Optimization 26, no. 1 (January 1988): 1–22. http://dx.doi.org/10.1137/0326001.

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Yong, Jiongmin. "On Differential Pursuit Games." SIAM Journal on Control and Optimization 26, no. 2 (March 1988): 478–95. http://dx.doi.org/10.1137/0326029.

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Browne, Sid. "Stochastic differential portfolio games." Journal of Applied Probability 37, no. 1 (March 2000): 126–47. http://dx.doi.org/10.1239/jap/1014842273.

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We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. This leads to a stochastic differential game with controlled drift and variance. For the most part, we consider games with payoffs that depend on the achievement of relative performance goals and/or shortfalls. We provide conditions under which a game with a general payoff function has an achievable value, and give an explicit representation for the value and resulting equilibrium portfolio strategies in that case. It is shown that non-perfect correlation is required to rule out trivial solutions. We then use this general result explicitly to solve a variety of specific games. For example, we solve a probability maximizing game, where each investor is trying to maximize the probability of beating the other's return by a given predetermined percentage. We also consider objectives related to the minimization or maximization of the expected time until one investor's return beats the other investor's return by a given percentage. Our results allow a new interpretation of the market price of risk in a Black-Scholes world. Games with discounting are also discussed, as are games of fixed duration related to utility maximization.

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Dissertations / Theses on the topic "Differential games"

1

Li, Dongxu. "Multi-player pursuit-evasion differential games." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1164738831.

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Hosking, Thomas Shannon. "Differential games of exhaustible resource extraction." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:0e740dad-4dd8-4f49-9dbb-3de5d7328960.

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This thesis is concerned with game-theoretic models of oligopoly resource markets. They revolve around an open market, on which a number of firms sell a common resource. The market price-demand relationship means that the price (demand) that results from the firm’s production (pricing) decisions is a function of the decisions of all firms selling to that market. This means that firms must generally anticipate the actions of competing firms when determining their own strategies, which means that these models often need to be analysed using game theory. We focus on games in which the resource is exhaustible, with the exception of Chapter 5, in which the majority of the analysis is carried out in an inexhaustible resources setting. Exhaustibility introduces an additional complication into these games; that of allocating the extraction and sale of a limited resource pool over time. We consider several separate areas of extension, which we outline below. In Chapter 2, we consider a dynamic Stackelberg game. Stackelberg competition is an asymmetric form of competition in which one player (the leader) has the ability to pre-commit to and announce a strategy in advance. The ability to pre-commit to a strategy is almost always highly valuable, and in this case allows the leader to drive down the follower’s production by pre-committing to drive up their own. We follow the framework used in [62] to analyse Cournot competition to derive our results. In Chapter 3, we compare the two settings in which resource extraction models are usually formulated: Open-Loop, in which the players determine their strategies as functions of time and the initial resource levels of the players only; and Feedback-Loop, in which the players determine their strategies at each point in time as a function of the current resource levels at that time. Our focus is on the investigation of the relationship between the difference in the production or value of a firm under these two models, and the distribution of resources across the firms. In Chapter 4, we consider a common property resource game. These involve multiple firms which can extract from a common resource pool. We study a widely-used Open- viii Loop model, as formulated in [79]. We examine the result that analysis of the problem by standard methods results in two candidate equilibria, and argue that one of these equilibria can be ruled out by construction of a superior response. In Chapter 5, we analyse joint constraints on production, namely constraints which are met when the total production is above or below a certain level. It is a well- established result that these constraints can result in multiple equilibria. We provide several brief extensions to existing uniqueness results. We also demonstrate methods by which these results can be utilised to analyse games with piecewise-linear windfall taxes or congestion charges. Finally, we discuss the problems of extending these results to games with resource exhaustibility.

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Khadem, Varqa. "Pricing corporate securities and stochastic differential games." Thesis, University of Oxford, 2001. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393555.

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Ling, Chen. "THREE ESSAYS ON DIFFERENTIAL GAMES AND RESOURCE ECONOMICS." Doctoral diss., University of Central Florida, 2010. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3887.

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This dissertation consists of three chapters on the topic of differential games and resource economics. The first chapter extends the envelope theorem to the class of discounted infinite horizon differential games that posses locally differentiable Nash equilibria. The theorems cover both the open-loop and feedback information structures, and are applied to a simple analytically solvable linear-quadratic game. The results show that the conventional interpretation of the costate variable as the shadow value of the state variable along the equilibrium path is only valid for feedback Nash equilibria, but not for open-loop Nash equilibria. The specific linear-quadratic structure provides some extra insights on the theorem. For example, the costate variable is shown to uniformly overestimate the shadow value of the state variable in the open-loop case, but the growth rate of the costate variable are the same as the shadow value under open-loop and feedback information structures. Chapter two investigates the qualitative properties of symmetric open-loop Nash equilibria for a ubiquitous class of discounted infinite horizon differential games. The results show that the specific functional forms and the value of parameters used in the game are crucial in determining the local asymptotic stability of steady state, the steady state comparative statics, and the local comparative dynamics. Several sufficient conditions are provided to identify a local saddle point type of steady state. An important steady state policy implication from the model is that functional forms and parameter values are not only quantitatively important to differentiate policy tools, but they are also qualitatively important. Chapter three shifts the interests to the lottery mechanism for rationing public resources. It characterizes the optimal pricing strategies of lotteries for a welfare-maximization agency. The optimal prices are shown to be positive for a wide range of individual private value distributions, suggesting that the sub-optimal pricing may result in a significant efficiency loss and that the earlier studies under zero-pricing may need to be re-examined. In addition, I identify the revenue and welfare equivalency propositions across lottery institutions. Finally, the numerical simulations strongly support the findings.
Ph.D.
Department of Economics
Business Administration
Economics PhD

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Yang, James Ting Feng. "Singular Perturbation of Stochastic Control and Differential Games." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/22979.

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The defining trait of singular perturbation problems in dynamical systems is the degeneracy of the highest order differential term when a small parameter is formally set to be zero. The implication is that the limiting solution does not entirely coincide with the solution to the degenerated system. It then becomes apparent that the derivation of the limiting solution is non-trivial. However, under certain circumstances, this has been resolved by the Tikhonov's theorem. On the other hand, these problems arise naturally in slow-fast or multiscale models where the small parameter represents the ratio between the evolutionary speeds. Moreover, the limiting solution is often of lower dimensionality and offers a viable method for dimension reduction. For these reasons, singular perturbation techniques have been widely applied in optimisation theory to disciplines such as ecology, robotics, finance and physics, to name a few. In this thesis, we propose three optimisation problems described by a quadratic cost function and a coupled pair of slow-fast linear state equations driven by Brownian motion. The first one is an optimal control problem when the state and control appear in the diffusion coefficient of the noise. The second one is a two-player zero-sum differential game with a constant diffusion coefficient. And third, is an optimal control problem with processes taking values in infinite dimensional spaces. Our aim is to investigate the limiting behaviour of these optimisation problems and its value functions. The general approach is to convert the stochastic and controlled singular perturbation problem into a classical and deterministic singular perturbation problem via the Riccati equation. Consequently, a version of Tikhonov's theorem has to be formulated.

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Hoof, Simon [Verfasser]. "Essays on cooperation in differential games / Simon Hoof." Paderborn : Universitätsbibliothek, 2020. http://d-nb.info/1222587947/34.

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Lin, Wei. "Differential Games for Multi-Agent Systems under Distributed Information." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5973.

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In this dissertation, we consider differential games for multi-agent systems under distributed information where every agent is only able to acquire information about the others according to a directed information graph of local communication/sensor networks. Such games arise naturally from many applications including mobile robot coordination, power system optimization, multi-player pursuit-evasion games, etc. Since the admissible strategy of each agent has to conform to the information graph constraint, the conventional game strategy design approaches based upon Riccati equation(s) are not applicable because all the agents are required to have the information of the entire system. Accordingly, the game strategy design under distributed information is commonly known to be challenging. Toward this end, we propose novel open-loop and feedback game strategy design approaches for Nash equilibrium and noninferior solutions with a focus on linear quadratic differential games. For the open-loop design, approximate Nash/noninferior game strategies are proposed by integrating distributed state estimation into the open-loop global-information Nash/noninferior strategies such that, without global information, the distributed game strategies can be made arbitrarily close to and asymptotically converge over time to the global-information strategies. For the feedback design, we propose the best achievable performance indices based approach under which the distributed strategies form a Nash equilibrium or noninferior solution with respect to a set of performance indices that are the closest to the original indices. This approach overcomes two issues in the classical optimal output feedback approach: the simultaneous optimization and initial state dependence. The proposed open-loop and feedback design approaches are applied to an unmanned aerial vehicle formation control problem and a multi-pursuer single-evader differential game problem, respectively. Simulation results of several scenarios are presented for illustration.
Ph.D.
Doctorate
Electrical Engineering and Computer Science
Engineering and Computer Science
Electrical Engineering

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Mylvaganam, Thulasi. "Approximate feedback solutions for differential games : theory and applications." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/24975.

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Differential games deal with problems involving multiple players, possibly competing, that influence common dynamics via their actions, commonly referred to as strategies. Thus, differential games introduce the notion of strategic decision making and have a wide range of applications. The work presented in this thesis has two aims. First, constructive approximate solutions to differential games are provided. Different areas of application for the theory are then suggested through a series of examples. Notably, multi-agent systems are identified as a possible application domain for differential game theory. Problems involving multi-agent systems may be formulated as nonlinear differential games for which closed-form solutions do not exist in general, and in these cases the constructive approximate solutions may be useful. The thesis is commenced with an introduction to differential games, focusing on feedback Nash equilibrium solutions. Obtaining such solutions involves solving coupled partial differential equations. Since closed-form solutions for these cannot, in general, be found two methods of constructing approximate solutions for a class of nonlinear, nonzero-sum differential games are developed and applied to some illustrative examples, including the multi-agent collision avoidance problem. The results are extended to a class of nonlinear Stackelberg differential games. The problem of monitoring a region using a team of agents is then formulated as a differential game for which ad-hoc solutions, using ideas introduced previously, are found. Finally mean-field games, which consider differential games with infinitely many players, are considered. It is shown that for a class of mean-field games, solutions rely on a set of ordinary differential equations in place of two coupled partial differential equations which normally characterise the problem.

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Tsukahara, Shinya. "Applied Differential Games in Resource Economics and Political Economy." Kyoto University, 2012. http://hdl.handle.net/2433/158069.

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Priuli, Fabio Simone. "On feedback strategies in control problems and differential games." Doctoral thesis, SISSA, 2006. http://hdl.handle.net/20.500.11767/3999.

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This thesis consists of two parts. In the first part we study the existence and uniqueness of Nash equilibrium solutions for a class of infinite horizon, non-cooperative differential games. The second part is concerned with the construction of nearly-optimal patchy feedbacks, for problems of optimal control.

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Books on the topic "Differential games"

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Lewin, Joseph. Differential Games. London: Springer London, 1994. http://dx.doi.org/10.1007/978-1-4471-2065-0.

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Mehlmann, Alexander. Applied Differential Games. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-3731-5.

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Mehlmann, Alexander. Applied differential games. New York: Plenum Press, 1988.

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Yeung, David W. K. Cooperative stochastic differential games. New York: Springer, 2010.

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Bardi, Martino, T. E. S. Raghavan, and T. Parthasarathy, eds. Stochastic and Differential Games. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1592-9.

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Başar, Tamer S., and Pierre Bernhard, eds. Differential Games and Applications. Berlin/Heidelberg: Springer-Verlag, 1989. http://dx.doi.org/10.1007/bfb0004258.

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Jørgensen, Steffen, and Georges Zaccour. Differential Games in Marketing. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4419-8929-1.

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1935-, Yavin Yaakov, Pachter M, and Rodin Ervin Y. 1932-, eds. Pursuit-evasion differential games. Oxford, England: Pergamon Press, 1987.

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Georges, Zaccour, ed. Differential games in marketing. Boston: Kluwer Academic Publishers, 2004.

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Başar, Tamer S. Differential Games and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989.

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Book chapters on the topic "Differential games"

1

Erickson, Gary M. "Differential Games." In Encyclopedia of Operations Research and Management Science, 413–18. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_1150.

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Bardi, Martino, and Italo Capuzzo-Dolcetta. "Differential Games." In Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, 431–70. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-0-8176-4755-1_8.

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Aubin, Jean-Pierre. "Differential Games." In Viability Theory, 451–84. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4910-4_16.

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Sethi, Suresh P. "Differential Games." In Optimal Control Theory, 385–407. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98237-3_13.

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Quincampoix, Marc. "Differential Games." In Encyclopedia of Complexity and Systems Science, 1–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-642-27737-5_123-2.

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Quincampoix, Marc. "Differential Games." In Computational Complexity, 854–61. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1800-9_55.

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Clemhout, Simone, and Henry Y. Wan. "Differential Games." In The New Palgrave Dictionary of Economics, 2872–74. London: Palgrave Macmillan UK, 2018. http://dx.doi.org/10.1057/978-1-349-95189-5_75.

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Quincampoix, Marc. "Differential Games." In Encyclopedia of Complexity and Systems Science, 1948–56. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-30440-3_123.

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Subbotin, Andreĭ I. "Differential Games." In System & Control: Foundations & Applications, 115–200. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-0847-1_3.

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Bensoussan, Alain. "Differential Games." In Interdisciplinary Applied Mathematics, 459–92. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75456-7_16.

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Conference papers on the topic "Differential games"

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Yong, Jiongmin. "Differential pursuit games." In 26th IEEE Conference on Decision and Control. IEEE, 1987. http://dx.doi.org/10.1109/cdc.1987.272573.

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Petrosyan, Leon Aganesovich. "Cooperative differential games." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Moscow: Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22847.

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Molloy, Timothy L., Jason J. Ford, and Tristan Perez. "Inverse noncooperative differential games." In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. http://dx.doi.org/10.1109/cdc.2017.8264504.

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Fioretto, Ferdinando, Lesia Mitridati, and Pascal Van Hentenryck. "Differential Privacy for Stackelberg Games." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/481.

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This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and interdependent markets. This coordination represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents. The paper is motivated by the observation that the perturbation introduced by traditional DP mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of feasibility and fidelity (i.e. near-optimality) of the privacy-preserving information to the original problem objective. PPSM complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the proposed approach. A full version of this paper [Fioretto et al., 2020b] contains complete proofs and additional discussion on the motivating application.

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Kun, Gabor. "Differential games on Lie groups." In 2001 European Control Conference (ECC). IEEE, 2001. http://dx.doi.org/10.23919/ecc.2001.7075873.

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Mellies, Paul-Andre. "Template games and differential linear logic." In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2019. http://dx.doi.org/10.1109/lics.2019.8785830.

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Ledyaev, Yurii Semenovich. "Program-predictive control for differential games." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Moscow: Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22844.

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Engwerda, J. C., and P. V. Reddy. "A Positioning of Cooperative Differential Games." In 5th International ICST Conference on Performance Evaluation Methodologies and Tools. ACM, 2011. http://dx.doi.org/10.4108/icst.valuetools.2011.245831.

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Solo, Victor. "Adaptive estimation of stochastic differential games." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426983.

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Mukai, H., A. Tanikawa, P. Rinaldi, and S. Louis. "Sequential quadratic methods for differential games." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.945538.

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Reports on the topic "Differential games"

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Platzer, Andre. Differential Game Logic for Hybrid Games. Fort Belvoir, VA: Defense Technical Information Center, March 2012. http://dx.doi.org/10.21236/ada561153.

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Dupuis, Paul, and Hui Wang. Importance Sampling, Large Deviations, and Differential Games. Fort Belvoir, VA: Defense Technical Information Center, January 2002. http://dx.doi.org/10.21236/ada461855.

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Rodin, Ervin Y. Artificial Intelligence Methods in Pursuit Evasion Differential Games. Fort Belvoir, VA: Defense Technical Information Center, July 1990. http://dx.doi.org/10.21236/ada227366.

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Kushner, Harold J. Numerical Approximations for Stochastic Differential Games: The Ergodic Case. Fort Belvoir, VA: Defense Technical Information Center, December 2001. http://dx.doi.org/10.21236/ada461762.

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Breckenridge, Amar. Developing an Issues-Based Approach to Special and Differential Treatment. Inter-American Development Bank, March 2002. http://dx.doi.org/10.18235/0011005.

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Trade liberalization is a positive sum game from which all can benefit. Well-defined rules, and the mechanisms of making binding commitments and concessions, are beneficial to increasing the stability of reforms.

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Rodin, Ervin Y. Artificial Intelligence Methodologies in Flight Related Differential Game, Control and Optimization Problems. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada262405.

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