Relevant bibliographies by topics / Perfect nash equilibrium in subgames

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Academic literature on the topic 'Perfect nash equilibrium in subgames'

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Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Perfect nash equilibrium in subgames"

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Demeze-Jouatsa, Ghislain-Herman. "A complete folk theorem for finitely repeated games." International Journal of Game Theory 49, no. 4 (September 28, 2020): 1129–42. http://dx.doi.org/10.1007/s00182-020-00735-z.

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AbstractThis paper analyzes the set of pure strategy subgame perfect Nash equilibria of any finitely repeated game with complete information and perfect monitoring. The main result is a complete characterization of the limit set, as the time horizon increases, of the set of pure strategy subgame perfect Nash equilibrium payoff vectors of the finitely repeated game. This model includes the special case of observable mixed strategies.
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Gibbons, Robert. "An Introduction to Applicable Game Theory." Journal of Economic Perspectives 11, no. 1 (February 1, 1997): 127–49. http://dx.doi.org/10.1257/jep.11.1.127.

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This paper offers an introduction to game theory for applied economists. The author gives simple definitions and intuitive examples of four kinds of games and their corresponding solution concepts: Nash equilibrium in static games of complete information; subgame-perfect Nash equilibrium in dynamic games of complete information; Bayesian Nash equilibrium in static games with incomplete (or 'private') information; and perfect Bayesian (or sequential) equilibrium in dynamic games with incomplete information. The main theme of the paper is that there are important differences among the games but important similarities among the solution concepts.
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Abreu, Dilip, Benjamin Brooks, and Yuliy Sannikov. "Algorithms for Stochastic Games With Perfect Monitoring." Econometrica 88, no. 4 (2020): 1661–95. http://dx.doi.org/10.3982/ecta14357.

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We study the pure‐strategy subgame‐perfect Nash equilibria of stochastic games with perfect monitoring, geometric discounting, and public randomization. We develop novel algorithms for computing equilibrium payoffs, in which we combine policy iteration when incentive constraints are slack with value iteration when incentive constraints bind. We also provide software implementations of our algorithms. Preliminary simulations indicate that they are significantly more efficient than existing methods. The theoretical results that underlie the algorithms also imply bounds on the computational complexity of equilibrium payoffs when there are two players. When there are more than two players, we show by example that the number of extreme equilibrium payoffs may be countably infinite.
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Weber, Thomas A. "Quantifying Commitment in Nash Equilibria." International Game Theory Review 21, no. 02 (June 2019): 1940011. http://dx.doi.org/10.1142/s0219198919400115.

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To quantify a player’s commitment in a given Nash equilibrium of a finite dynamic game, we map the corresponding normal-form game to a “canonical extension,” which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average overall adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.
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Góngora, Pedro A., and David A. Rosenblueth. "A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria." International Journal of Applied Mathematics and Computer Science 25, no. 3 (September 1, 2015): 577–96. http://dx.doi.org/10.1515/amcs-2015-0043.

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AbstractConsider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending the Bellman-Ford algorithm for computing shortest paths, we obtain a model-checking algorithm for graph games with respect to formulas in an appropriate logic. Hence, when given a certain formula, our model-checking algorithm computes the subgame-perfect Nash equilibrium (as opposed to simply determining whether or not a given collection of paths is a Nash equilibrium). Next, we develop a symbolic version of our model checker allowing us to handle larger graph games. We illustrate our formalism on the critical-path method as well as games with perfect information. Finally, we report on the execution time of benchmarks of an implementation of our algorithms
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Correa, José, Jasper de Jong, Bart de Keijzer, and Marc Uetz. "The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing." Mathematics of Operations Research 44, no. 4 (November 2019): 1286–303. http://dx.doi.org/10.1287/moor.2018.0968.

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This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n − 2)/(2n + 1), where n is the number of players. This paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n − 2)/(2n + 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Second, we ask whether sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: we show that the sequential price of anarchy equals 7/5 and that computing the outcome of a subgame perfect equilibrium is NP-hard.
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Ohnishi, Kazuhiro. "Non-altruistic Equilibria." Indian Economic Journal 67, no. 3-4 (December 2019): 185–95. http://dx.doi.org/10.1177/0019466220953124.

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Which choice will a player make if he can make one of two choices in which his own payoffs are equal, but his rival’s payoffs are not equal, that is, one with a large payoff for his rival and the other with a small payoff for his rival? This paper introduces non-altruistic equilibria for normal-form games and extensive-form non-altruistic equilibria for extensive-form games as equilibrium concepts of non-cooperative games by discussing such a problem and examines the connections between their equilibrium concepts and Nash and subgame perfect equilibria that are important and frequently encountered equilibrium concepts.
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COULOMB, JEAN MICHEL, and VLADIMIR GAITSGORY. "ON A CLASS OF NASH EQUILIBRIA WITH MEMORY STRATEGIES FOR NONZERO-SUM DIFFERENTIAL GAMES." International Game Theory Review 02, no. 02n03 (June 2000): 173–92. http://dx.doi.org/10.1142/s021919890000010x.

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A two-player nonzero-sum differential game is considered. Given a pair of threat payoff functions, we characterise a set of pairs of acceptable feedback controls. Any such pair induces a history-dependent Nash δ-equilibrium as follows: the players agree to use the acceptable controls unless one of them deviates. If this happens, a feedback control punishment is implemented. The problem of finding a pair of "acceptable" controls is significantly simpler than the problem of finding a feedback control Nash equilibrium. Moreover, the former may have a solution in case the latter does not. In addition, if there is a feedback control Nash equilibrium, then our technique gives a subgame perfect Nash δ-equilibrium that might improve the payoff function for at least one player.
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Caruso, Francesco, Maria Carmela Ceparano, and Jacqueline Morgan. "Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move." Dynamic Games and Applications 9, no. 2 (July 28, 2018): 416–32. http://dx.doi.org/10.1007/s13235-018-0277-3.

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Li, Xianghui, Wei Zheng, and Yang Li. "An axiomatic and non-cooperative approach to the multi-step Shapley value." RAIRO - Operations Research 55, no. 3 (May 2021): 1541–57. http://dx.doi.org/10.1051/ro/2021073.

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Inspired by the two-step Shapley value, in this paper we introduce and axiomatize the multi-step Shapley value for cooperative games with levels structures. Moreover, we design a multi-step bidding mechanism, which implements the value strategically in subgame perfect Nash equilibrium for superadditve games.
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Dissertations / Theses on the topic "Perfect nash equilibrium in subgames"

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Del, Fiori Diogo. "Industrialização do Brasil na década de 1930 : uma aplicação com teoria dos jogos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2011. http://hdl.handle.net/10183/40254.

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O presente trabalho propõe-se analisar a industrialização do Brasil no contexto de mudanças econômicas e políticas no primeiro governo de Getúlio Vargas, de 1930 até 1945. Na literatura de economia brasileira com relação ao surgimento da indústria no Brasil, duas visões se contrapõem: de um lado, a industrialização como subproduto da intervenção do governo no setor cafeeiro; de outro, a industrialização intencionalmente promovida pelo governo. Com base em uma análise de equilíbrio em um jogo dinâmico de informação imperfeita, é evidenciada a racionalidade da criação de instituições para o desenvolvimento industrial na década de 1930. Este resultado de equilíbrio mostra as mudanças pela qual o Brasil passou a partir da década de 1930, com mudanças da estrutura tributária, educacional, financeira e relações de trabalho, ou seja, essa mudança institucional gerou campo fértil para o surgimento do processo de industrialização que caracterizou o primeiro governo Vargas e também mostra a intencionalidade desse governo, quando se observa a transformação do sistema tributário, de tal modo a ficar imune das oscilações econômicas externas e também as mudanças educacionais, que passou a incentivar o ensino primário, secundário e técnico profissionalizante, medidas essas feitas para atender o novo panorama econômico brasileiro. Outro ponto que corrobora o resultado do equilíbrio de Nash perfeito em subjogos é a perda da importância do setor cafeeiro no período que engloba o século XIX até o final do primeiro governo Vargas, onde as evidências mostram que os cafeicultores tinham, antes e durante a década de 1930, tendências a diversificarem investimentos por conta da perda da renda com o setor cafeicultor.
This study proposes to examine the industrialization of Brazil in the context of economic and political changes in the first government of Getulio Vargas, from 1930 until 1945. In the literature of the Brazilian economy with the coming of industry in Brazil, two visions are in opposition: on one hand, industrialization as a byproduct of government intervention in the coffee sector, on the other, deliberately promoted industrialization by the government. Based on an analysis of equilibrium in a dynamic game of imperfect information, rationality is evident from the creation of institutions for industrial development in the 1930s. The result shows the changes of equilibrium in which Brazil went from the 1930s, with changes in the tax structure, educational, financial and labor relations, that institutional change created fertile ground for the rise of industrialization that characterized the first Vargas government and also shows the intention of this government, when one observes the transformation of the tax system, so be immune to external economic fluctuations and also educational changes, which came to encourage the primary, secondary and technical vocational, measures designed to meet the new economic landscape of Brazil. Another point that confirms the outcome of the Nash equilibrium is perfect in subgame the loss of the importance of the coffee sector in the period that includes the nineteenth century until the end of the first Vargas government, where the evidence shows that farmers had, since the decade of 1930, to diversify investment trends due to the loss of income to the grower industry.
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Dimitry, El Baghdady Johan. "Equilibrium Strategies for Time-Inconsistent Stochastic Optimal Control of Asset Allocation." Thesis, KTH, Optimeringslära och systemteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-202520.

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We have examinined the problem of constructing efficient strategies for continuous-time dynamic asset allocation. In order to obtain efficient investment strategies; a stochastic optimal control approach was applied to find optimal transaction control. Two mathematical problems are formulized and studied: Model I; a dynamic programming approach that maximizes an isoelastic functional with respect to given underlying portfolio dynamics and Model II; a more sophisticated approach where a time-inconsistent state dependent mean-variance functional is considered. In contrast to the optimal controls for Model I, which are obtained by solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation; the efficient strategies for Model II are constructed by attaining subgame perfect Nash equilibrium controls that satisfy the extended HJB equation, introduced by Björk et al. in [1]. Furthermore; comprehensive execution algorithms where designed with help from the generated results and several simulations are performed. The results reveal that optimality is obtained for Model I by holding a fix portfolio balance throughout the whole investment period and Model II suggests a continuous liquidation of the risky holdings as time evolves. A clear advantage of using Model II is concluded as it is far more efficient and actually takes time-inconsistency into consideration.
Vi har undersökt problemet som uppstår vid konstruktion av effektiva strategier för tidskontinuerlig dynamisk tillgångsallokering. Tillvägagångsättet för konstruktionen av strategierna har baserats på stokastisk optimal styrteori där optimal transaktionsstyrning beräknas. Två matematiska problem formulerades och betraktades: Modell I, en metod där dynamisk programmering används för att maximera en isoelastisk funktional med avseende på given underliggande portföljdynamik. Modell II, en mer sofistikerad metod som tar i beaktning en tidsinkonsistent och tillståndsberoende avvägning mellan förväntad avkastning och varians. Till skillnad från de optimala styrvariablerna för Modell I som satisfierar Hamilton-Jacobi-Bellmans (HJB) partiella differentialekvation, konstrueras de effektiva strategierna för Modell II genom att erhålla subgame perfekt Nashjämvikt. Dessa satisfierar den utökade HJB ekvationen som introduceras av Björk et al. i [1]. Vidare har övergripande exekveringsalgoritmer skapats med hjälp av resultaten och ett flertal simuleringar har producerats. Resultaten avslöjar att optimalitet för Modell I erhålls genom att hålla en fix portföljbalans mellan de riskfria och riskfyllda tillgångarna, genom hela investeringsperioden. Medan för Modell II föreslås en kontinuerlig likvidering av de riskfyllda tillgångarna i takt med, men inte proportionerligt mot, tidens gång. Slutsatsen är att det finns en tydlig fördel med användandet av Modell II eftersom att resultaten påvisar en påtagligt högre grad av effektivitet samt att modellen faktiskt tar hänsyn till tidsinkonsistens.
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Addo, Sandra E. "A Game-Theoretic Framework To Competitive Individual Targeting." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1258403779.

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Ming, Hui Yang, and Zhang Lei. "The Audit Pricing Decisions for Accounting Firms in China : A Case Study from RSM China." Thesis, Umeå universitet, Handelshögskolan vid Umeå universitet, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-45314.

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Carvalho, Luís. "Three essays on game theory and bargaining." Doctoral thesis, NSBE - UNL, 2014. http://hdl.handle.net/10362/11851.

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A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics
Equilibrium Outcomes of Repeated Two-Person Zero-Sum Games - We consider discounted repeated two-person zero-sum games. We show that even when players have different discount factors (in which case the repeated game is not a zero-sum game), an outcome is subgame perfect if and only if all of its components are Nash equilibria of the stage game. This implies that in all subgame perfect equilibria, each player's payoff is equal to his minmax payoff. In conclusion, the competitive nature of two-player zero-sum games is not altered when the game is repeated.
A Constructive Proof of the Nash Bargaining Solution - We consider the classical axiomatic Nash bargaining framework and propose a constructive proof of its solution. On the first part of this paper we prove Nash’s solution is the result of a maximization problem; on the second part, through the properties of maximand’s indifference curves we derive that it must be equal to xy.
Equilibria and Outcomes in Multiplayer Bargaining - Multiplayer bargaining is a game in which all possible divisions are equilibrium outcomes. This paper presents the classical subgame perfect equilibria strategies and analyses their weak robustness, namely the use of weakly dominated strategies. The paper then develops a refined equilibrium concept, based on trembling hand perfection, in order to overcome such weakness. Concluding that none of the classical equilibrium strategies survives the imposition of the extra robustness and, albeit using more complex strategies, the equilibrium outcomes don't change.
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Book chapters on the topic "Perfect nash equilibrium in subgames"

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Gintis, Herbert. "Extensive Form Rationalizability." In The Bounds of Reason. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691160849.003.0005.

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The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible). Backward induction, by far the most popular technique, employs the iterated elimination of weakly dominated strategies, arriving at the subgame perfect Nash equilibria—the equilibria that remain Nash equilibria in all subgames. An extensive form game is considered generic if it has a unique subgame perfect Nash equilibrium. This chapter develops the tools of modal logic and presents Robert Aumann's famous proof that common knowledge of rationality (CKR) implies backward induction. It concludes that Aumann is perfectly correct, and the real culprit is CKR itself. CKR is in fact self-contradictory when applied to extensive form games.
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Bresson, Alain. "The Greek Cities and the Market." In The Making of the Ancient Greek Economy, translated by Steven Rendall, 415–38. Princeton University Press, 2018. http://dx.doi.org/10.23943/princeton/9780691183411.003.0015.

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This chapter examines the extent and the limits of the market system in ancient Greece. It begins with a historical overview of the center-periphery model that emerged during the period, predation as a defining characteristic of the ancient Greek market, and the divergence of prices from one region to another—often seen as a symptom of a lack of market integration. It then compares the overall performance of the market in the city-states with those of the cities of medieval and modern Europe before discussing the disequilibrium between supply and demand and the form of risk management adopted by individuals and by cities that made the market of ancient Greece far from being a “perfect market.” The chapter concludes with an analysis of the Nash equilibrium that characterized the market and the factors that limited the production of grain to be sold on the market.
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Conference papers on the topic "Perfect nash equilibrium in subgames"

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Sabbaghi, Mostafa, and Sara Behdad. "Design for Repair: A Game Between Manufacturer and Independent Repair Service Provider." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67986.

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Design for ease-of-repair is an efficient solution to effectively use resources by extending the lifespan of products. However, designing a repairable product may not be necessarily an economically viable solution for manufacturers. Repairable products enable independent repair businesses to compete with original manufacturers on offering repair services. On the other hand, although designing a less repairable product may dissuade competition, it increases the cost of repair for manufacturers at the same time, in addition to decreasing consumers’ satisfaction. In this paper, a game-theoretic model is developed to represent the competition between a manufacturer acting as a leader, and a coalition of independent repair service providers acting as a follower. The subgame perfect Nash equilibrium is derived, representing the optimal prices for repair services offered by the two service-providers based on the level of repairability. In addition, based on the information extracted from a repair-related survey, we provide insights about consumers’ attitudes towards repairability of products to help manufacturers make better design decisions.
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Kroer, Christian, Gabriele Farina, and Tuomas Sandholm. "Smoothing Method for Approximate Extensive-Form Perfect Equilibrium." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/42.

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Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium. Equilibrium refinements can mend this issue, but have experienced little practical adoption. This is largely due to a lack of scalable algorithms.Sparse iterative methods, in particular first-order methods, are known to be among the most effective algorithms for computing Nash equilibria in large-scale two-player zero-sum extensive-form games. In this paper, we provide, to our knowledge, the first extension of these methods to equilibrium refinements. We develop a smoothing approach for behavioral perturbations of the convex polytope that encompasses the strategy spaces of players in an extensive-form game. This enables one to compute an approximate variant of extensive-form perfect equilibria. Experiments show that our smoothing approach leads to solutions with dramatically stronger strategies at information sets that are reached with low probability in approximate Nash equilibria, while retaining the overall convergence rate associated with fast algorithms for Nash equilibrium. This has benefits both in approximate equilibrium finding (such approximation is necessary in practice in large games) where some probabilities are low while possibly heading toward zero in the limit, and exact equilibrium computation where the low probabilities are actually zero.
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Hsin, Pei-Han. "Forecasting Taiwan's GDP by the novel nash nonlinear grey Bernoulli model with trembling-hand perfect equilibrium." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823908.

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Bagheri, Mostafa, Alexander Bertino, and Peiman Naseradinmousavi. "Experimental and Analytical Nonzero-Sum Differential Game-Based Control of a 7-DOF Robotic Manipulator." In ASME 2020 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/dscc2020-3114.

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Abstract We formulate a Nash-based feedback control law for an Euler-Lagrange system to yield a solution to non-cooperative differential game. The robot manipulators are broadly utilized in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler-Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution in order to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.
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Liu, Chunsheng, and Mark V. Trevorrow. "Optimal Strategy for Multiple Evaders Against an Agile Pursuer." In ASME 2019 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/dscc2019-8924.

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Abstract This paper focuses on the problem of multiple slow moving and less maneuverable evaders against an agile pursuer, addressing the optimal strategy for multiple evaders. This is the so-called wolf-sheep game. Two scenarios are examined: 1) both pursuer and evaders have perfect knowledge about opponents, and 2) the pursuer has limited detection capability. Since the wolf-sheep game involves the Boolean value state, the game is hard to solve using traditional methods. This paper adopts a hierarchical approach. The two player game is solved first. Then the solution of the multiplayer game is based on the two-player game and the pursuer chasing order. The optimal strategy is calculated based on Nash equilibrium. The game with limited detection capability is solved by maximizing the Close Point of Approach (CPA). The optimal solution will be found theoretically and numerically.
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