Articoli di riviste: "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, n. 4 (28 settembre 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, n. 1 (1 febbraio 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 e Yuliy Sannikov. "Algorithms for Stochastic Games With Perfect Monitoring". Econometrica 88, n. 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, n. 02 (giugno 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., e David A. Rosenblueth. "A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria". International Journal of Applied Mathematics and Computer Science 25, n. 3 (1 settembre 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 e Marc Uetz. "The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing". Mathematics of Operations Research 44, n. 4 (novembre 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, n. 3-4 (dicembre 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, e VLADIMIR GAITSGORY. "ON A CLASS OF NASH EQUILIBRIA WITH MEMORY STRATEGIES FOR NONZERO-SUM DIFFERENTIAL GAMES". International Game Theory Review 02, n. 02n03 (giugno 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 e Jacqueline Morgan. "Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move". Dynamic Games and Applications 9, n. 2 (28 luglio 2018): 416–32. http://dx.doi.org/10.1007/s13235-018-0277-3.

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Li, Xianghui, Wei Zheng e Yang Li. "An axiomatic and non-cooperative approach to the multi-step Shapley value". RAIRO - Operations Research 55, n. 3 (maggio 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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Noussair, Charles N., Daan van Soest e Jan Stoop. "Cooperation in a Dynamic Fishing Game: A Framed Field Experiment". American Economic Review 105, n. 5 (1 maggio 2015): 408–13. http://dx.doi.org/10.1257/aer.p20151018.

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We derive a dynamic theoretical model of renewable resource extraction. In the social optimum, maximum extraction occurs in the last period only, while in the unique subgame perfect Nash equilibrium, the resource is depleted immediately. The predictions are tested in a field experiment conducted at a recreational fishing pond. The subjects, experienced recreational fishermen, face a dynamic social dilemma, in which they risk depletion of the resource by overfishing. We find strong support for the Nash equilibrium. Fishermen exert as much effort in the last period as in preceding periods, and effort is independent of the stock of fish.

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Ambrus, Attila, e Shih En Lu. "A Continuous-Time Model of Multilateral Bargaining". American Economic Journal: Microeconomics 7, n. 1 (1 febbraio 2015): 208–49. http://dx.doi.org/10.1257/mic.20100029.

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We propose a finite-horizon continuous-time framework for coalitional bargaining, in which players can make offers at random discrete times. In our model: (i) expected payoffs in Markov perfect equilibrium (MPE) are unique, generating sharp predictions and facilitating comparative statics; and (ii) MPE are the only subgame perfect Nash equilibria (SPNE) that can be approximated by SPNE of nearby discrete-time bargaining models. We investigate the limit MPE payoffs as the time horizon goes to infinity and players get infinitely patient. In convex games, we establish that the set of these limit payoffs achievable by varying recognition rates is exactly the core of the characteristic function. (JEL C78)

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Brams, Steven J., e D. Marc Kilgour. "A Note on Stabilizing Cooperation in the Centipede Game". Games 11, n. 3 (20 agosto 2020): 35. http://dx.doi.org/10.3390/g11030035.

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In the much-studied Centipede Game, which resembles the Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even though continuing play can benefit both players—but not if the rival defects immediately, which it has an incentive to do. We show that, without changing the structure of the game, interchanging the payoffs of the two players provides each with an incentive to cooperate whenever its turn comes up. The Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, wherein there are several Nash equilibria. The Reciprocity Game can be implemented noncooperatively by adding, at the start of the Centipede Game, a move to exchange payoffs, which it is rational for the players to choose. What this interchange signifies, and its application to transforming an arms race into an arms-control treaty, are discussed.

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Kamiński, Marek M. "BACKWARD INDUCTION: MERITS AND FLAWS". Studies in Logic, Grammar and Rhetoric 50, n. 1 (27 giugno 2017): 9–24. http://dx.doi.org/10.1515/slgr-2017-0016.

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Abstract Backward induction (BI) was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such a troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria.

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VOLDEN, CRAIG, e ALAN E. WISEMAN. "Erratum to “Bargaining in Legislatures over Particularistic and Collective Goods” American Political Science Review 101(1): 79–92." American Political Science Review 102, n. 3 (agosto 2008): 385–86. http://dx.doi.org/10.1017/s000305540808026x.

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The symmetric, stationary subgame-perfect Nash equilibrium in Volden and Wiseman (2007) is characterized by cutpoints between regions of purely collective, mixed, and purely particularistic budget allocations. The cutpoints in our published article were derived by finding conditions under which the proposer receives a higher utility in one region than in another. However, a stationary equilibrium requires that the proposer would not unilaterally offer a different type of proposal, given that all other players continue to play their present strategies.

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Feng, Leidong, e Mengdi Gu. "Endogenous timing in a vertically differentiated mixed duopoly with Cournot competition". Archives of Control Sciences 26, n. 2 (1 giugno 2016): 161–75. http://dx.doi.org/10.1515/acsc-2016-0009.

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Abstract This paper compares the equilibrium outcomes under simultaneous and sequential output setting in a mixed duopoly in a vertically differentiated market. When the timing of the output game is determined endogenously, it is shown that simultaneous play in the quality stage with the public firm acting as the high-quality producer and simultaneous play in the second period in the output stage turn out to be the unique subgame perfect Nash equilibrium, which contrasts with the endogenous timing in a purely private duopoly.

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Bruyère, Véronique. "Synthesis of equilibria in infinite-duration". ACM SIGLOG News 8, n. 2 (aprile 2021): 4–29. http://dx.doi.org/10.1145/3467001.3467003.

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In this survey, we propose a comprehensive introduction to game theory applied to computer-aided synthesis. We study multi-player turn-based infinite-duration games played on a finite directed graph such that each player aims at maximizing a payoff function. We present the well-known notions of Nash equilibrium and subgame perfect equilibrium, as well as interesting strategy profiles of players as response to the strategy announced by a specific player. We provide classical and recent results about the related threshold synthesis problem.

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Feng, Zhongwei, e Chunqiao Tan. "Subgame Perfect Equilibrium in the Rubinstein Bargaining Game with Loss Aversion". Complexity 2019 (26 marzo 2019): 1–23. http://dx.doi.org/10.1155/2019/5108652.

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Rubinstein bargaining game is extended to incorporate loss aversion, where the initial reference points are not zero. Under the assumption that the highest rejected proposal of the opponent last periods is regarded as the associated reference point, we investigate the effect of loss aversion and initial reference points on subgame perfect equilibrium. Firstly, a subgame perfect equilibrium is constructed. And its uniqueness is shown. Furthermore, we analyze this equilibrium with respect to initial reference points, loss aversion coefficients, and discount factor. It is shown that one benefits from his opponent’s loss aversion coefficient and his own initial reference point and is hurt by loss aversion coefficient of himself and the opponent’s initial reference point. Moreover, it is found that, for a player who has a higher level of loss aversion than the other, although this player has a higher initial reference point than the opponent, this player can(not) obtain a high share of the pie if the level of loss aversion of this player is sufficiently low (high). Finally, a relation with asymmetric Nash bargaining is established, where player’s bargaining power is negatively related to his own loss aversion and the initial reference point of the other and positively related to loss aversion of the opponent and his own initial reference point.

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Long, Jun, e Sanyun Zeng. "Equilibrium Time-Consistent Strategy for Corporate International Investment Problem with Mean-Variance Criterion". Mathematical Problems in Engineering 2016 (2016): 1–20. http://dx.doi.org/10.1155/2016/3295041.

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We analyze a continuous-time model for corporate international investment problem (CIIP) with mean-variance criterion. Based on Nash subgame perfect equilibrium theory, we define an infinitesimal operator and directly derive an extended Hamilton-Jacobi-Bellman (HJB) equation. Besides, we also obtain the equilibrium time-consistent strategy for CIIP. In addition, we discuss two cases of risk aversion coefficient; one is constant and the other is state dependent. Finally, the simulation results are given to illustrate our conclusions and the influence of some parameters on the optimal solution.

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Herings, P. Jean-Jacques, Andrey Meshalkin e Arkadi Predtetchinski. "Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment". Dynamic Games and Applications 10, n. 2 (17 settembre 2019): 478–92. http://dx.doi.org/10.1007/s13235-019-00328-w.

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Abstract The paper considers a class of decision problems with an infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. Our results are twofold: Firstly, we demonstrate that the set of subgame optimal policies coincides with the set of subgame perfect equilibria of the decision problem. Furthermore, the set of subgame optimal policies is contained in the set of optimal policies and the set of optimal policies is contained in the set of Nash equilibria. Secondly, we show that the set of pure subgame optimal policies is the unique minimal curb set of the decision problem. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.

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ARAMENDIA, M., L. RUIZ e F. VALENCIANO. "THE FORGIVING TRIGGER STRATEGY: AN ALTERNATIVE TO THE TRIGGER STRATEGY". International Game Theory Review 06, n. 02 (giugno 2004): 247–64. http://dx.doi.org/10.1142/s0219198904000186.

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The grim-trigger strategy introduced by Friedman is often used in economic models, mainly because of its simplicity, to show that collusion can be sustained by means of a subgame perfect equilibrium. In this work we show that, under simple conditions, it is possible to improve on the grim-trigger strategy while retaining subgame perfection and in some cases adding weak renegotiation proofness (in the sense of Farrell and Maskin). The basic idea is that, following a deviation, the cheater, instead of continuing in the Nash equilibrium forever, chooses an autopenalty which signals, in a very strong way, that he/she would not deviate any more if cooperation were reestablished. We check the nice working of this strategy in the Cournot's oligopoly model.

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BEJAN, CAMELIA, e JUAN CAMILO GÓMEZ. "USING THE ASPIRATION CORE TO PREDICT COALITION FORMATION". International Game Theory Review 14, n. 01 (marzo 2012): 1250004. http://dx.doi.org/10.1142/s0219198912500041.

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This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

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Ou, Tsung-Yin, e Yenming J. Chen. "Optimal Segmentation over a Generalized Customer Distribution". Axioms 10, n. 2 (21 maggio 2021): 98. http://dx.doi.org/10.3390/axioms10020098.

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This paper investigates the impact of consumer preferences on the intensity of competition for companies in a duopoly market. A classical Hotelling’s competition problem will be different if consumers are allowed to distribute non-uniformly. New results in competition intensity are established and conditions for the existence of a subgame perfect Nash equilibrium is identified through a model that considers generic distribution in consumer preferences. A competition strategy is demonstrated to depend on the signs of local change rates of the density function at the endpoints of market segments.

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Chen, Xiaofeng, Qiankun Song e Zhenjiang Zhao. "Two-Player Location Game in a Closed-Loop Market with Quantity Competition". Complexity 2020 (25 agosto 2020): 1–12. http://dx.doi.org/10.1155/2020/4325454.

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This paper considers the two-player location game in a closed-loop market with quantity competition. Based on the Cournot and Hotelling models, a circle model is established for a closed-loop market in which two players (firms) play a location game under quantity competition. Using a two-stage (location-then-quantity) pattern and backward induction method, the existence of subgame-perfect Nash equilibria is proved for the location game in the circle model with a minimum distance transportation cost function. In addition, sales strategies are proposed for the two players for every local market on the circle when the players are in the equilibrium positions. Finally, an algorithm for simulating the competitive dynamics of the closed-loop market is designed, and two numerical simulations are provided to substantiate the effectiveness of the obtained results.

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Fu, Jing, Yan Hui Li e Xue Dong Wang. "Complete Information Dynamic Game Analysis in Tacit Knowledge Sharing Process within Modern Companies". Advanced Materials Research 421 (dicembre 2011): 553–58. http://dx.doi.org/10.4028/www.scientific.net/amr.421.553.

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In an era of knowledge economy, building an internal knowledge baseis is one of basic conditions to improve competitiveness and to develop sustainablely for modern companies . In this paper, we develop a complete information dynamic game model on this problem and analyze the strategic behavior of the risk averse participators to find out the subgame perfect Nash equilibrium from perspective of individual employees. We also offer some managerial recommendations on how to balance individual interest and collective interests in modern companies. At last, a series of corresponding management enlightenments are given out based on the above analysis.

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RUSINOWSKA, AGNIESZKA. "REFINEMENTS OF NASH EQUILIBRIA IN VIEW OF JEALOUS OR FRIENDLY BEHAVIOR OF PLAYERS". International Game Theory Review 04, n. 03 (settembre 2002): 281–99. http://dx.doi.org/10.1142/s0219198902000707.

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In this paper, several bargaining models, differing in some assumptions from each other, are analyzed. We consider a discrete case and a continuous case. In the former model, players bargain over a division of n objects. In the latter, parties divide one unit of infinitely divisible good. We start with an analysis of the one-round model, and then we consider a model in which players can continue to bargain. For each model, simultaneous moves as well as alternating offers of players are considered. The assumption that each player receives no more than his/her opponent proposes giving to him/her is the common assumption for all cases analyzed. Moreover, we adopt some assumptions concerning players' attitudes towards their opponents' payments, assuming that players can be either jealous or friendly. In view of the jealousy or friendliness of players, Nash equilibrium and subgame perfect equilibrium are described.

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Bolle, Friedel. "Simultaneous and sequential voting under general decision rules". Journal of Theoretical Politics 30, n. 4 (1 agosto 2018): 477–88. http://dx.doi.org/10.1177/0951629818791041.

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In an economic theory of voting, voters have positive or negative costs of voting in favor of a proposal and positive or negative benefits from an accepted proposal. When votes have equal weight then simultaneous voting mostly has a unique pure strategy Nash equilibrium which is independent of benefits. Voting with respect to (arbitrarily small) costs alone, however, often results in voting against the ‘true majority’ . If voting is sequential as in the roll call votes of the US Senate then, in the unique subgame perfect equilibrium, the ‘true majority’ prevails. It is shown that the result for sequential voting holds also with different weights of voters (shareholders), with multiple necessary majorities (European Union decision-making), or even more general rules. Simultaneous voting in the general model has more differentiated results.

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Li, Shuang, Shican Liu, Yanli Zhou, Yonghong Wu e Xiangyu Ge. "Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate". Journal of Function Spaces 2020 (19 novembre 2020): 1–10. http://dx.doi.org/10.1155/2020/3153297.

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In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.

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Zimper, Alexander. "Optimal Liquidity Provision Through a Demand Deposit Scheme: The Jacklin Critique Revisited". German Economic Review 14, n. 1 (1 febbraio 2013): 89–107. http://dx.doi.org/10.1111/j.1468-0475.2012.0566.x.

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Abstract We derive conditions such that optimal liquidity provisions through a demand deposit scheme can be sustainably implemented in a subgame perfect Nash equilibrium under the assumption that renegade investors have free access to ex post asset markets. As our qualitative main finding we demonstrate that such sustainability is more likely for ‘poor’ than for ‘rich’ scheme participants in terms of future income. By establishing sustainability for low future income populations, our formal analysis therefore offers an important qualification of Jacklin’s (1987) influential claim that an optimal demand deposit scheme is not sustainable whenever there exists the possibility of an ex post asset market.

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Duman, Papatya, e Walter Trockel. "On Non-Cooperative Foundation and Implementation of the Nash Solution in Subgame Perfect Equilibrium via Rubinstein's Game". Journal of Mechanism and Institution Design 1, n. 1 (19 dicembre 2016): 83–106. http://dx.doi.org/10.22574/jmid.2016.12.003.

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Schenone, Pablo. "Revealed Preference Implications of Backward Induction and Subgame Perfection". American Economic Journal: Microeconomics 12, n. 2 (1 maggio 2020): 230–56. http://dx.doi.org/10.1257/mic.20180077.

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Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

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Castro, Luis E., e Nazrul I. Shaikh. "Optimal Advertisement Spending in a Duopoly with Incomplete Information". International Journal of Business Analytics 5, n. 3 (luglio 2018): 1–21. http://dx.doi.org/10.4018/ijban.2018070101.

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This article presents the relationship between a firm's advertisement spending and sales in a duopoly when information about the competitors' advertisement spending is unavailable. The competitive interaction between the firms has been modeled as imperfect information Cournot and Stackelberg games and the conditions for subgame perfect Bayesian Nash equilibrium are presented. The results suggest that when the firms are similar in size and advertisement effectiveness, both firms are better off sharing their advertising plans with each other. On the other hand, when one of the firms is a market leader, the follower may profit from the leader's advertisement spending and so is better off keeping the leader guessing. A practical approach to estimate the optimum advertisement budget based on the expected values of the competitors' historic advertising spending is presented as well.

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Santos, Henrique P. Z., Bruno N. Guedes e Claudio T. Cristino. "Optimal pricing structure in a maintenance contract: a game theory approach". Contributions to Game Theory and Management 13 (2020): 388–401. http://dx.doi.org/10.21638/11701/spbu31.2020.21.

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This essay presents a novel look at Murthy and Asgharizadeh's study (Murthy & Asgharizadeh, 1998). The authors developed a decision problem applied to maintenance outsourcing involving two decision-makers (players). If a consumer buys a product, then outsources the maintenance actions to a maintenance agent (agent) who offers two maintenance options; a maintenance contract that holds a penalty clause which is activated if the agent's time to repair is higher than a specified time, and services on-demand. The model yields equilibrium strategies based on the subgame-perfect Nash equilibrium. The agent defines the optimal pricing structure for the maintenance options considering the equipment's useful life while the consumer maximizes their expected payoff by choosing one maintenance option. Our contribution to this research branches in three ways. First, once the model deals with random variables, it represents a stochastic optimization problem. We propose a different approach to estimate this penalty time by using the Monte Carlo method. The second contribution is to present a formal definition of this decision problem as a game, emphasizing the game theory's components. Finally, we reinterpret the players' equilibrium strategies.

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Fan, Tijun, Yang Song, Huan Cao e Haiyang Xia. "Optimal eco-labeling strategy with imperfectly informed consumers". Industrial Management & Data Systems 119, n. 6 (8 luglio 2019): 1166–88. http://dx.doi.org/10.1108/imds-06-2018-0256.

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Purpose The purpose of this paper is to find the optimal environmental quality criteria for a strategic eco-labeling authority with three objectives (i.e. maximizing the aggregate environmental quality, maximizing the industry profit and maximizing the social welfare). Particularly, the authors investigate how the existence of imperfectly informed consumers affects labeling criteria determination and competition among firms. Design/methodology/approach A game-theoretic modeling approach was adopted in this paper. A three-stage sequential game was modeled and backward induction was used to solve for a subgame perfect Nash equilibrium. To investigate the impacts of the existence of imperfectly informed consumers, the equilibrium, if all consumers are perfectly informed of the eco-label, was studied as a benchmark. Findings A more strict eco-labeling criterion improves revenues for both the labeled and unlabeled firms. It is interesting to find that the eco-labeling criteria to maximize industry profits are stricter than the criteria to maximize social welfare. Moreover, when the fraction of imperfectly informed consumers increases, the eco-labeling criteria to maximize aggregate environmental quality or industry profits will be more strict, while the criteria to maximize the social welfare will be looser. Originality/value The authors analyze the equilibrium strategies for firms against the eco-labeling criteria certified by authority with different objectives. The obtained optimal labeling strategies could provide insightful guidelines for the certifying authority to select the best suitable labeling criteria to achieve its goals.

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Li, Guang-Shun, Ying Zhang, Mao-Li Wang, Jun-Hua Wu, Qing-Yan Lin e Xiao-Fei Sheng. "Resource Management Framework Based on the Stackelberg Game in Vehicular Edge Computing". Complexity 2020 (20 gennaio 2020): 1–11. http://dx.doi.org/10.1155/2020/8936064.

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With the emergence and development of the Internet of Vehicles (IoV), quick response time and ultralow delay are required. Cloud computing services are unfavorable for reducing delay and response time. Mobile edge computing (MEC) is a promising solution to address this problem. In this paper, we combined MEC and IoV to propose a specific vehicle edge resource management framework, which consists of fog nodes (FNs), data service agents (DSAs), and cars. A dynamic service area partitioning algorithm is designed to balance the load of DSA and improve the quality of service. A resource allocation framework based on the Stackelberg game model is proposed to analyze the pricing problem of FNs and the data resource strategy of DSA with a distributed iteration algorithm. The simulation results show that the proposed framework can ensure the allocation efficiency of FN resources among the cars. The framework achieves the optimal strategy of the participants and subgame perfect Nash equilibrium.

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Gurtuev, Alim, Elena Derkach e Anzor Sabanchiev. "Efficient multi-period distribution mechanism for the innovation investment system under uncertainty". E3S Web of Conferences 295 (2021): 01058. http://dx.doi.org/10.1051/e3sconf/202129501058.

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In this paper, we study the problem of a venture investor who distributes the budget between several innovation projects under conditions of uncertainty. A common method for solving this problem is through bilateral negotiations with the external evaluation of projects. However, the effectiveness almost entirely depends on the evaluation quality, but external evaluation seldom reduces the knowledge asymmetry for innovation projects. We propose an iterative revelation mechanism for this problem when the investor sequentially offers possible allocations of the limited budget in the form of threshold dividing questions. The binary choices of innovators serve as a signal of internal estimates of the project implementation costs. Under perfect information, such a mechanism, regardless of the method for determining budget allocations, always produces an effective allocation in subgame-perfect Nash equilibrium. Under uncertainty, the method of offering distribution options matters – the optimal solution is found under the English auction class of mechanisms. In an efficient iterative allocation mechanism for innovation investment, the investor proposes a new allocation of the budget each round until an efficient allocation is achieved. The proposed mechanism does not necessarily need to identify the exact minimum budgets for each innovator. Another advantage of the proposed mechanism is the ability to use different processes for organizing rounds.

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Tsai, Shoou-Rong, Pan-Long Tsai e Yungho Weng. "Cournot-Bertrand competition: a revisit of strategic trade policy in the third-market model". Journal of Economic Studies 43, n. 3 (8 agosto 2016): 475–87. http://dx.doi.org/10.1108/jes-02-2015-0028.

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Purpose – The purpose of this paper is to discuss the optimal policy settings of the home government for any combination of strategic variables adopted by home and foreign firms under Brander and Spencer’s third-market model framework. Design/methodology/approach – This paper follows all the assumptions of Brander and Spencer with only two modifications: firms produce differentiated products, and firms choose different strategic variables. A two-stage game is set and the subgame-perfect Nash equilibrium is deduced following backward induction. Findings – The authors arrive at a general, simple rule to determine the optimal policy of the home government for any combination of strategic variables: regardless of the strategic variable of the domestic firm, the optimal policy of the home country is an export subsidy (tax) as long as the foreign firm’s strategic variable is output (price). The optimal subsidy or tax of the home country is shown to move the equilibrium to the Stackelberg equilibrium where the domestic firm behaves as the leader while the foreign firm behaves as a follower under free trade. With appropriate interpretations and a suitable caveat, the above results still hold in the case with multiple foreign firms which may choose different strategic variables. Originality/value – This paper fills the gap in the literature, and provides some more general results not easily detected in the original model of Brander and Spencer or Eaton and Grossman.

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Koskela, Erkki, e Markku Ollikainen. "A game-theoretic model of timber prices with capital stock: an empirical application to the Finnish pulp and paper industry". Canadian Journal of Forest Research 28, n. 10 (1 ottobre 1998): 1481–93. http://dx.doi.org/10.1139/x98-105.

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The paper provides a framework to approach price and quantity determination in the roundwood market from a new perspective. In the spirit of the trade union literature, a model of timber price determination is formulated according to which the forest owners' association determines timber prices and then forest firms unilaterally decide on the timber to be used. The novelty here is to incorporate investment decisions of firms as a strategic factor into the model. The structure of the model is the following. The game is played in two stages. First, the forest owners' association and the firms in the forest industry decide on timber price and capital stock, respectively. In the second stage, the firms determine timber demand conditional on the timber price - capital stock game, so that the equilibrium concept is the subgame perfect Nash equilibrium. This game-theoretic model is applied to the annual data from the Finnish pulp and paper industry over the period 1960-1992. Estimation and testing results concerning the price and quantity determination of timber as well as capital stock behavior are generally favorable for the hypotheses presented. In particular, diagnostics and various test procedures indicate that these equations outperform conventional specifications derived from the theory of the demand for factors of production.

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Wang, Xiao-yuan, Ya-qi Liu, Fang Wang, Zhi-guo Liu, Hai-xia Zhao e Jun-Feng Xin. "Driver’s lane selection model based on multi-player dynamic game". Advances in Mechanical Engineering 11, n. 1 (gennaio 2019): 168781401881990. http://dx.doi.org/10.1177/1687814018819903.

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With a view to the background of Internet of Things, the vehicle group situation, especially the propensity of different drivers, and the corresponding vehicle types were given a comprehensive consideration on the basis of the factors which influence driving behavior, and the drivers’ lane selection model based on multi-player dynamic game with complete information was built. The drivers’ payoffs under different combination of lane selection strategies were analyzed, and on this basis, the subgame perfect Nash equilibrium solution was solved through backward induction, and the drivers’ optimal lane selection strategy was obtained. Next-Generation Simulation datasets and other data were applied for model calibration and validation. The results showed that the proposed model can objectively reflect the actual operation characteristic of traffic flow on road section. So, it is of great significance to apply the multi-person dynamic game in the field of intelligent transportation. And the theoretical basis of the research on lane selection decision-making can be provided for the command system of intelligent driving especially anthropomorphic driving under the condition of Internet of Things.

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Saglam, Ismail. "Perverse Effects of Non-sterilized Interventions on Spot Foreign Exchange Rates". South Asian Journal of Macroeconomics and Public Finance 8, n. 1 (1 maggio 2019): 26–56. http://dx.doi.org/10.1177/2277978719836307.

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We study the effects of non-sterilized intervention on a spot foreign exchange (forex) rate using a multi-period game-theoretical model which involves an unspeciﬁed number of competitive traders, a ﬁnite number of strategic traders (forex dealers) with heterogenous initial money balances, and the central bank of the home country. Simulating the subgame-perfect Nash equilibrium of the two-stage game played by the forex dealers in each period, we show that the non-sterilized intervention of the central bank may lead to a perverse effect on the spot forex rate. We call the mechanism underlying this effect strategic trade switching channel that works when an increase in the central bank’s forex currency demand (supply) exerts such a big upward (downward) effect on the forex rate that some sufficiently big dealers, who optimally bought (sold) forex currency in the previous period when the forex rate was sufficiently low, ﬁnd in the current period selling (buying) it more proﬁtable, thus moving the forex rate in a direction undesired by the central bank. JEL Classiﬁcation: D43, F31, G20

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Abe, Takaaki, Yukihiko Funaki e Taro Shinoda. "Invitation Games: An Experimental Approach to Coalition Formation". Games 12, n. 3 (17 agosto 2021): 64. http://dx.doi.org/10.3390/g12030064.

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This paper studies how to form an efficient coalition—a group of people. More specifically, we compare two mechanisms for forming a coalition by running a laboratory experiment and reveal which mechanism leads to higher social surplus. In one setting, we invite the subjects to join a meeting simultaneously, so they cannot know the other subjects’ decisions. In the other setting, we ask them sequentially, which allows each subject to know his or her predecessor’s choice. Those who decide to join the meeting form a coalition and earn payoffs according to their actions and individual preferences. As a result, we obtain the following findings. First, the sequential mechanism induces higher social surplus than the simultaneous mechanism. Second, most subjects make choices consistent with the subgame-perfect Nash equilibrium in the sequential setting and choose the dominant strategy in the simultaneous setting, when a dominant strategy exists. Finally, when the subjects need to look further ahead to make a theoretically rational choice, they are more likely to fail to choose rationally.

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Xiao, Yiyong, Pei Yang, Siyue Zhang, Shenghan Zhou, Wenbing Chang e Yue Zhang. "Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach". Sustainability 12, n. 2 (13 gennaio 2020): 581. http://dx.doi.org/10.3390/su12020581.

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This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model with two opposing goals to minimize/maximize the loss from both the designer (leader) and attacker (follower) sides. The first goal was to identify the most cost-effective plan to build and fortify the facility considering minimum loss, whereas the attacker followed the designer to seek the most destructive way of attacking to cause maximum loss. We found that the two sides could not reach a static equilibrium with a single pair of confrontational plans in an ordinary case, but were able to reach a dynamically cyclic equilibrium when the plan involved multiple pairs. The proposed bi-objective model aimed to discover the optimal cyclic plans for both sides to reach a dynamic equilibrium. To solve this problem, we first started from the designer’s side with a design and fortification plan, and then the attacker was able to generate their worst attack plan based on that design. After that, the designer changed their plan again based on the attacker’s plan in order to minimize loss, and the attacker correspondingly modified their plan to achieve maximum loss. This game looped until, finally, a cyclic equilibrium was reached. This equilibrium was deemed to be optimal for both sides because there was always more loss for either side if they left the equilibrium first. This game falls into the subgame of a perfect Nash equilibrium—a kind of complete game. The proposed bi-objective model was directly solved by the CPLEX solver to achieve optimal solutions for small-sized problems and near-optimal feasible solutions for larger-sized problems. Furthermore, for large-scale problems, we developed a heuristic algorithm that implemented dynamic iterative partial optimization alongside MILP (DIPO-MILP), which showed better performance compared with the CPLEX solver when solving large-scale problems.

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Leonardos, Stefanos, e Costis Melolidakis. "Endogenizing the Cost Parameter in Cournot Oligopoly". International Game Theory Review 22, n. 02 (giugno 2020): 2040004. http://dx.doi.org/10.1142/s0219198920400046.

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We study the effects of endogenous cost formation in the classic Cournot oligopoly through an extended two-stage game. The competing Cournot firms produce low-cost but limited quantities of a single homogeneous product. For additional procurements, they may refer to a revenue-maximizing supplier who sets a wholesale price prior to their orders. We express this chain as a two-stage game and study its equilibrium under two different information levels: complete and incomplete information on the side of the supplier about the actual market demand. In the deterministic case, we derive the unique subgame-perfect Nash equilibrium for different values of the retailers’ capacity levels, supplier’s cost and market demand. To study the incomplete information case, we model demand uncertainty via a continuous probability distribution. Under mild assumptions, we characterize the supplier’s optimal pricing policy as a fixed point of a proper translation of his expectation about the orders that he will receive from the retailers. If this expectation is decreasing in his price, then such an optimal policy always exists and is unique. Based on this characterization, we are able to proceed with comparative statics and sensitivity analysis, both analytically and numerically. Incomplete information gives rise to market inefficiencies because the supplier may ask for a too high price. Increasing supplier’s cost results in increasing wholesale prices, decreasing orders from the retailers and hence decreasing consumer surplus. Increasing retailers’ production capacities results in decreasing wholesale prices and increasing consumer surplus. Finally, as the number of second-stage retailers increases, the supplier’s profit may initially rise but eventually drops.

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Gnecco, Giorgio, Berna Tuncay e Fabio Pammolli. "A Comparison of Game-Theoretic Models for Parallel Trade". International Game Theory Review 20, n. 03 (settembre 2018): 1850003. http://dx.doi.org/10.1142/s0219198918500032.

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Within the EU Single Market for medicines, differences in drug prices, regulations, and transaction costs may create, under suitable conditions, arbitrage opportunities well before patent expiration, giving an incentive to the occurrence of parallel trade. When this is permitted, parallel traders may obtain a profit from buying drugs in a country where prices are lower, then re-selling them in a country where prices are higher. This phenomenon may cause inefficiencies from a global welfare perspective, and reduce the manufacturers’ incentive to invest in Research and Development (R & D). Given this framework, in this paper, we investigate the efficiency (expressed in terms of the price of anarchy) of the subgame-perfect Nash equilibria associated with five dynamic noncooperative game-theoretic models for the parallel trade of pharmaceuticals. We also compare such models with regard to the manufacturer’s incentive to invest in R & D. More specifically, first we find in closed form the optimal value of the global welfare of two countries, which is obtained by solving a suitable quadratic optimization problem modeling the decision-making process of a global planner. Then, we use such a result to evaluate and compare the prices of anarchy of five games modeling the interaction between a manufacturer in the first country and a potential parallel trader in the second country. The first three games refer, respectively, to the cases of no parallel trade threat, parallel trade threat, and parallel trade occurrence at equilibrium. Then, we investigate two modifications of the third game, in which its transfer payment from the potential parallel trader to the manufacturer is, respectively, removed/determined by Nash bargaining. For completeness, we also consider a decision-theoretic model of no parallel trade threat. For what concerns the incentive for the manufacturer to invest in R & D, the results of our numerical comparison show that the decision-theoretic model of no parallel trade threat is always the one with the highest incentive, whereas the two game-theoretic models of parallel trade threat/occurrence that do not include the transfer payment provide typically the lowest incentives. Moreover, the latter two models have the highest prices of anarchy (i.e., their equilibria have the lowest efficiencies). From a policy-making perspective, improvements are obtained if suitable countermeasures are taken to help the manufacturer recover from the costs of R & D, such as the inclusion of a transfer payment in the model.

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Becker, K., e E. T. von Ende. "Nash and subgame-perfect equilibria for natural monopoly markets". International Advances in Economic Research 4, n. 2 (maggio 1998): 205. http://dx.doi.org/10.1007/bf02295499.

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Boros, Endre, Vladimir Gurvich e Emre Yamangil. "Chess-Like Games May Have No Uniform Nash Equilibria Even in Mixed Strategies". Game Theory 2013 (22 maggio 2013): 1–10. http://dx.doi.org/10.1155/2013/534875.

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Recently, it was shown that Chess-like games may have no uniform (subgame perfect) Nash equilibria in pure positional strategies. Moreover, Nash equilibria may fail to exist already in two-person games in which all infinite plays are equivalent and ranked as the worst outcome by both players. In this paper, we extend this negative result further, providing examples that are uniform Nash equilibria free, even in mixed or independently mixed strategies. Additionally, in case of independently mixed strategies we consider two different definitions for effective payoff: the Markovian and the a priori realization.

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Huang, Wei, Dong Cai, Yuge Lu, Wen Huang, Qian Tang e Youqiang Li. "Computing the Subgame Perfect Nash Equilibriums in Parallel Allocation Indivisible Items". Journal of Physics: Conference Series 1621 (agosto 2020): 012073. http://dx.doi.org/10.1088/1742-6596/1621/1/012073.

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Rincón-Zapatero, J. P., J. Martínez e G. Martín-Herrán. "New Method to Characterize Subgame Perfect Nash Equilibria in Differential Games". Journal of Optimization Theory and Applications 96, n. 2 (febbraio 1998): 377–95. http://dx.doi.org/10.1023/a:1022674215872.

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SHINOHARA, RYUSUKE. "COALITION-PROOF NASH EQUILIBRIA IN A NORMAL-FORM GAME AND ITS SUBGAMES". International Game Theory Review 12, n. 03 (settembre 2010): 253–61. http://dx.doi.org/10.1142/s0219198910002659.

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The relationship between coalition-proof (Nash) equilibria in a normal-form game and those in its subgame is examined. A subgame of a normal-form game is a game in which the strategy sets of all players in the subgame are subsets of those in the normal-form game. In this paper, focusing on a class of aggregative games, we provide a sufficient condition for the aggregative game under which every coalition-proof equilibrium in a subgame is also coalition-proof in the original normal-form game. The stringency of the sufficient condition means that a coalition-proof equilibrium in a subgame is rarely a coalition-proof equilibrium in the whole game.

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Rincón-Zapatero, J. P., G. Martín-Herrán e J. Martínez. "Identification of Efficient Subgame-Perfect Nash Equilibria in a Class of Differential Games1". Journal of Optimization Theory and Applications 104, n. 1 (gennaio 2000): 235–42. http://dx.doi.org/10.1023/a:1004693109541.

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