Journal articles: 'Nash and cooperation'

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Roemer, John E. "Cooperation and market socialism: Kant versus Nash." Acta Oeconomica 72, S1 (July 15, 2022): 9–21. http://dx.doi.org/10.1556/032.2022.00016.

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Abstract The idea that socialism depends upon cooperation, as capitalism depends on competition, has always been inherent in the conception of socialism. Yet precise models of market socialism – ones, that is, that are sufficiently articulated so as to be able to discuss and compute an equilibrium in the economy – do not model cooperation in production, or more generally, in economic behavior. We introduce a Kantian optimization protocol, which, in contrast to Nash optimization, models how individuals can cooperate in labor and/or investment decisions. We prove that the ‘cooperative equilibrium’, thus modeled, is Pareto efficient whenever, in addition to receiving wages and rents, profits are distributed not to shareholders, but to workers and investors in proportion to their contributions to the firm. Pareto efficiency is achieved when the firms entire output is distributed to factor owners and shareholders do not exist.

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Gromova, Ekaterina, Anastasiia Zaremba, and Nahid Masoudi. "Reclamation of a Resource Extraction Site Model with Random Components." Mathematics 10, no. 24 (December 17, 2022): 4805. http://dx.doi.org/10.3390/math10244805.

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We compute the cooperative and the Nash equilibrium solutions for the discounted optimal control problem in a two-player differential game of reclamation of a resource extraction site, where each firm’s planning horizon presents the period that extraction of the resources from their site is economically viable. Hence, the planning horizon is defined by a random duration determined on the infinite time horizon. The comparison of the cooperative and Nash solutions and also the comparative statics are provided numerically. We also define the concept of “normalized value of cooperation” and explain how this concept could help us to better characterize the losses the players will face if they continue to refrain from cooperation.

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Wen, Shuhuan, Baozhu Hu, Ahmad B. Rad, Xinbin Li, Huibin Lu, and Jianhua Zhang. "Robust Nash Dynamic Game Strategy for User Cooperation Energy Efficiency in Wireless Cellular Networks." Mathematical Problems in Engineering 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/636159.

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Recently, there is an emerging trend of addressing “energy efficiency” aspect of wireless communications. It has been shown that cooperating users relay each other's information to improve data rates. The energy is limited in the wireless cellular network, but the mobile users refuse to relay. This paper presents an approach that encourages user cooperation in order to improve the energy efficiency. The game theory is an efficient method to solve such conflicts. We present a cellular framework in which two mobile users, who desire to communicate with a common base station, may cooperate via decode-and-forward relaying. In the case of imperfect information assumption, cooperative Nash dynamic game is used between the two users' cooperation to tackle the decision making problems: whether to cooperate and how to cooperate in wireless networks. The scheme based on “cooperative game theory” can achieve general pareto-optimal performance for cooperative games, and thus, maximize the entire system payoff while maintaining fairness.

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PETROSYAN, LEON. "STRATEGICALLY SUPPORTED COOPERATION." International Game Theory Review 10, no. 04 (December 2008): 471–80. http://dx.doi.org/10.1142/s0219198908002059.

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An n-person differential game Γ(x, T-t) with independent motions from the initial state x and with prescribed duration T - t is considered. Suppose that y(s) is the cooperative trajectory maximizing the sum of players' payoffs. Suppose also that before starting the game players agree to divide the joint maximal payoff V(x, T - t; N) according to the imputation α, which is considered as a solution of a cooperative version of the game Γ(x, T - t). Using individual rationality of the imputation α we prove that if in the game Γ(y(s),T - s) along the cooperative trajectory y(s), the solution will be derived from the imputation α with the use of the imputation distribution procedure (IDP), for each given ε > 0 there exists ε-Nash equilibrium in Γ(x, T - t) for which the payoffs of the players in the game will be equal exactly to the components of the imputation α (cooperative outcome). This means that the imputation α is strategically supported by some specially constructed ε-Nash equilibrium in Γ(x, T - t). A similar result is true for a discrete game with perfect information.

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Ding, Yangke, Lei Ma, Ye Zhang, and Dingzhong Feng. "Analysis of Evolution Mechanism and Optimal Reward-Penalty Mechanism for Collection Strategies in Reverse Supply Chains: The Case of Waste Mobile Phones in China." Sustainability 10, no. 12 (December 12, 2018): 4744. http://dx.doi.org/10.3390/su10124744.

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The aim of this paper is to discuss the coopetition (cooperative competition) relationship between a manufacturer and a collector in the collection of waste mobile phones (WMPs) and examine the evolution mechanism and the internal reward-penalty mechanism (RPM) for their collection strategies. A coopetition evolutionary game model based on evolutionary game theory was developed to obtain their common and evolutional collection strategies. The pure-strategy Nash equilibriums of this model were obtained which showed their collection strategy choices of perfect competition or cooperation. The mixed strategy Nash equilibrium was obtained which revealed evolution trends and laws. In addition, the optimal RPM was obtained in the sensitivity analysis of related parameters. The example of WMPs in China was taken to examine the simulation of the RPM. Results show that (i) although the manufacturer and the collector may change their strategies of cooperation and competition over time, cooperation is their best choice to increase payoffs; (ii) the optimal RPM is beneficial to propel their cooperation tendency and then to increase their payoffs.

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Parilina, Elena, and Artem Sedakov. "Stable Cooperation in a Game with a Major Player." International Game Theory Review 18, no. 02 (June 2016): 1640005. http://dx.doi.org/10.1142/s0219198916400053.

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The theory of cooperative games with restricted cooperation has been rapidly developing over the last decades. In our study, we present a special game with restricted cooperation — a game with a major player — a modified version of the landlord game presented in Moulin [1988]. Cooperation of players is supposed to be restricted by a communication structure (a star-graph) as well as a coalition structure. We adopt two well-known cooperative allocations — the Myerson value and the ES-value — to the case when there exist restrictions on the cooperation of players and provide their analytical expressions. Additionally, we examine stability of coalition structures using the concept of the Nash equilibrium and formulate conditions guaranteeing such stability for a given coalition structure.

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Moehler, Michael. "Rational Cooperation and the Nash Bargaining Solution." Ethical Theory and Moral Practice 18, no. 3 (October 17, 2014): 577–94. http://dx.doi.org/10.1007/s10677-014-9541-9.

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Xu, Shiqi, and Yuejin Fan. "Differential Game Analysis on University-Enterprise Cooperation considering Social Responsibility." Discrete Dynamics in Nature and Society 2021 (November 2, 2021): 1–12. http://dx.doi.org/10.1155/2021/5880286.

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Aiming at not only economic benefits but also social benefits in university-enterprise cooperation, this paper considers both technological innovation and social responsibility in university-enterprise cooperation. By using differential game theory, this paper provides three models of Nash noncooperative game, Stackelberg game, and cooperative game and discusses the impact of these three models on university-enterprise cooperation. Our results show that the Stackelberg game model can improve the innovation level of the university based on innovation cost-sharing and does not change the social responsibility level of the university without sharing the social cost. Among the three game models, the cooperative game model can bring the greatest innovation level and social responsibility level to the university-enterprise cooperation and make the whole system realize Pareto optimal. Our research can provide a theoretical basis and practical guidance for university-enterprise cooperation.

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Yao, Koffi Serge William. "An Experiment on Cooperation in a CPR Game with a Disapproval Option." Games 12, no. 4 (October 26, 2021): 83. http://dx.doi.org/10.3390/g12040083.

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This paper studies the standard version of the approval mechanism with two players in a common pool resource (CPR) extraction game. In the case of disapproval, the Nash extraction level is implemented. The paper investigates, experimentally, the extent to which the Nash threat leads to Pareto-improving extraction levels. Through our experiment, we confirm the effectiveness of the Nash threat in reducing CPR over-extraction. Although participants’ behavior is mainly explained by rational thinking, inequity in payoff can also motivate their behavior. Moreover, we show that there is neither an order effect nor a framing effect. Finally, the reduction persists when the Nash threat is no longer in place.

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Liu, Xiaoming, Gang Wang, and Chuang Zhang. "A Nash-bargaining-solution Based Cooperation Scheme for Rational Cooperative Communication Networks." Information Technology Journal 13, no. 10 (May 1, 2014): 1743–48. http://dx.doi.org/10.3923/itj.2014.1743.1748.

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Zhaoyang Zhang, Jing Shi, Hsiao-Hwa Chen, M. Guizani, and Peiliang Qiu. "A Cooperation Strategy Based on Nash Bargaining Solution in Cooperative Relay Networks." IEEE Transactions on Vehicular Technology 57, no. 4 (July 2008): 2570–77. http://dx.doi.org/10.1109/tvt.2007.912960.

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Wan, Xianglan. "Cooperation and Game between Producers and Managers Based on the Linear Contract." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/547136.

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There is a cooperative game between the manager and the producer in the enterprise. In this paper, we firstly construct the cooperative game model based on the principal-agent theory. Under the conditions of Nash equilibrium and linear contract, the paper calculates the net income of the client, the total risk and welfare of the agents when the agents have the cooperation or not. The result shows that the correlation coefficient between their output has a direct relationship with the cooperation. Secondly, according to the power distribution theory another model is developed. We analyze the game process and critical state. Furthermore, we deduce the share proportion of the profit and the control size when they have the cooperation. Finally, we summarize all the research achievements, which are of universal significance for the practical cooperation game problems.

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MOEHLER, MICHAEL. "The (Stabilized) Nash Bargaining Solution as a Principle of Distributive Justice." Utilitas 22, no. 4 (November 2, 2010): 447–73. http://dx.doi.org/10.1017/s0953820810000348.

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It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice in the form ‘each according to her basic needs and above this level according to her relative bargaining power’. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls’ original position.

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PINTASSILGO, PEDRO, and MARKO LINDROOS. "COALITION FORMATION IN STRADDLING STOCK FISHERIES: A PARTITION FUNCTION APPROACH." International Game Theory Review 10, no. 03 (September 2008): 303–17. http://dx.doi.org/10.1142/s0219198908001959.

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In this paper the management of straddling fish stocks is approached through a coalition game in partition function form. A two-stage game is applied, assuming ex ante symmetric players and the classical Gordon-Schaefer bioeconomic model. It is shown that the game is characterized by positive externalities — the merger of coalitions increases the payoffs of players who belong to other coalitions. A key result is that, apart from the case of two players, the grand coalition is not a Nash equilibrium outcome. Furthermore, in the case of three or more players the only Nash equilibrium coalition structure is the one formed by singletons. The results indicate that the prospects of cooperation in straddling stock fisheries are low if players can free ride cooperative agreements. Thus, in order to protect cooperation, under the aegis of regional fishery management organizations, unregulated fishing must be prevented.

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Brams, Steven J., and D. Marc Kilgour. "A Note on Stabilizing Cooperation in the Centipede Game." Games 11, no. 3 (August 20, 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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CRITCH, ANDREW. "A PARAMETRIC, RESOURCE-BOUNDED GENERALIZATION OF LÖB’S THEOREM, AND A ROBUST COOPERATION CRITERION FOR OPEN-SOURCE GAME THEORY." Journal of Symbolic Logic 84, no. 4 (April 2, 2019): 1368–81. http://dx.doi.org/10.1017/jsl.2017.42.

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AbstractThis article presents two theorems: (1) a generalization of Löb’s Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and (2) a theorem on the robust cooperation of agents that employ proofs about one another’s source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner’s Dilemma while remaining unexploitable, i.e., sometimes achieving the outcome (Cooperate, Cooperate), and never receiving the outcome (Cooperate, Defect) as player 1.

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Ma, Kai, Xin-Ping Guan, Juan Wang, and Xiao-Min Wei. "Multi-user symmetric cooperation based on nash bargaining solution in cooperative relay networks." International Journal of Automation and Computing 8, no. 4 (November 2011): 452–58. http://dx.doi.org/10.1007/s11633-011-0603-3.

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Garro, Alfredo. "Computing Nash Equilibria in Non-Cooperative Games." International Journal of Intelligent Mechatronics and Robotics 3, no. 3 (July 2013): 29–42. http://dx.doi.org/10.4018/ijimr.2013070103.

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Game Theory has recently drawn attention in new fields which go from algorithmic mechanism design to cybernetics. However, a fundamental problem to solve for effectively applying Game Theory in real word applications is the definition of well-founded solution concepts of a game and the design of efficient algorithms for their computation. A widely accepted solution concept for games in which any cooperation among the players must be self-enforcing (non-cooperative games) is represented by the Nash equilibrium. However, even in the two players case, the best algorithm known for computing Nash equilibria has an exponential worst-case running time; furthermore, if the computation of equilibria with simple additional properties is required, the problem becomes NP-hard. The paper aims to provide a solution for efficiently computing the Nash equilibria of a game as the result of the evolution of a system composed by interacting agents playing the game.

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Noussair, Charles N., Daan van Soest, and Jan Stoop. "Cooperation in a Dynamic Fishing Game: A Framed Field Experiment." American Economic Review 105, no. 5 (May 1, 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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KOZLOVSKAYA, NADEZHDA, and NIKOLAY ZENKEVICH. "STABLE COOPERATION UNDER ENVIRONMENTAL CONSTRAINTS." International Game Theory Review 12, no. 04 (December 2010): 453–70. http://dx.doi.org/10.1142/s0219198910002775.

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A game-theoretic model of territorial environmental production under Cournot competition is studied. The process is modeled as cooperative differential game. The stable distribution mechanism of the common cooperative benefit among players is proposed. We proved that the cooperative total stock of accumulated pollution is strictly less then the pollution under Nash equilibrium for the whole duration of the game. We design a stable Shapley value as a cooperative solution, which is time-consistent. The Shapley value is also strategic stable and satisfies the irrational-behavior-proofness condition. The numerical example is given.

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Li, Angsheng, and Xi Yong. "Dynamics, morphogenesis and convergence of evolutionary quantum Prisoner's Dilemma games on networks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2186 (February 2016): 20150280. http://dx.doi.org/10.1098/rspa.2015.0280.

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The authors proposed a quantum Prisoner's Dilemma (PD) game as a natural extension of the classic PD game to resolve the dilemma. Here, we establish a new Nash equilibrium principle of the game, propose the notion of convergence and discover the convergence and phase-transition phenomena of the evolutionary games on networks. We investigate the many-body extension of the game or evolutionary games in networks. For homogeneous networks, we show that entanglement guarantees a quick convergence of super cooperation, that there is a phase transition from the convergence of defection to the convergence of super cooperation, and that the threshold for the phase transitions is principally determined by the Nash equilibrium principle of the game, with an accompanying perturbation by the variations of structures of networks. For heterogeneous networks, we show that the equilibrium frequencies of super-cooperators are divergent, that entanglement guarantees emergence of super-cooperation and that there is a phase transition of the emergence with the threshold determined by the Nash equilibrium principle, accompanied by a perturbation by the variations of structures of networks. Our results explore systematically, for the first time, the dynamics, morphogenesis and convergence of evolutionary games in interacting and competing systems.

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Liu, Wei, and Jing Min Tang. "Dynamic Subcarrier and Power Allocation Based on Nash Bargaining Solution in Symmetric Cooperative OFDMA Networks." Advanced Materials Research 187 (February 2011): 510–15. http://dx.doi.org/10.4028/www.scientific.net/amr.187.510.

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In this paper, subcarrier and power allocation are jointly considered in a three-node symmetric cooperation orthogonal frequency-division multiple access uplink system. With the help of Nash bargaining solution, the dynamic subcarrier allocation scheme and the adaptive power allocation scheme are proposed for joint optimization. The joint resource allocation is decomposed and solved by dynamic subcarrier allocation algorithm and adaptive power allocation algorithm. Simulation results show the effectiveness of the proposed cooperative scheme.

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Janjua, Shahmir, Ishtiaq Hassan, Mahdi Zarghami, and Shafiqul Islam. "Addressing the supply-demand gap in shared rivers using water diplomacy framework: utility of game theory in the Indus river within Pakistan." Water Policy 22, no. 5 (September 21, 2020): 789–810. http://dx.doi.org/10.2166/wp.2020.109.

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Abstract The question of how to govern and manage transboundary river basin for competing and often conflicting demands due to limited supplies continues to be an issue of concern, conflict, and cooperation. A key novelty of this paper is the use of the Water Diplomacy Framework (WDF) to address supply-demand mismatch using the notion of collaborative problem-solving and joint fact-finding. It builds on innovative applications of game-theoretic approaches and uses equity and sustainability as guiding principles to address the supply-demand mismatch. Five different bankruptcy methods (net benefit ranges between US$17,462M to US$18,201M) and the Nash Bargaining Solution (net benefit ranges between US$18,132M to US$19,216M) are used to resolve supply-demand mismatch in the Indus basin among four provinces within Pakistan. The maximum total benefit generated from the Nash Bargaining Solution is 5.5% higher compared to the best bankruptcy method. Moving from the non-cooperative and rule-based bankruptcy methods to the Nash Bargaining Solutions provided increased benefit for all stakeholders. Reallocation of these increased benefits among the four provinces is done by applying the Nash Bargaining Solutions for homogenous and heterogeneous weights. These findings suggest that aspects of WDF – cooperative problem-solving approaches involving joint fact-finding and exploring different options – has the potential to simultaneously resolve supply-demand mismatch and generate more benefits for all stakeholders.

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FACKRELL, M., C. LI, P. G. TAYLOR, and J. WANG. "THE VALUE OF COMMUNICATION AND COOPERATION WHEN SERVERS ARE STRATEGIC." ANZIAM Journal 61, no. 4 (October 2019): 349–67. http://dx.doi.org/10.1017/s1446181120000048.

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In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability; one of the two servers is always inactive; each server knows the other’s successful transmission probability and they are willing to cooperate.Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III.

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Madani, Kaveh, Faraz Farhidi, and Sona Gholizadeh. "Bargaining Power in Cooperative Resource Allocations Games." Algorithms 15, no. 12 (November 25, 2022): 445. http://dx.doi.org/10.3390/a15120445.

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Cooperative game theory provides an appropriate framework to assess the likelihood of conflict resolution, encourage cooperation among parties, and determine each party’s share in resource sharing conflicts. In calculating the fair and efficient allocation of the incremental benefits of cooperation, cooperative game theory methods often do not consider the exogenous bargaining powers of the players based on factors, that are external to the game, such as their political, economic, and military powers. This study reformulates three well-known cooperative game theory methods, namely, Nash-Harsanyi, Shapley, and Nucleolus, to account for the exogenous bargaining powers of the players in cooperative games. Using the Caspian Sea international conflict as an example, this paper shows how the negotiators’ exogenous bargaining power can change the outcome of resource sharing games. The proposed weighted cooperative game theory approach can help determine practical resolutions for real-world conflicts in which the exogenous powers of players can have a significant influence on the outcome of negotiations.

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Awaya, Yu, and Vijay Krishna. "Communication and cooperation in repeated games." Theoretical Economics 14, no. 2 (2019): 513–53. http://dx.doi.org/10.3982/te3049.

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We study the role of communication in repeated games with private monitoring. We first show that without communication, the set of Nash equilibrium payoffs in such games is a subset of the set ofε‐coarse correlated equilibrium payoffs (ε‐CCE) of the underlying one‐shot game. The value ofεdepends on the discount factor and the quality of monitoring. We then identify conditions under which there are equilibria with “cheap talk” that result in nearly efficient payoffs outside the setε‐CCE. Thus, in our model, communication is necessary for cooperation.

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Fackrell, Mark, Cong Li, Peter Taylor, and Jiesen Wang. "The value of communication and cooperation when servers are strategic." ANZIAM Journal 61 (May 6, 2020): 349–67. http://dx.doi.org/10.21914/anziamj.v61i0.14157.

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In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability; one of the two servers is always inactive; each server knows the other’s successful transmission probability and they are willing to cooperate. Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III. doi:10.1017/S1446181120000048

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Crawford, Vincent P. "New Directions for Modelling Strategic Behavior: Game-Theoretic Models of Communication, Coordination, and Cooperation in Economic Relationships." Journal of Economic Perspectives 30, no. 4 (November 1, 2016): 131–50. http://dx.doi.org/10.1257/jep.30.4.131.

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In this paper, I discuss the state of progress in applications of game theory in economics and try to identify possible future developments that are likely to yield further progress. To keep the topic manageable, I focus on a canonical economic problem that is inherently game-theoretic, that of fostering efficient coordination and cooperation in relationships, with particular attention to the role of communication. I begin with an overview of noncooperative game theory's principal model of behavior, Nash equilibrium. I next discuss the alternative “thinking” and “learning” rationales for how real-world actors might reach equilibrium decisions. I then review how Nash equilibrium has been used to model coordination, communication, and cooperation in relationships, and discuss possible developments

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Kalai, Adam, and Ehud Kalai. "Cooperation in Strategic Games Revisited*." Quarterly Journal of Economics 128, no. 2 (April 6, 2013): 917–66. http://dx.doi.org/10.1093/qje/qjs074.

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Abstract For two-person complete-information strategic games with transferable utility, all major variable-threat bargaining and arbitration solutions coincide. This confluence of solutions by luminaries such as Nash, Harsanyi, Raiffa, and Selten, is more than mere coincidence. Staying in the class of two-person games with transferable unility, the article presents a more complete theory that expands their solution. Specifically, it presents: (1) a decomposition of a game into cooperative and competitive components, (2) an intuitive and computable closed-form formula for the solution, (3) an axiomatic justification of the solution, and (4) a generalization of the solution to games with private signals, along with an arbitration scheme that implements it. The objective is to restart research on cooperative solutions to strategic games and their applications.

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Arce, Daniel G. "On the cooperative and competitive aspects of strategic monitoring." Rationality and Society 30, no. 3 (July 12, 2018): 377–90. http://dx.doi.org/10.1177/1043463118774785.

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Strategic monitoring occurs in myriad situations such as principal–agent relationships, law enforcement and treaty verification. Such situations are generally known as enforcement or inspection games, with the focus largely being on the (counterintuitive) properties of their associated mixed strategy Nash equilibrium. This article instead characterizes the cooperative resolution of the mixed motives of the players involved. It does so through an illustrative decomposition of the enforcement/inspection game into its cooperative and competitive constituent parts. The results are interpreted within an efficiency wage context and the distribution of the saved monitoring costs that cooperation engenders.

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Corley, H. W. "A Mixed Cooperative Dual to the Nash Equilibrium." Game Theory 2015 (September 15, 2015): 1–7. http://dx.doi.org/10.1155/2015/647246.

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A mixed dual to the Nash equilibrium is defined for n-person games in strategic form. In a Nash equilibrium every player’s mixed strategy maximizes his own expected payoff for the other n-1 players’ strategies. Conversely, in the dual equilibrium every n-1 players have mixed strategies that maximize the remaining player’s expected payoff. Hence this dual equilibrium models mutual support and cooperation to extend the Berge equilibrium from pure to mixed strategies. This dual equilibrium is compared and related to the mixed Nash equilibrium, and both topological and algebraic conditions are given for the existence of the dual. Computational issues are discussed, and it is shown that for each n>2 there exists a game for which no dual equilibrium exists.

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Nakamura, G. M., G. S. Contesini, and A. S. Martinez. "Cooperation risk and Nash equilibrium: Quantitative description for realistic players." Physica A: Statistical Mechanics and its Applications 515 (February 2019): 102–11. http://dx.doi.org/10.1016/j.physa.2018.09.194.

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Lu, Xi, Yong Xian Liu, and Hong Mei Pang. "Technology Spillover and Enterprise Innovation Cooperation in Complementary Products of Different Industrie." Advanced Materials Research 694-697 (May 2013): 3642–47. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.3642.

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R&D activities have become the embodiment of an enterprise's core competitiveness. Based on the classic AJ model, this paper constructs the expected profit model in the non-cooperation, cooperation and social welfare maximizing conditions, and analyses the behavior effects to R&D and production behavior in the heterogeneous complementary enterprises. Through comparing Nash equilibrium R&D investment and production output, we conclude that R&D behavior plays a positive role on the cooperation between the heterogeneous complementary enterprises.

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MENESTREL, M. LE. "A ONE-SHOT PRISONERS' DILEMMA WITH PROCEDURAL UTILITY." International Game Theory Review 08, no. 04 (December 2006): 655–68. http://dx.doi.org/10.1142/s0219198906001168.

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This article introduces a model of rationality that combines procedural utility over actions with consequential utility over payoffs. It applies the model to the Prisoners' Dilemma and shows that empirically observed cooperative behaviors can be rationally explained by a procedural utility for cooperation. The model characterizes the situations in which cooperation emerges as a Nash equilibrium. When rational individuals are not solely concerned by the consequences of their behavior but also care for the process by which these consequences are obtained, there is no one single rational solution to a Prisoners' Dilemma. Rational behavior depends on the payoffs at stake and on the procedural utility of individuals. In this manner, this model of procedural utility reflects how ethical considerations, social norms or emotions can transform a game of consequences.

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Zhukovskiy, V. I., L. V. Zhukovskaya, K. N. Kudryavtsev, and V. E. Romanova. "ON ONE MODIFICATION OF NASH EQUILIBRIUM." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 13–30. http://dx.doi.org/10.14529/mmph220202.

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By the end of the last century there were four areas in the mathematical theory of positional differential games: non-coalitional positional differential games, cooperative, hierarchical and, finally, the least-understood coalitional positional differential games. In their turn, coalitional games are divided into games with transferable payoffs (games with side payments when players can split profits in the course of the game) and with non-transferable payoffs (games with side payments when there are no such distributions for this or that reason). The coalitional games with side payments are being extensively explored at the Faculties of Applied Mathematics and Management Processes of St. Petersburg University and the Institute of Mathematics and Information Technologies of Petrozavodsk State University (by Professors L.A. Petrosyan, V.V. Mozalov, E.M. Parilina, A.N. Rettieva and their numerous students). However, side payments are not always present even in economic cooperation; moreover, side payments can be legislated against. We believe that the research of the equilibrium of threats and counter-threats (sanctions and counter-sanctions) in non-coalitional differential games that we have carried out over the last years allows to also cover some aspects of non-transferable payoff coalitional games. The article considers the issues of namely the internal and external stability of coalitions in the class of positional differential games. The coefficient constraints were identified for the mathematical model of a linear-quadratic differential positional game with twin-coalitional structure for six persons where this coalitional structure is internally and externally stable.

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Zhang, Yan Chao, and Guo Ding Chen. "Optimization Design of Finger Seal Performances Based on Game Theory." Advanced Materials Research 156-157 (October 2010): 1275–80. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.1275.

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To reach the expecting goal of lower leakage ratio and longer operation life(lower wear ratio) for finger seal, great efforts have been made continuously to obtain good structure of finger seal with advanced optimization design technology. A cooperation Nash equilibrium mathematical model of multi-objective optimization for finger seal is presented in current work based on Nash equilibrium of game theory. In this solution, the reciprocal of leakage ratio and the wear ratio value for finger seal are thought as the payoff functions and the game is solved by genetic algorithm. The numerical simulation in the paper shows that the finger seal with better performances can be achieved by using Nash equilibrium method. This means Nash equilibrium method can be used as a new multi-objective optimization method for finger seal performances optimization.

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Yin, Shi, and Baizhou Li. "A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment." Open Mathematics 16, no. 1 (June 14, 2018): 607–22. http://dx.doi.org/10.1515/math-2018-0056.

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AbstractConsidering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.

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Golsefid, Narges Torabi, and Maziar Salahi. "Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations." RAIRO - Operations Research 55, no. 6 (November 2021): 3677–99. http://dx.doi.org/10.1051/ro/2021170.

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In this paper, for evaluating the efficiency in a three-stage DEA structure we use the additive and the multiplicative cooperative models that comply with the cooperation paradigm in the organizations, where for improving efficiency of system, stages cooperate together. Since the overall efficiency from the cooperative models may not be unique and consequently the stages’ efficiencies, then we combine them with the Nash bargaining game approach that besides maximizing efficiency scores for stages and the whole system, provides a unique and fair efficiency decomposition. Second order programming relaxation of the proposed nonlinear models are given in contrast to the parametric linear models in the literature. Finally, the effectiveness of the proposed models are illustrated with two numerical examples.

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Sánchez Carrera, Edgar J. "On feedback nash equilibrium and cooperation in the neoclassical growth model." econoquantum 9, no. 2 (December 15, 2012): 29–43. http://dx.doi.org/10.18381/eq.v9i2.147.

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Zhang, Guangsheng, Xiao Wang, Yu Zhang, and Jiayun Kang. "Research on the Emission Reduction Decision of Cost-Sharing Logistics Service Supply Chain in the O2O Model." Sustainability 14, no. 20 (October 14, 2022): 13247. http://dx.doi.org/10.3390/su142013247.

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As an effective way to realize energy savings and environmental protection, cost sharing is gradually becoming an important measure to reduce emissions in the logistics service supply chain under O2O mode in recent years. How to conduct contract selection and design optimization under the cost-sharing situation, and then improve the operational efficiency of the logistics service supply chain is an important issue that needs to be addressed. Firstly, based on the initial market demand for logistics, this paper involves the influence of both online logistics service integrators and onsite functional logistics service providers on logistics market demand in terms of emission reduction and platform brand image and develops a model based on the logistics service demand function in the O2O mode. Secondly, for the role of online and onsite emission reduction services in multi-cycle continuous cooperation to enhance the platform integrator’s brand image, a cost-sharing differential game model between online and onsite services is developed to facilitate providers’ adoption of high-quality emission reduction services. Finally, the HJB equation is used to compare the non-cooperative Nash game, the cost-sharing Stackelberg game, and the cooperative game to make the optimal abatement decision, the optimal benefit, and the cost-sharing ratio of the abatement service supply chain in the non-cooperative Nash game, the cost-sharing Stackelberg game, and the cooperative game. By comparing the results of the three games, we find that the optimal onsite and online abatement service decision is related to the cost, marginal revenue, and the impact of the service on demand; the abatement cost-sharing contract and cooperation are both better than the non-cooperative independent decision state, which can effectively guide the provision of high-quality onsite abatement service and improve the revenue of both parties involved in the logistics service supply chain and the total system’s revenue in the O2O mode. Compared with the cooperative game model, the cost-sharing contract can more effectively facilitate close cooperation between the actors, and the relationship between onsite and online marginal revenue affects the improvement of both parties’ revenue. The findings of the study can provide useful managerial insights for the selection and design optimization of abatement contracts for logistics service supply chains considering cost-sharing via the O2O model.

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Murase, Yohsuke, and Seung Ki Baek. "Friendly-rivalry solution to the iterated n-person public-goods game." PLOS Computational Biology 17, no. 1 (January 21, 2021): e1008217. http://dx.doi.org/10.1371/journal.pcbi.1008217.

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Repeated interaction promotes cooperation among rational individuals under the shadow of future, but it is hard to maintain cooperation when a large number of error-prone individuals are involved. One way to construct a cooperative Nash equilibrium is to find a ‘friendly-rivalry’ strategy, which aims at full cooperation but never allows the co-players to be better off. Recently it has been shown that for the iterated Prisoner’s Dilemma in the presence of error, a friendly rival can be designed with the following five rules: Cooperate if everyone did, accept punishment for your own mistake, punish defection, recover cooperation if you find a chance, and defect in all the other circumstances. In this work, we construct such a friendly-rivalry strategy for the iterated n-person public-goods game by generalizing those five rules. The resulting strategy makes a decision with referring to the previous m = 2n − 1 rounds. A friendly-rivalry strategy for n = 2 inherently has evolutionary robustness in the sense that no mutant strategy has higher fixation probability in this population than that of a neutral mutant. Our evolutionary simulation indeed shows excellent performance of the proposed strategy in a broad range of environmental conditions when n = 2 and 3.

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Li, Ling, Yao Song, and Zhiqiang Zhang. "A Tripartite Game Analysis of Environmental Pollution Control Based on Complicated Intergovernmental Relations." Complexity 2021 (August 21, 2021): 1–28. http://dx.doi.org/10.1155/2021/8148799.

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An excellent ecological environment is conducive for improving economic benefits and social benefits. The environmental pollution control requires the cooperation of governments at all levels and a large amount of capital investment. However, under the system with Chinese characteristics, the intergovernmental relations present complex and dynamic characteristics: the central government is authoritative, the local governments are obedient and self-interested, and the environmental pollution control usually involves multiple government departments, while it has strong externality, which makes it easy to breed “free rider” behavior in the process of environmental pollution control. Therefore, the cross-regional environmental pollution control cooperation model of governments at all levels is a complex and worthwhile research problem. Based on this, the paper studies a tripartite game problem of environmental pollution control from both horizontal and vertical intergovernmental relations. The Hamilton–Jacobi–Bellman equation was used to obtain the optimal effort strategy, environmental pollution control level, and environmental pollution losses under the Nash game model, the Stackelberg game model, and the Cooperative game model. The results show the following: firstly, the governments’ environmental pollution control efforts are positively related to their own execution ability and influence ability and negatively related to the cost coefficient; secondly, from the perspectives of environmental pollution control level and environmental pollution losses, the Cooperative game model is superior to the Nash game model and the Stackelberg game; thirdly, this paper analyzes the relationship between the loss-bearing ratio, the special financial funds, the effort level of government, and the environmental pollution control level; finally, the conclusions are verified by numerical analysis, which proves the validity of the models.

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43

Eshel, Ilan, and Daphna Weinshall. "Cooperation in a repeated game with random payment function." Journal of Applied Probability 25, no. 3 (September 1988): 478–91. http://dx.doi.org/10.2307/3213977.

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A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.

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Eshel, Ilan, and Daphna Weinshall. "Cooperation in a repeated game with random payment function." Journal of Applied Probability 25, no. 03 (September 1988): 478–91. http://dx.doi.org/10.1017/s0021900200041206.

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A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.

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MAZALOV, VLADIMIR V., and ANNA N. RETTIEVA. "FISH WARS WITH MANY PLAYERS." International Game Theory Review 12, no. 04 (December 2010): 385–405. http://dx.doi.org/10.1142/s0219198910002738.

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Discrete-time game-theoretic models related to a bioresource management problem (fish catching) are investigated. There are some players (countries or fishing firms) which harvest the fish stock. Power population's growth function and logarithmic players' profits are considered. We derive the Nash and cooperative equilibria. We construct the characteristic function for cooperative game in two unusual forms and determine the Shapley value and time-consistent imputation distribution procedure [Petrosjan (1977)]. We propose the condition which gives an incentive for the players to keep cooperation at each stage and compare it with the "irrational-behavior-profness" condition [Yeung (2006)]. We propose the linear programming method to find the time-consistent "rational" solution in C-core. The numerical modelling and the results' comparison were carried out.

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Bi, Fei, Haiwei Zhou, Min Zhu, and Weiwei Wang. "Economic benefit evaluation of water resources allocation in transboundary basins based on particle swarm optimization algorithm and cooperative game model—A case study of Lancang-Mekong River Basin." PLOS ONE 17, no. 7 (July 19, 2022): e0265350. http://dx.doi.org/10.1371/journal.pone.0265350.

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The present work aims to find the optimal solution of Nash Equilibrium (NE) in the traditional Game Theory (GT) applied to water resources allocation. Innovatively, this paper introduces Particle Swarm Optimization (PSO) into GT to propose a cooperative game model to solve the NE problem. Firstly, the basic theory of the PSO algorithm and cooperative game model is described. Secondly, the PSO-based cooperative game model is explained. Finally, the PSO-based cooperative game model is compared with the Genetic Algorithm (GA) to test the performance. Besides taking the countries in Lancang Mekong River Basin as the research object, this paper discusses each country’s water consumption and economic benefits under different cooperation patterns. Then, a series of improvement measures and suggestions are put forward accordingly. The results show that the average server occupancy time of the PSO-based cooperative game model is 78.46% lower than that of GA, and the average waiting time is 79.24% lower than that of the GA. Thus, the model reported here has higher computational efficiency and excellent performance than the GA and is more suitable for the current study. In addition, the multi-country cooperation mode can obtain more economic benefits than the independent water resource development mode. This model can quickly find the optimal combination of 16 cooperation modes and has guiding significance for maximizing the benefits of cross-border water Resource Utilization. This research can provide necessary technical support to solve the possible contradictions and conflicts between cross-border river basin countries and build harmonious international relations.

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Akçay, Erol, and Joan Roughgarden. "Negotiation of mutualism: rhizobia and legumes." Proceedings of the Royal Society B: Biological Sciences 274, no. 1606 (September 26, 2006): 25–32. http://dx.doi.org/10.1098/rspb.2006.3689.

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The evolution and persistence of biological cooperation have been an important puzzle in evolutionary theory. Here, we suggest a new approach based on bargaining theory to tackle the question. We present a mechanistic model for negotiation of benefits between a nitrogen-fixing nodule and a legume plant. To that end, we first derive growth rates for the nodule and plant from metabolic models of each as a function of material fluxes between them. We use these growth rates as pay-off functions in the negotiation process, which is analogous to collective bargaining between a firm and a workers' union. Our model predicts that negotiations lead to the Nash bargaining solution, maximizing the product of players' pay-offs. This work introduces elements of cooperative game theory into the field of mutualistic interactions. In the discussion of the paper, we argue for the benefits of such an approach in studying the question of biological cooperation.

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Yao, Changhua, Lei Zhu, Yongxing Jia, and Lei Wang. "Demand-aware traffic cooperation for self-organizing cognitive small-cell networks." International Journal of Distributed Sensor Networks 15, no. 1 (January 2019): 155014771881728. http://dx.doi.org/10.1177/1550147718817289.

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This article investigates the problem of efficient spectrum access for traffic demands of self-organizing cognitive small-cell networks, using the coalitional game approach. In particular, we propose a novel spectrum and time two-dimensional Traffic Cooperation Coalitional Game model which aims to improve the network throughput. The main motivation is to complete the data traffics of users, and the main idea is to make use of spectrum resource efficiently by reducing mutual interference in the spectrum dimension and considering cooperative data transmission in the time dimension at the same time. With the approach of coalition formation, compared with the traditional binary order in most existing coalition formation algorithms, the proposed functional order indicates a more flexibly preferring action which is a functional value determined by the environment information. To solve the distributed self-organizing traffic cooperation coalition formation problem, we propose three coalition formation algorithms: the first one is the Binary Preferring Traffic Cooperation Coalition Formation Algorithm based on the traditional Binary Preferring order; the second one is the Best Selection Traffic Cooperation Coalition Formation Algorithm based on the functional Best Selection order to improve the converging speed; and the third one is the Probabilistic Decision Traffic Cooperation Coalition Formation Algorithm based on the functional Probabilistic Decision order to improve the performance of the formed coalition. The proposed three algorithms are proved to converge to Nash-stable coalition structure. Simulation results verify the theoretic analysis and the proposed approaches.

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Neck, R., and D. Blueschke. "Every Country for Itself and the Central Bank for Us All?" International Advances in Economic Research 26, no. 4 (October 12, 2020): 377–89. http://dx.doi.org/10.1007/s11294-020-09803-2.

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AbstractThis paper used a small stylized nonlinear three-country macroeconomic model of a monetary union to analyse the interactions between fiscal (governments) and monetary (common central bank) policymakers. The three fiscal players were divided into a financially stable core and a less stable periphery. The periphery itself consisted of two players with different perceptions of the trade-off between fiscal stability and output growth. Using the OPTGAME algorithm, solutions were calculated for two game strategies: one cooperative (Pareto optimal) and one non-cooperative game type (the Nash game for the feedback information pattern). Introducing a negative demand shock, the performance of different coalition options between players were analysed. A higher level of cooperation leads in general to a better overall outcome of the game, however, with highly varying burdens to be borne by the players.

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Yao, Hong, Guang Yang, Deze Zeng, Chao Liu, Qingzhong Liang, and Chengyu Hu. "An Advertiser-Centric Cooperative Mechanism in Smartphone Advertising Based on Stackelberg Game Analysis." International Journal of Web Services Research 12, no. 4 (October 2015): 1–15. http://dx.doi.org/10.4018/ijwsr.2015100101.

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The popularity of smart phones has greatly promoted the development of mobile advertising, especially the development of mobile application (app) advertising. An ad network as a medium between advertisers and app developers can not only provide advertising services for advertisers, but also bring app developers incomes. Existing forms of advertising partnership between advertisers and advertising networks (ad networks) are generally centered on ad networks. However, the advertising-centric cooperation model sometimes cannot meet the specialized advertising needs of advertisers, and the advertisers have to spend more to find the suitable partners. In this paper, the authors consider the advertising problem from the perspective of advertisers. They design an advertiser-centric cooperative mechanism to help an advertiser to attract cooperation from ad networks. They formulate the advertiser-centric cooperative problem into a noncooperative game between an advertiser and a number of ad networks. It is proved that a unique Stackelberg equilibrium exists in the game and the authors have calculated the Nash equilibrium for each ad network. An algorithm that can achieve the unique equilibrium point is proposed. Extensive experiments' results are also conducted to verify the performance of the proposed mechanism in terms of the investment related factors.

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Journal articles on the topic 'Nash and cooperation'

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