A dual description of the class of games with a population monotonic allocation scheme

A vector of balanced weights infers an inequality that games with a nonempty core obey. This paper gives a generalization of the notion ‘vector of balanced weights.’ Herewith, it provides necessary and sufficient conditions to determine whether a TU-game has a population monotonic allocation scheme or not. Furthermore, it shows that every four-person integer valued game with a population monotonic allocation scheme has an integer valued population monotonic allocation scheme and it gives an example of a seven-person integer valued game that has only noninteger valued population monotonic allocation schemes.     

The brief history of game theory and the dissemination in China

After the year of 1944, Von Neumann and Morgenstem published the book ＂Theory of Games and Economic Behavior＂, the game theory had gradually become an emerging discipline. At present, game theory has already penetrated to every industry and widespread application in economy, politics and military and so on. The paper introduces the history and the developed situation of game theory about the foreign and domestic state.     

基于Shapley模型的KTV音乐版权费征收策略

在KTV中收取音乐版权费可以激发音乐人的创作热情,推动我国文化产业蓬勃发展。然而这涉及到唱片公司、音乐著作人、KTV场所经营者等多方面的利益,将版权费在多个主体间进行合理分配成为当务之急。本文基于合作博弈论中的Shapley模型,对当前我国KTV音乐版权费用的征收方式进行了分析。结合当前存在的问题提出了"版权费与经营收益挂钩,版权费按Shapley模型分配"的解决方式,既保证了KTV经营者、消费者的利益,又能将版权费用在音乐著作权人之间进行合理分配。为解决Shapley模型的缺陷,本文基于具体问题,提出了"贡献因子"、"渴望函数"、"意愿因子"等概念,对原始Shapley模型进行加权改进,并结合具体案例对模型进行了解释与验证。最后对模型的应用进行了评价,并提出进一步的研究方向。     

企业采用新技术的时点博弈分析

技术创新可以为企业带来超额利润,具有极大的经济价值,然而新技术的不确定性和风险性又使得企业不会立即采用。本文通过构建双寡头垄断博弈模型对企业采用新技术的时点进行研究,证明企业采用新技术时存在一个最佳时点,在这个最佳时点之前,企业应采取等待策略。     

Competition vs. collaboration in the generation and adoption of a sequence of new technologies: a game theory approach

The study provides a game theoretic exploration of firms’ decisions on whether to compete or collaborate in the generation and adoption of a sequence of new technologies. Different from models proposed by previous studies, which concentrates on process innovation and a two-strategy set (innovation or do nothing), the present game theory model emphasises product innovation and a three-strategy set (innovation, collaboration, or do nothing). The study makes three contributions. The proposed game theory model extends current understanding of the impacts of collaboration possibilities and collaboration cost in a dynamic game theory. Further, the model clarifies the impact of transaction costs on the outcome. Finally, the study finds that the relationship between collaboration costs is not univariate, but depends on the market type and various market characteristics, such as technology gap, technology level, the product substitution index, transaction costs, and the discount rate of price sensitiveness.     

The Colonel Blotto game

In the Colonel Blotto game, two players simultaneously distribute forces across n battlefields. Within each battlefield, the player that allocates the higher level of force wins. The payoff of the game is the proportion of wins on the individual battlefields. An equilibrium of the Colonel Blotto game is a pair of n-variate distributions. This paper characterizes the unique equilibrium payoffs for all (symmetric and asymmetric) configurations of the players’ aggregate levels of force, characterizes the complete set of equilibrium univariate marginal distributions for most of these configurations, and constructs entirely new and novel equilibrium n-variate distributions.I am grateful to Jason Abrevaya, Dan Kovenock, James C. Moore, Roger B. Nelsen, and three anonymous referees for very helpful comments. A version of this paper was presented at the 2005 Midwest Economic Theory Meetings. This paper is based on the first chapter of my Ph.D. dissertation     

Existence and efficiency of a stationary subgame-perfect equilibrium in coalitional bargaining models with nonsuperadditive payoffs

We provide the existence theorem of stationary subgame-perfect equilibrium (SSPE) in a noncooperative coalitional bargaining game model with random proposers. Our model contains a bargaining situation where the coalitional game is nonsuperadditive. We also provide a necessary and sufficient condition for the existence of a pure-strategy SSPE satisfying the efficiency property when the discount factor is close to one. Furthermore, we provide examples where the delay in agreement occurs, even in a random-proposers model, when the game is nonsuperadditive. I am grateful to Akira Okada and an anonymous referee for their useful comments and helpful suggestions.     

A note on a value with incomplete communication

The Myerson's models on partial cooperation have been studied extensively [SIAM J. Discrete Math. 5 (1992) 305; Math. Methods Operations Res. 2 (1977) 225; Int. J. Game Theory 19 (1980) 421; 20 (1992) 255]. In [Game Econ. Behav. 26 (1999) 565], Hamiache proposes a new solution concept for communication situations. In this work, we analyze this value making some deficiencies clear and generalize this value to union stable cooperation structures emphasizing the differences in the extension.     

The e-mail game phenomenon

The e-mail game in Rubinstein (1989) shows that types with arbitrarily close higher-order beliefs may differ substantially in strategic behaviors. We define a notion called strategic discontinuity in arbitrary incomplete-information scenarios to generalize this e-mail game phenomenon. We show that almost all types involved in economic analysis — types in finite or common-prior models — display strategic discontinuity in simple games.     

Supervision of higher executives in commercial banks ——From the view of game theory

After reviewing the bad news and corruptions of the higher executives in commercial banks recent years, the article first analyzes the characteristics of all these things, and use game theory to analyzes the actions between the higher executives and administrative sections and further construes with cost and benefit utility model, and finally put up some countermeasures.     

Games superheroes play: Teaching game theory with comic book favorites

The valuable insights of game theory sometimes remain out of reach for students who are overwhelmed by the subject's complexity. Comic book applications of game theory, with superheroes as players, can facilitate enthusiasm and classroom interaction to enhance the learning of game theory. Drawing from content in superhero movies and books, the authors construct games to illustrate pure-strategy Nash equilibrium, Bayes-Nash equilibrium, mixed strategies, sub-game perfection, and perfect Bayesian equilibrium. To help instructors build students' skills in finding and interpreting game solutions, they translate comic book scenarios into specific game forms; however, not all scenarios are obvious so they suggest instructors help students develop their own game-theoretic judgments to determine what game forms, payoffs, and solution concepts might be appropriate for understanding a situation.     

Evolutionary game dynamics and distributed recency-weighted learning

This paper presents a relationship between evolutionary game dynamics and distributed recency-weighted Monte Carlo learning. After reviewing some existing theories of replicator dynamics and agent-based Monte Carlo learning, we provide proofs of the formulation-level equivalence between these two models. The relationship will be revealed not only from a theoretical viewpoint, but also by computational simulations of the models. As a consequence, macro dynamic patterns generated by distributed micro-decisions can be explained by parameters defined at an individual level. In particular, given the equivalent formulations, we investigate how the rate of agents’ recency weighting in learning affects the emergent evolutionary game dynamic patterns. An increase in this rate negatively affects the inertia, making the evolutionary stability condition more strict, and positively affecting the evolutionary speed toward equilibrium.JEL Classification: C63, C73Supervisions and advice given by Arthur J. Caplan have greatly contributed to this paper. I am also grateful to the anonymous reviewers for their valuable comments redirecting my presentation to a more appropriate one.     

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Debreu and Scarf (1963), Hildenbrand (1974), Aumann (1964), Dierker (1975), Bewley (1973), and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined. This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.     

A dynamic framework for analyzing technology standardisation using network analysis and game theory

As more technologies and industries converge, technology standards are more likely to be a strategic factor for firms and governments that are interested in the market with standards-based competition. From the previous research, a new standardisation framework was proposed by combining network analysis and the game theory model but was constrained by feasibility and dynamic approach. In this study, the case of the standards war between HD-DVD and Blu-ray was analyzed with patent data as an empirical case considering a dynamic framework. With this framework, we observed a change in a firm’s technology relations and could predict the decline in a firm’s preference and the shift of equilibrium ahead of Toshiba’s resignation.     

On a master-slave Bertrand game model

A master-slave Bertrand game model is proposed for upstream and downstream monopolies owned by different parties, in which the upstream monopolist's output is used as the main factor of production by the downstream monopolist who is a small purchaser of the upstream monopolist's output. The bifurcation of the Bertrand-Nash equilibrium is analyzed with Schwarzian derivative. Numerical simulations are employed to show the model's complex dynamics by means of the largest Lyapunov exponents (LLEs), bifurcation, time series diagrams and phase portraits. With the modified straight-line stabilization method, chaos control is used to improve the aggregate profits of the two oligopolists. Lastly the welfare impacts of price fluctuations and chaos controls are briefly discussed.     

Analysis of evolutionary game in structural formation of market power in remanufacturing supply chains

It is normal for enterprises to engage in remanufacturing nowadays. Nevertheless, the concern of enterprises and researchers is whether remanufacturers should compete for leadership in supply chains. Considering the WTP for new and remanufactured products differs, this article the evolutionary game theory model in three structures of leadership in supply chains. It investigates the processes of market evolution and choices of strategies when manufacturers and retailers compete or do not compete for leadership in the market. It has been shown in the case of market evolution, according to the 12 conditions formed from different prices that manufacturer and retailer have to pay for competing for leadership, there are five types of ultimate evolutionary stability about the choices of strategies. Further analyses show that these five different evolutionary stability results include nine different evolutionary paths. Analyses of examples further show the evolutionary processes and results in distinct circumstances. This article extends the application of the evolutionary game in remanufacturing supply chains in theory and provides some guidance for enterprises to make decisions when they consider whether they compete for leaders in remanufacturing supply chains in reality.     

Credibility and determinism in a game of persuasion

This paper studies a game of persuasion. A speaker attempts to persuade a listener to take an action by presenting evidence. Glazer and Rubinstein (2006) showed that when the listener's decision is binary, neither randomization nor commitment have any value for the listener, and commented that the binary nature of the decision was important for the commitment result. In this paper, I show that concavity is the critical assumption for both results: no value to commitment and no value to randomization. Specifically, the key assumption is that the listener's utility function is a concave transformation of the speaker's utility function. This assumption holds vacuously in the binary model. The result that concavity implies credibility allows us to dispense with the assumption that the listener's decision is binary and significantly broadens the scope of the model.     

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.     

A video game to supplement a hybrid principles of microeconomics course

In this article, the author describes the structure and content of a video game that she developed for a hybrid principles of microeconomics course that consists of two 50-minute lectures and a 50-minute online portion per week. The game comprises seven modules, each of which was assigned to be played during the course of the semester for the online portion of the class. The concepts covered in the game include the circular flow model, demand and supply, externalities, comparative advantage, types of market structure, sunk costs, and game theory, and the article explains in detail how the gameplay was related to these concepts. The game can be downloaded for either Windows or Mac computers, or played online at https://sites.google.com/site/gamesforecon/.