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1
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Online Resource
Handbook of game theory with economic applications : volume 2 (1994)
Amsterdam : North-Holland
Details
UID:
gbv_789712520
Format: Online Ressource (xvii, 735-1520 pages) , illustrations.
Edition: Online-Ausg.
ISBN: 0444894276 , 9780444894274
Series Statement: Handbooks in economics 11
Content: This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology
Content: This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology
Note: Includes bibliographical references and indexes , Vol. 2 .Zero-sum two-person games , Game theory and statistics , Differential games , Differential gameseconomic applications , Communication, correlated equilibria and incentive compatibility , Signalling , Moral hazard , Search , Game theory and Evolutionary biology , Game theory models of peace and war , Voting procedures , Social choice , Power and stability in politics , Game theory and public economics , Cost allocation , Cooperative models of bargaining , Games in coalitional form , Coalition structure , Game-theoretic aspects of computing , Utility and subjective probability , Common knowledge
Language: English
Subjects: Economics , Mathematics
RVK:
QH 430
RVK:
SK 860
Keywords: Spieltheorie ; Wirtschaftswissenschaften ; Electronic books
URL: Volltext  (Deutschlandweit zugänglich)
URL: lizenzpflichtig
URL: Inhaltstext
Author information: Aumann, Robert J. 1930-
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  • 2
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    Chapter 20 Zero-sum two-person games (1994)
    Details
    UID:
    gbv_1831641720
    ISBN: 0444894276
    Content: This chapter discusses the zero-sum two-person games. Given a two-person game with just one move for each player, the players independently and simultaneously select one among the finitely many actions resulting in a payoff for each player. If i , j are their independent choices in a play, then the game is defined by a pair of real matrices A ( a ij ), B ( b ij ), where a ij is the payoff to player I and b ij is the payoff to player II. The game is called zero sum if a ij b ij 0. Thus, in zero-sum games, what one player gains, the opponent loses. In such games, A suffices to determine the payoff. The chapter describes the equivalence of the minimax theorem and the duality theorem. To prove minimax theorems in greater generality, Kakutani's theorem is further extended to arbitrary locally convex topological vector spaces. These are real vector spaces with a Hausdorff topology admitting convex bases, where vector operations of addition and scalar multiplication are continuous.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 735-768, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:735-768
    Language: English
    DOI: 10.1016/S1574-0005(05)80052-9
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 3
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    Chapter 21 Game theory and statistics (1994)
    Details
    UID:
    gbv_1831641712
    ISBN: 0444894276
    Content: Game theory, in particular the theory of two-person zero-sum games, has played a multiple role in statistics. Its principal role has been to provide a unifying framework for the various branches of statistical inference. Statistics, regarded from the game-theoretic point of view, became known as decision theory. While unifying statistical inference, decision theory has also proved useful as a tool for weeding out procedures and approaches that have taken hold in statistics without good reason. On a less fundamental level, game theory has contributed to statistical inference the minimax criterion. While the role of this criterion in two-person zero-sum games is central, its application in statistics is problematic. Its justification in game theory is based on the direct opposition of interests between the players, as expressed by the zero-sum assumption. Together with the minimax criterion, randomized, or mixed, strategies also appear in decision theory. The degree of importance of randomization in statistics differs according to which player is randomizing. Mixed strategies for Nature are a priori distributions. In the Bayes approach, these are assumed to represent the Statistician's states of knowledge prior to seeing the data, rather than Nature's way of playing the game. Therefore, they are often assumed to be known to the Statistician before he or she makes his or her move, unlike the situation in the typical game-theoretic set-up. Mixed strategies for the Statistician, on the other hand, are, strictly speaking, superfluous from the Bayesian point of view, while according to the minimax criterion, it may be advantageous for the Statistician to randomize, and it is certainly reasonable to grant him or her this option.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 769-779, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:769-779
    Language: English
    DOI: 10.1016/S1574-0005(05)80053-0
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 4
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    Chapter 22 Differential games (1994)
    Details
    UID:
    gbv_1831641704
    ISBN: 0444894276
    Content: This chapter discusses differential games. In control theory, a certain evolutionary process (typically given by a time-dependent system of differential equations) depends on a control variable. A certain cost is associated with the control variable and with the corresponding evolutionary process. The goal is to choose the best controlthat is, the control for which the cost is minimized. A similar evolutionary process is used in differential games, but it depends on two (or more) controls. Each player is in charge of one of the controls. Each player wishes to minimize its own cost (the cost functions of the different players may be related). However, at each time t , a player must decide on its control without knowing what the other (usually opposing) players intend to do. The strategy of each player at time t depends only on whatever information the player was able to gain by observing the evolving process up to time t only.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 781-799, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:781-799
    Language: English
    DOI: 10.1016/S1574-0005(05)80054-2
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  • 5
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    Chapter 23 Differential games — Economic applications (1994)
    Details
    UID:
    gbv_1831641690
    ISBN: 0444894276
    Content: This chapter discusses the differential games economic applications. Much of the application of N-person, general-sum differential games is in economics, where observed regularities are rarely invariant as in natural sciences. Thus, expenditure patterns in America offer little insights upon the consumption habits in Papua-New Guinea. Out of those differential games that depend on specific function forms (e.g., the linear-quadratic game), useful theoretic examples may be constructed but not the basis for robust predictions. In the case of optimal control, broad conclusions are often obtained by means of the globally analytic phase diagram for those problems with a low-dimension state space. On the other hand, from the viewpoint of economics, there are two distinct types of contributions that differential games can offer. First is regarding the multiplicity of solutions: differential game can yield broad conceptual contributions that do not require the detailed solution(s) of a particular game. Second, there remains an unsatisfied need that differential games may meet. For situations where a single decision maker faces an impersonal environment, the system dynamics can be studied fruitfully with optimal control models. There are analogous situations where the system dynamics is decided by the interactions of a few players. Differential games seem to be the natural tool. What economists wish to predict is not only the details about a single time profile, such as existence and stability of any long run configuration and the monotonicity and speed of convergence toward that limit, but also the findings from the sensitivity analysis: how such a configuration responds to parametric variations.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 801-825, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:801-825
    Language: English
    DOI: 10.1016/S1574-0005(05)80055-4
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  • 6
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    Chapter 24 Communication, correlated equilibria and incentive compatibility (1994)
    Details
    UID:
    gbv_1831641682
    ISBN: 0444894276
    Content: In principle, anything that a player can do to communicate and coordinate with other players could be described by moves in an extensive-form game, so that planning these communication moves would become part of the player's strategy choice itself. Adding a communication system does not eliminate any of the equilibria of the original game because there are always equilibria of the communication game in which reports and messages are treated as having no meaning and hence are ignored by all players. Such equilibria of the communication game are called babbling equilibria. The set of correlated equilibria of a strategic-form game has a simple and tractable mathematical structure because it is closed by convex and is characterized by a finite system of linear inequalities. The revelation principle for strategic-form games asserted that any equilibrium of any communication system can be simulated by a communication system in which the only communication is from a central mediator to the players, without any communication from the players to the mediator. The one-way nature of this communication is not surprising, because the players have no private information to tell the mediator about, within the structure of the strategic-form game. However, players in a Bayesian game may have private information about their types, and two-way communication would then allow the players' actions to depend on each other's types as well as on extraneous random variables, such as coin tosses. Thus, in Bayesian games with communication, there may be a need for players to talk as well as to listen in mediated communication systems.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 827-847, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:827-847
    Language: English
    DOI: 10.1016/S1574-0005(05)80056-6
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  • 7
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    Chapter 25 Signalling (1994)
    Details
    UID:
    gbv_1831641674
    ISBN: 0444894276
    Content: This chapter presents some of the main developments in the theory of market signaling and its connection to noncooperative game theory. One of the most important applications of game theory to micro-economics has been in the domain of market signaling. The standard story is a simple one: for example, two parties wish to engage in exchange; the owner of a used car wants to sell the car to a potential buyer. One party has information (e.g., the seller knows the quality of the car) that the other lacks. The quality of a car is outside of the control of the owner and quality depends on things done or undone at the factory when the car was assembled. Under certain conditions, the first party wishes to convey that information to the second. But direct communication of the information is for some reason impossible, and the first party must engage in some activity that indicates to the second what the first knows; e.g., the owner of a good car will offer a limited warranty. The range of applications for this story is largefor example, a worker wishing to signal his or her ability to a potential employer and using education as a signal, an insuree who is relatively less risk prone signaling this to an insurer by accepting a larger deductible or only partial insurance, and a firm that is able to produce high-quality goods signaling this by offering a warranty for the goods sold.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 849-867, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:849-867
    Language: English
    DOI: 10.1016/S1574-0005(05)80057-8
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 8
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    Chapter 26 Moral hazard (1994)
    Details
    UID:
    gbv_1831641666
    ISBN: 0444894276
    Content: This chapter discusses moral hazard. The principalagent relationship embodies a special form of moral hazard, which can be called one-sided, but moral hazard can also be many-sided. The paradigmatic model of many-sided moral hazard is the partnership in which there are many agents but no principal. The output of the partnership depends jointly on the actions of the partners and on the stochastic environment; each partner observes only the output (and his or her own action) but not the actions of the other partners or the environment. This engenders a free-rider problem. As in the case of principalagent relationships, a partnership, too, may last many periods. The chapter presents the principalagent model formally and describes some salient features of optimal principalagent contracts when the relationship lasts a single period. In a large class of cases, equilibrium in the one-period game is Pareto-inefficient. This is a well-known problem in providing risk-averse agent insurance while simultaneously giving the agent the incentives to take, from the principal's perspective, appropriate actions. The chapter also discusses other properties of static contracts such as monotonicity of the agent's compensation in observed profits.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 869-903, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:869-903
    Language: English
    DOI: 10.1016/S1574-0005(05)80058-X
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 9
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    Chapter 27 Search (1994)
    Details
    UID:
    gbv_1831641658
    ISBN: 0444894276
    Content: Search theory has provided a simple and robust laboratory that economic theorists have used to examine a wide variety of questions about the acquisition of information. Early work on search modeled an individual's searching decisions and drew inferences about the value of information and the nature of frictional unemployment. More recent work, building on sequential-bargaining analysis, has focused on the interactions among searching agents and has deepened the understanding of the nature and meaning of competition. The chapter discusses the classical search problem: the optimal search rule for an individual who can, for a fixed and constant cost, take a random sample from a distribution F ( ) of economic opportunities. The marriage of search theory and bargaining theory has produced some of the more interesting recent economic theory. This research has shown such diverse and important topics as the nature of the competitive mechanism and the possible impact of externalities and multiple equilibria on macroeconomic performance.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 905-927, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:905-927
    Language: English
    DOI: 10.1016/S1574-0005(05)80059-1
    URL: Volltext  (Deutschlandweit zugänglich)
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  • 10
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    Chapter 28 Game theory and evolutionary biology (1994)
    Details
    UID:
    gbv_183164164X
    ISBN: 0444894276
    Content: The subject matter of evolutionary game theory is the analysis of conflict and cooperation in animals and plants. Originally, game theory was developed as a theory of human strategic behavior based on an idealized picture of rational decision making. Evolutionary game theory does not rely on rationality assumptions but on the idea that the Darwinian process of natural selection drives organisms toward the optimization of reproductive success. Most of evolutionary game theory focuses on those cases where stable equilibrium is reached. However, the dynamics of evolutionary processes in disequilibrium is also an active area of research. In principle, evolutionary game theory deals only with fully symmetric games. Asymmetric conflicts are embedded in symmetric games where each player has the same chance to be on each side of the conflict. The mathematical definition of evolutionary stability refers to symmetric games only. Because asymmetric conflicts can be embedded in symmetric games, this is no obstacle for the treatment of asymmetric conflicts.
    In: Handbook of game theory with economic applications, Amsterdam : North-Holland, 1994, (1994), Seite 929-993, 0444894276
    In: 9780444894274
    In: year:1994
    In: pages:929-993
    Language: English
    DOI: 10.1016/S1574-0005(05)80060-8
    URL: Volltext  (Deutschlandweit zugänglich)
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