An Overview of Game Theory and Some Applications 113 114 Philosophy and Progress

Total Page:16

File Type:pdf, Size:1020Kb

An Overview of Game Theory and Some Applications 113 114 Philosophy and Progress 112 Philosophy and Progress Philosophy and Progress: Vols. LIX-LX, January-June, July-December, 2016 behavior. The purpose of this paper is to clarify the following ISSN 1607-2278 (Print), DOI : http://dx.doi.org/10.3329/pp.v59i1-2.36683 issues: firstly, to provide very brief overview of game and game theory; secondly, to discuss background and impact of game theory; thirdly, to analyze the prisoner’s dilemma game and finally, to present applications of game theory with special attention to philosophy. Key Words: game, game theory, strategy, prisoner’s dilemma, philosophy. i. Game AN OVERVIEW OF GAME THEORY AND The ‘game’ is the object of studying in game theory. The SOME APPLICATIONS complete set of rules describes a game. A play is an instance of the game. Most games played for fun, entertainment and Bellal Ahmed Bhuiyan* leisure. When someone over reacts, we sometimes say ‘it’s just a game’. Checkers, chess, football, judo, and squash and thousands of other formalized contests are examples of games Introduction in which there are two players or teams. Most of these games Game theory is an autonomous discipline that is used in have only one winner after played (Geckil, 2010). But there are applied mathematics, social sciences, most considerably in many other situations that can be formulated as games. A game economics, as well as in biology, engineering, political science, follows as: international relations, computer science and philosophy. Game A game is an abstract, which is defined as a formal theory is the mathematical study of strategy and conflict, in description of a strategic situation. Any strategic which an agent’s success in making choices depends on the interaction involves two or more decision- makers choice of others. It was initially developed in economics to (players), each with two or more ways of acting understand a large collection of economic behaviors, including (strategies), such that the outcome depends on the behaviors of firms, markets and consumers. Game theory has strategy choices of all the players. Each player has well- been used to attempt to develop theories of ethical or normative defined preferences among all the possible outcomes, behavior as well. In economics and philosophy, scholars have enabling corresponding utilities (payoffs) to be applied game theory to help in the understanding of rational assigned. A game makes explicit the rules governing players’ interactions, the players feasible strategies, and * Lecturer, Department of Philosophy, University of Dhaka their preferences over outcomes (Bicchieri and Sillari, Email: [email protected] 2005, P. 296). An Overview of Game Theory And Some Applications 113 114 Philosophy and Progress All games have three essential elements- players, strategies, d) Normal and extensive form: The strategic form which is payoffs. So, a game in normal form consists of: also called normal form is the basic type of game studied in non-cooperative game theory. A game in strategic form lists a) A (finite) number of players. P= {1,2,3….,n}, each player, and the outcomes that result from each possible {P1,……,Pn} combination of choices. The extensive form, which is also b) A Strategy set Si assigned to each player: {S1 ,…,Sn} known as a game tree, is more detailed than the strategic form c) A utility/payoff function- set players gains: {U1,…,Un} of a game. It is a complete description of how the game is played over time. Different Categories of Game e) Zero-sum and non-zero-sum games: Zero- sum games Games can be distinguished according to various criteria: have the property that the sum of the payoffs to the players a) According to number of players: Usually there should be equals zero. For example, chess, poker, and most sports game more than one player. Maximum number of players is finite. A like basketball are zero-sum game. Real- world games are player may be expounded as a nation, or a team comprising rarely zero-sum game. It is also called constant-sun games. In many people, companies, associates etc. Game categorized as a non-zero-sum games, all players could win or loss together. one- person, two persons, or n-person (n>2) game. Most of the games in our real life and the business world are non-zero-sum game. For example, price wars between firms b) According to rationality of players: A key supposition in are non-zero-sum games. In non-zero-sum game players have many variants of game theory is that the players are rational. A common and conflicting interests (Geckil, 2010). rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his ii) Game Theory competitors to do. There can be distinguished two extreme Game theory is the logical analysis of situations of conflict and ways. The first one is called ‘intelligent’ player who is acting cooperation. Game theory could be formally defined as a rationally. The other extreme is the player who chooses random theory of rational decision in conflict situations. Model of such actions. situations, as they are conceived in game theory, involve c) According to cooperation: Games can be categorized into a) a set of decision makers, called players; cooperative and non- cooperative. A game in which players are allowed to cooperate with each other on a joint strategy is b) a set of strategies available to each player, courses of called a ‘cooperative game’. For example, a cooperative game action which he or she may choose to follow; is a bargaining game between parties in a transaction over the c) a set of outcomes, the strategies chosen by each player value of a target company. For non- cooperative is basic determine the outcome of the game; assumption that individual players can not cooperate. In this d) a set of payoffs accorded to each player in each of the game is associated with the analysis of strategic choices. possible outcomes. (Rapoport, 1974, p.1) An Overview of Game Theory And Some Applications 115 116 Philosophy and Progress So, Game theory is the study of how players should rationally not only mathematical apparatus, but also an important tool in play games. Each player would like to the game to end in an economics, political science, law, psychology, philosophy and outcome which gives him as large a payoff as possible. He has other disciplines. some control over the outcome, since his choice of strategy iii) Background and impact of Game Theory will influence it. Game theory has been widely recognized as an important tool The field known as ‘game theory’ was introduced in the last in different fields. The developments of Game theory is largely century by mathematicians and economists as a tool to analyze broadened. The initial discussion of game theory occurred in a both economic competition and political conflicts. Two letter written by James Waldegrave in 1713. In this letter, distinguished game theorists Robert Aumann and Oliver Hart, Waldegrave provides a mixed strategy solution to a two-person explain the attraction in the following way: version of the card game le Her. James Madison made what we Game Theory may be viewed as a sort of umbrella or now recognize as a game theoretic analysis of the ways states ‘unified field’ theory for the rational side of social can be expected to behave under different system of taxation. science, where ‘social’ is interpreted broadly, to include The earliest example of a formal game-theoretic analysis is the human as well as non- human players (computers, study of a dupopoly by Antoine Cournot in 1838. His animals, plants) … It does not use different, ad hoc publication Researches into the Mathematical Principles of the constructs … It develops methodologies that apply in Theory of Wealth presents a solution that is a restricted version principle to all interactive situations (Aumann and Hart, of the Nash equilibrium (Crider, 2012, p. 4). A formal theory 1992, P. 3) of games was suggested by the mathematician Emile Borel in 1921, which was furthered by the mathematician John Von The subject of Game theory are situations, where the result for Neumann in a “theory of parlor games” in 1928. a player does not only depend on his own decisions, but also on the behavior of the other players. Game theory is the theory of John Von Neumann and Oskar Morgenstern published the independent and interdependent decision making in Theory of Games and Economic Behavior in 1944. It organizations where the outcome depends on the decisions of introduced the economic and mathematical basis for the field two or more autonomous players, one of which may be nature we now call ‘Game theory’. This book contained much of the itself, and where no single decision maker has full control over basic terminology and problem setup that is still in use recent the outcomes (Kelly, 2003). times. Von Neumann and Morgenstern established the field that economic and social questions can often be described as The concepts of game theory provide a common language to mathematical models of suitable games of strategy. This formulate, structure, analyze and eventually understand gigantic work provides the method for finding mutually different strategic scenarios. Game theory is a scientific consistent solutions for two-person zero-sum games (Geckil discipline that investigates conflict situations, the interaction and Anderson, 2010). between the agents and their decisions (Hotz, 2006). To perform the analysis of critical situations, Game theory uses An Overview of Game Theory And Some Applications 117 118 Philosophy and Progress Game theory became closely associated with the Rand having laid the foundations of mechanism design theory” with Corporation after the second world war.
Recommended publications
  • Nash-Type Bargaining with Coherent Acceptability Measures
    Splitting a Random Pie: Nash-Type Bargaining with Coherent Acceptability Measures Walter J. Gutjahr University of Vienna, Vienna, Austria, [email protected] Raimund M. Kovacevic Vienna University of Technology, Vienna, Austria, [email protected] David Wozabal Technische Universit¨atM¨unchen, Munich, Germany, [email protected] We propose an axiomatic solution for cooperative stochastic games where risk averse players bargain for the allocation of profits from a joint project that depends on management decisions by the agents. We model risk preferences by coherent acceptability functionals and show that in this setting the axioms of Pareto optimality, symmetry, and strategy proofness fully characterize a bargaining solution, which can be efficiently computed by solving a stochastic optimization problem. Furthermore, we demonstrate that there is no conflict of interest between players about management decisions and characterize special cases where random payoffs of players are simple functions of overall project profit. In particular, we show that for players with distortion risk functionals, the optimal bargaining solution can be represented by an exchange of standard options contracts with the project profit as the underlying. We illustrate the concepts in the paper by a detailed example of risk averse households that jointly invest into a solar plant. Key words : Stochastic bargaining games; coherent risk measures; stochastic programming; photovoltaics History : 1. Introduction If a project is undertaken jointly by several agents and there is no efficient market for individual contributions, the question of how to distribute the project's profits arises. The case when profits are deterministic is well studied in the field of cooperative game theory.
    [Show full text]
  • Game Theory- Prisoners Dilemma Vs Battle of the Sexes EXCERPTS
    Lesson 14. Game Theory 1 Lesson 14 Game Theory c 2010, 2011 ⃝ Roberto Serrano and Allan M. Feldman All rights reserved Version C 1. Introduction In the last lesson we discussed duopoly markets in which two firms compete to sell a product. In such markets, the firms behave strategically; each firm must think about what the other firm is doing in order to decide what it should do itself. The theory of duopoly was originally developed in the 19th century, but it led to the theory of games in the 20th century. The first major book in game theory, published in 1944, was Theory of Games and Economic Behavior,byJohnvon Neumann (1903-1957) and Oskar Morgenstern (1902-1977). We will return to the contributions of Von Neumann and Morgenstern in Lesson 19, on uncertainty and expected utility. Agroupofpeople(orteams,firms,armies,countries)areinagame if their decision problems are interdependent, in the sense that the actions that all of them take influence the outcomes for everyone. Game theory is the study of games; it can also be called interactive decision theory. Many real-life interactions can be viewed as games. Obviously football, soccer, and baseball games are games.Butsoaretheinteractionsofduopolists,thepoliticalcampaignsbetweenparties before an election, and the interactions of armed forces and countries. Even some interactions between animal or plant species in nature can be modeled as games. In fact, game theory has been used in many different fields in recent decades, including economics, political science, psychology, sociology, computer science, and biology. This brief lesson is not meant to replace a formal course in game theory; it is only an in- troduction.
    [Show full text]
  • Stable Allocations and the Practice of Market Design
    15 OCTOBER 2012 Scientific Background on the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2012 STABLE ALLOCATIONS AND THE PRACTICE OF MARKET DESIGN compiled by the Economic Sciences Prize Committee of the Royal Swedish Academy of Sciences THE ROYAL SWEDISH ACADEMY OF SCIENCES has as its aim to promote the sciences and strengthen their influence in society. BOX 50005 (LILLA FRESCATIVÄGEN 4 A), SE-104 05 STOCKHOLM, SWEDEN TEL +46 8 673 95 00, FAX +46 8 15 56 70, [email protected] HTTP://KVA.SE 1 Introduction Economists study how societies allocate resources. Some allocation problems are solved by the price system: high wages attract workers into a particu- lar occupation, and high energy prices induce consumers to conserve energy. In many instances, however, using the price system would encounter legal and ethical objections. Consider, for instance, the allocation of public-school places to children, or the allocation of human organs to patients who need transplants. Furthermore, there are many markets where the price system operates but the traditional assumption of perfect competition is not even approximately satis…ed. In particular, many goods are indivisible and het- erogeneous, whereby the market for each type of good becomes very thin. How these thin markets allocate resources depends on the institutions that govern transactions. This year’s prizewinning work encompasses a theoretical framework for analyzing resource allocation, as well as empirical studies and actual redesign of real-world institutions such as labor-market clearinghouses and school ad- missions procedures. The foundations for the theoretical framework were laid in 1962, when David Gale and Lloyd Shapley published a mathematical inquiry into a certain class of allocation problems.
    [Show full text]
  • Strong Reciprocity and Human Sociality∗
    Strong Reciprocity and Human Sociality∗ Herbert Gintis Department of Economics University of Massachusetts, Amherst Phone: 413-586-7756 Fax: 413-586-6014 Email: [email protected] Web: http://www-unix.oit.umass.edu/˜gintis Running Head: Strong Reciprocity and Human Sociality March 11, 2000 Abstract Human groups maintain a high level of sociality despite a low level of relatedness among group members. The behavioral basis of this sociality remains in doubt. This paper reviews the evidence for an empirically identifi- able form of prosocial behavior in humans, which we call ‘strong reciprocity,’ that may in part explain human sociality. A strong reciprocator is predisposed to cooperate with others and punish non-cooperators, even when this behavior cannot be justified in terms of extended kinship or reciprocal altruism. We present a simple model, stylized but plausible, of the evolutionary emergence of strong reciprocity. 1 Introduction Human groups maintain a high level of sociality despite a low level of relatedness among group members. Three types of explanation have been offered for this phe- nomenon: reciprocal altruism (Trivers 1971, Axelrod and Hamilton 1981), cultural group selection (Cavalli-Sforza and Feldman 1981, Boyd and Richerson 1985) and genetically-based altruism (Lumsden and Wilson 1981, Simon 1993, Wilson and Dugatkin 1997). These approaches are of course not incompatible. Reciprocal ∗ I would like to thank Lee Alan Dugatkin, Ernst Fehr, David Sloan Wilson, and the referees of this Journal for helpful comments, Samuel Bowles and Robert Boyd for many extended discussions of these issues, and the MacArthur Foundation for financial support. This paper is dedicated to the memory of W.
    [Show full text]
  • Prisoners of Reason Game Theory and Neoliberal Political Economy
    C:/ITOOLS/WMS/CUP-NEW/6549131/WORKINGFOLDER/AMADAE/9781107064034PRE.3D iii [1–28] 11.8.2015 9:57PM Prisoners of Reason Game Theory and Neoliberal Political Economy S. M. AMADAE Massachusetts Institute of Technology C:/ITOOLS/WMS/CUP-NEW/6549131/WORKINGFOLDER/AMADAE/9781107064034PRE.3D iv [1–28] 11.8.2015 9:57PM 32 Avenue of the Americas, New York, ny 10013-2473, usa Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107671195 © S. M. Amadae 2015 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2015 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Amadae, S. M., author. Prisoners of reason : game theory and neoliberal political economy / S.M. Amadae. pages cm Includes bibliographical references and index. isbn 978-1-107-06403-4 (hbk. : alk. paper) – isbn 978-1-107-67119-5 (pbk. : alk. paper) 1. Game theory – Political aspects. 2. International relations. 3. Neoliberalism. 4. Social choice – Political aspects. 5. Political science – Philosophy. I. Title. hb144.a43 2015 320.01′5193 – dc23 2015020954 isbn 978-1-107-06403-4 Hardback isbn 978-1-107-67119-5 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
    [Show full text]
  • Repeated Games
    REPEATED GAMES 1 Early PD experiments In 1950, Merrill Flood and Melvin Dresher (at RAND) devised an experiment to test Nash’s theory about defection in a two-person prisoners’ dilemma. Experimental Design – They asked two friends to play the PD 100 times. – They measured the success of Nash’s equilibrium concept by counting the number of times the players chose {D;D}. 2 Flood and Dresher’s results Player 1 cooperated in 68 rounds Player 2 cooperated in 78 rounds Both cooperated in 60 of last 89 rounds Flood Dresher Nash 3 Flood and Dresher’s results Player 1 cooperated in 68 rounds Player 2 cooperated in 78 rounds Both cooperated in 60 of last 89 rounds Wait a Ha! That jerk I can’tI’mOh a be Ha! Nash second... Nash was genius...%&@#!wrong! was wrong! wrong! Flood Dresher Nash 4 Nash’s response “If this experiment were conducted with various different players rotating the competition and with no information given to a player of what choices the others have been making until the end of all trials, then the experimental results would have been quite different, for this modification of procedure would remove the interaction between the trials.” 5 Nash’s response “The flaw in this experiment as a test of equilibrium point theory is that the experiment really amounts to having the players play one large multimove game. One cannot...think of the thing as a sequence of independent games...there is too much interaction.” In other words, Nash said that repeating the game changes the game itself.
    [Show full text]
  • Nudging Cooperation in Public Goods Provision
    A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Barron, Kai; Nurminen, Tuomas Article — Accepted Manuscript (Postprint) Nudging cooperation in public goods provision Journal of Behavioral and Experimental Economics Provided in Cooperation with: WZB Berlin Social Science Center Suggested Citation: Barron, Kai; Nurminen, Tuomas (2020) : Nudging cooperation in public goods provision, Journal of Behavioral and Experimental Economics, ISSN 2214-8043, Elsevier, Amsterdam, Vol. 88, Iss. (Article No.:) 101542, http://dx.doi.org/10.1016/j.socec.2020.101542 This Version is available at: http://hdl.handle.net/10419/216878 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von
    [Show full text]
  • Competition and Cooperation on Predation: Bifurcation Theory of Mutualism Author: Srijana Ghimire Xiang-Sheng Wang University of Louisiana at Lafayette
    Competition and Cooperation on Predation: Bifurcation Theory Of Mutualism Author: Srijana Ghimire Xiang-Sheng Wang University of Louisiana at Lafayette Introduction Existence and Stability of E1,E+ and E− Existence and property of Hopf bifurcation 3. R > 1 and R > 3R − 2R2. In this case, Q = Q , 1 2 1 1 c 1 points We investigate two predator-prey models which take into con- xc = 1/R1, E1 always exists, E1 is locally asymptotically H E + H E E sideration the cooperation between two different predators and stable if and only if Q < Q1, E− does not exist, and E+ exits + + R H within one predator species, respectively. Local and global dy- if and only if Q > Q1. 2.0 E E E - namics are studied for the model systems. By a detailed bi- - - Q Q Q Q Q Q furcation analysis, we investigate the dependence of predation + + h + h1 h2 1.5 no Hopf bifurcation Existence conditions of positive equilibria. (a) case 1(a) (b) case 1(b) (c) case 1(c) dynamics on mutualism (cooperative predation). H H E R + 2 E E two supercritical + + 1.0 R2 > 1 Q H E+ E - E Q1 - E y y - First Predator-Prey Model with Competition 1 E 1 E 1 1 y 1 E 1 0.5 one supercritical NA Q Q Q Q Q Q Q Q Q and Co-operation 1 + 1 + 1 h + h1 1 h2 R2 < one Q R1 NA if Q < Q1 (d) case 2(a) (e) case 2(b) (f) case 2(c) E± subcritical E+ if Q ≥ Q1 E+ d 0 H 0 2 4 6 8 E x = 1 − x − p xy − p xz − 2qxyz, (1) + 1 2 Q+ E Q1 + 0 Figure: Existence and property of Hopf bifurcation points in the (d, R) y = p xy + qxyz − d y, (2) 2 1 1 R2 = 3R1 − 2R NA 1 H parameter space.
    [Show full text]
  • PIER Working Paper 11-035
    Penn Institute for Economic Research Department of Economics University of Pennsylvania 3718 Locust Walk Philadelphia, PA 19104-6297 [email protected] http://economics.sas.upenn.edu/pier PIER Working Paper 11-035 “Identification and Estimation of Stochastic Bargaining Models Fourth Version” by Antonio Merlo and Xun Tang http://ssrn.com/abstract=1946367 Identification and Estimation of Stochastic Bargaining Models∗ Antonio Merlo† Xun Tang‡ Revised, October 2011 Abstract Stochastic sequential bargaining models (Merlo and Wilson (1995, 1998)) have found wide applications in different fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching an agreement. This paper presents new results in nonparametric identification and estimation of such models under different data scenarios. Key words: Nonparametric identification and estimation, non-cooperative bargaining, stochastic sequential bargaining, rationalizable counterfactual outcomes. JEL codes: C14, C35, C73, C78. ∗We thank co-editor Jean-Marc Robin and three anonymous referees for their helpful suggestions. Steven Berry, Herman Bierens, Hanming Fang, Philip Haile, Isabelle Perrigne, Katja Seim, Elie Tamer, Petra Todd, Quang Vuong, Ken Wolpin and seminar and conference participants at several institutions provided useful comments. We thank Hulya Eraslan for sharing her data with us and Chamna Yoon for providing excellent research assistance. The usual disclaimer applies. †Department of Economics, University of Pennsylvania, CEPR, CESifo and NBER, [email protected]. ‡Department of Economics, University of Pennsylvania, [email protected]. 1 1 Introduction Starting with the seminal contributions of Stahl (1972) and Rubinstein (1982), noncooper- ative (or strategic) bargaining theory has flourished in the past thirty years. The original model of bilateral bargaining with alternating offers and complete information has been extended in a number of directions allowing for more general extensive forms, information structure and more than two players (e.g.
    [Show full text]
  • Matchings and Games on Networks
    Matchings and games on networks by Linda Farczadi A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Doctor of Philosophy in Combinatorics and Optimization Waterloo, Ontario, Canada, 2015 c Linda Farczadi 2015 Author's Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract We investigate computational aspects of popular solution concepts for different models of network games. In chapter 3 we study balanced solutions for network bargaining games with general capacities, where agents can participate in a fixed but arbitrary number of contracts. We fully characterize the existence of balanced solutions and provide the first polynomial time algorithm for their computation. Our methods use a new idea of reducing an instance with general capacities to an instance with unit capacities defined on an auxiliary graph. This chapter is an extended version of the conference paper [32]. In chapter 4 we propose a generalization of the classical stable marriage problem. In our model the preferences on one side of the partition are given in terms of arbitrary bi- nary relations, that need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable mar- riage where preferences are allowed to have ties and to be incomplete. Our main result shows that deciding the existence of a stable matching in our model is NP-complete.
    [Show full text]
  • Game-Theoretic Analysis of Cooperation Incentive Strategies in Mobile Ad Hoc Networks
    1 Game-Theoretic Analysis of Cooperation Incentive Strategies in Mobile Ad Hoc Networks Ze Li and Haiying Shen Dept. of Electrical and Computer Engineering Clemson University, Clemson, SC 29631 fzel,[email protected] F Abstract—In mobile ad hoc networks (MANETs), tasks are conducted nodes will decrease the throughput of cooperative nodes and lead based on the cooperation of nodes in the networks. However, since the to complete network disconnection [6]. Therefore, encouraging nodes are usually constrained by limited computation resources, selfish nodes to be cooperative and detecting selfish nodes in packet nodes may refuse to be cooperative. Reputation systems and price-based transmission is critical to ensuring the proper functionalities of systems are two main solutions to the node non-cooperation problem. A reputation system evaluates node behaviors by reputation values and uses MANETs. a reputation threshold to distinguish trustworthy nodes and untrustworthy Recently, numerous approaches have been proposed to deal nodes. A price-based system uses virtual cash to control the transactions with the node non-cooperation problem in wireless networks. of a packet forwarding service. Although these two kinds of systems have They generally can be classified into two main categories: reputa- been widely used, very little research has been devoted to investigating the tion systems and price-based systems. The basic goal of reputation effectiveness of the node cooperation incentives provided by the systems. systems [7–18] is to evaluate each node’s trustworthiness based In this paper, we use game theory to analyze the cooperation incentives provided by these two systems and by a system with no cooperation on its behaviors and detect misbehaving nodes according to rep- incentive strategy.
    [Show full text]
  • John Von Neumann Between Physics and Economics: a Methodological Note
    Review of Economic Analysis 5 (2013) 177–189 1973-3909/2013177 John von Neumann between Physics and Economics: A methodological note LUCA LAMBERTINI∗y University of Bologna A methodological discussion is proposed, aiming at illustrating an analogy between game theory in particular (and mathematical economics in general) and quantum mechanics. This analogy relies on the equivalence of the two fundamental operators employed in the two fields, namely, the expected value in economics and the density matrix in quantum physics. I conjecture that this coincidence can be traced back to the contributions of von Neumann in both disciplines. Keywords: expected value, density matrix, uncertainty, quantum games JEL Classifications: B25, B41, C70 1 Introduction Over the last twenty years, a growing amount of attention has been devoted to the history of game theory. Among other reasons, this interest can largely be justified on the basis of the Nobel prize to John Nash, John Harsanyi and Reinhard Selten in 1994, to Robert Aumann and Thomas Schelling in 2005 and to Leonid Hurwicz, Eric Maskin and Roger Myerson in 2007 (for mechanism design).1 However, the literature dealing with the history of game theory mainly adopts an inner per- spective, i.e., an angle that allows us to reconstruct the developments of this sub-discipline under the general headings of economics. My aim is different, to the extent that I intend to pro- pose an interpretation of the formal relationships between game theory (and economics) and the hard sciences. Strictly speaking, this view is not new, as the idea that von Neumann’s interest in mathematics, logic and quantum mechanics is critical to our understanding of the genesis of ∗I would like to thank Jurek Konieczny (Editor), an anonymous referee, Corrado Benassi, Ennio Cavaz- zuti, George Leitmann, Massimo Marinacci, Stephen Martin, Manuela Mosca and Arsen Palestini for insightful comments and discussion.
    [Show full text]