(Tentative) Outline for Economics 201B, Winter 2012

Total Page：16

File Type：pdf, Size：1020Kb

(Tentative) Outline for Economics 201B, Winter 2012 1) What is Game? (Ch.2, OR) a) Examples b) Strategic Game and Extensive Game 2) Strategic Game a) Dominant Action and Dominant Strategy Equilibrium (Ch 2.3, Ch 10.3, OR) i) 2nd price auction ii) Median Voter Theorem (Location Game) iii) VCG Mechanism b) Nash Equilibrium (Ch. 2, OR) i) Nash Equilibrium ii) Applications (1st Price Auction, Cournot Duopoly, Bertrand Duopoly, Public Good Game, Rent Seeking Game, AdAuction) iii) Existence of Nash Equilibrium iv) Zero-Sum Game c) Mixed Strategy Nash Equilibrium (Ch. 3.1-3.2, OR) i) Mixed Strategy Nash Equilibrium ii) Interpretation and Discussion of Some Empirical Facts d) Rationalizability and Iterated Elimination of Dominated Actions (Ch. 4, OR) i) Rationalizability ii) Iterated Elimination of Dominated Actions e) Refinements and Other Equilibrium Notions i) Trembling-Hand Perfect Equilibrium (Ch. 12.5, OR) ii) Correlated Equilibrium (Ch. 3.3,OR) iii) Evolutionary Stable Equilibrium (Ch. 3.4, OR) iv) Quantal Response Equilibrium f) Supermodular Games i) Increasing Differences and Supermodularity ii) Supermodular Games and Nash Equilibrium g) Bayesian Games (Ch 2.6, OR) i) Bayesian Games ii) Bayesian Nash Equilibrium iii) Applications (1) Second Price Auction (2) First Price Auction (3) Cournot Competition with Private Cost (4) Currency Attack h) Common Knowledge (Ch 5,OR) i) E-mail game ii) State-Space Model of Knowledge iii) Common Knowledge iv) Agree to Disagree and No Trade Result 3) Extensive Games with Perfect Information a) Extensive Games with Perfect Information (Ch 6, OR) b) Backward Induction and Subgame Perfect Equilibrium (Ch 6. OR) c) Applications i) Stackelberg Competition ii) Chain-Store Paradox iii) Rank Order Tournament d) Infinite Horizon Game e) Bargaining Games (Ch. 7, OR) i) Nash Solution ii) Alternative Offer Bargaining f) Repeated Games (Ch. 8, OR) i) Application: Collusion ii) Folk Theorem 4) Extensive Games with Imperfect Information a) Extensive Games with Imperfect Information b) Mixed and Behavioral Strategies c) Sequential Equilibrium d) Perfect Bayesian Equilibrium .

Copy Link

Recommended publications

PRICING and MODULARITY DECISIONS UNDER COMPETITION Feng Tao Hao Shao and Kinkeung Lai (Communicated by Stefan Wolfgang Pickl) 1
JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2018152 MANAGEMENT OPTIMIZATION Volume 16, Number 1, January 2020 pp. 289{307 PRICING AND MODULARITY DECISIONS UNDER COMPETITION Feng Taoa aDepartment of Management Science and Engineering East China University of Science and Technology, Shanghai, 200237, China Hao Shaobc∗ and KinKeung Laide bShanghai University of International Business and Economics Gubei Road, 200336, Shanghai, China cShanghai Wage Intelligent Technology Co., Ltd dCollege of Economics, Shenzhen University, Shenzhen, China eInternational Business School, Shaanxi Normal University, Xian, China (Communicated by Stefan Wolfgang Pickl) Abstract. This paper considers price and modularity of competition between two firms with deterministic demand, in which demand is dependent on both the prices and the modularity levels determined by two firms. Bertrand com- petition and Stackelberg competition are formulated to derive the equilibrium solutions analytically. Because of the complexity, an intensive numerical study is conducted to investigate the impact of the sensitive parameters on equilib- rium prices and modularity levels, as well as optimal profits of the two firms. An important and interesting finding is that optimal profits of the two firms under both types of competition are decreasing with the modularity cost when the price and modularity sensitivities are low, where both firms are worse-off due to decrease of the modularity levels; but they are increasing when the price and modularity sensitivities are high, where both firms are better-off at the ex- pense of modular design. Our research reveals that Stackelberg game improves the modularity levels in most of the cases, though both firms perform better in Bertrand competition in these cases when jointly deciding the prices and modularity levels in the two firms.
[Show full text]
Loss of Commitment? an Evolutionary Analysis of BagwellS Example1
Loss of Commitment? An Evolutionary Analysis of Bagwells Example1 Jörg Oechssler2 Karl H. Schlag3 Department of Economics Economic Theory III Humboldt University, Berlin University of Bonn April, 1997 1 We wish to thank Wolfgang Leininger for starting this project by asking us about the relevance of noise for evolutionary predictions, and Wieland Müller and Larry Samuelson for contributing valuable comments. Financial support by the Deutsche Forschungsgemeinschaft through SFBs 303 and 373 is gratefully acknowledged. 2 Institut für Wirtschaftstheorie, Spandauer Str. 1, 10178 Berlin, Germany, FAX: +49302093-5619, Email: [email protected] 3 Adenauerallee 24-26, 53113 Bonn, Germany, Email: [email protected] bonn.de Abstract In a recent paper Bagwell (1995) pointed out that only the Cournot outcome, but not the Stackelberg outcome, can be supported by a pure Nash equilib- rium when actions of the Stackelberg leader are observed with the slightest error. The Stackelberg outcome, however, remains close to the outcome of a mixed equilibrium. We compare the predictions in various classes of evolutionary and learning processes in this game. Only the continuous best response dynamic uniquely selects the Stackelberg outcome under noise. All other dynamics analyzed allow for the Cournot equilibrium to be selected. In typical cases Cournot is the unique long run outcome even for vanishing noise in the signal. JEL classi cation numbers: C72, C73. Key words: imperfectly observable commitment, evolution, imitation, learn- ing, equilibrium selection. 1 Introduction In a recent paper Bagwell (1995) pointed out that a rst mover advantage in games depends crucially on the fact that the action taken by the rst mover is perfectly observable.
[Show full text]
Endogenous Maverick Behavior: a Model
ENDOGENOUS MAVERICK BEHAVIOR: A MODEL John Kwokaa Birzhan Batkeyevb David Hummela December 2020 a Professor of Economics and PhD Candidate, respectively, Northeastern University, Boston b Professor, International School of Economics, Kazakh-British Technical University, Almaty ABSTRACT Key questions about the concept of a maverick firm have long remained unanswered. These include what causes a firm to behave like a maverick and whether such behavior is an inherent characteristic of the firm or a strategy choice, and if the latter, what determines that choice. The latter possibility has important policy implications. This paper offers a model in which a small low-cost entrant into a market initially finds it optimal to engage in aggressive “maverick” behavior but as it grows or its cost advantage erodes, it switches to more cooperative behavior with its larger rival. This model highlights the observable determinants of endogenous maverick behavior, notably, the maverick’s capacity. We offer some observations on the maverick behavior of actual firms and implications of this model for competition policy. I. Introduction The concept of a maverick firm plays an important but unusual role in economic research and antitrust policy. It is important because it captures the commonsense notion that there are firms whose aggressive behavior disrupts otherwise greater cooperation in a market. The economics and business literature as well as the popular press, for example, have often referred to companies such as Southwest Airlines and T-Mobile as maverick firms, citing well- documented evidence of their disproportionate impact on pricing and promotion in their markets. Consistent with that, Merger Guidelines in the U.S.
[Show full text]
Investment Under Uncertainty, Competition and Regulation Adrien Nguyen Huu
Investment under uncertainty, competition and regulation Adrien Nguyen Huu To cite this version: Adrien Nguyen Huu. Investment under uncertainty, competition and regulation. 2013. hal- 00831263v2 HAL Id: hal-00831263 https://hal.archives-ouvertes.fr/hal-00831263v2 Preprint submitted on 6 Sep 2013 (v2), last revised 3 Feb 2014 (v4) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Investment under uncertainty, competition and regulation Adrien Nguyen Huu1 McMaster University, Hamilton, Canada Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Canada Abstract We investigate a randomization procedure undertaken in real option games which can serve as a raw model of regulation in a duopoly model of preemp- tive investment. We recall the rigorous framework of Grasselli and al. [7] and extend it to a random regulator. This model generalizes and unifies the different competitive frameworks proposed in the literature, and creates a new one similar to a Stackelberg leadership. We fully characterize strategic interactions in the several situations following from the parametrization of the regulator. Finally, we study the effect of the coordination game and un- certainty of outcome when agents are risk-averse, providing new intuitions for the standard case.
[Show full text]
Convergence Analysis and Implementation Details for Markov Chains Games
Int. J. Appl. Math. Comput. Sci., 2015, Vol. 25, No. 2, 337–351 DOI: 10.1515/amcs-2015-0026 COMPUTING THE STACKELBERG/NASH EQUILIBRIA USING THE EXTRAPROXIMAL METHOD: CONVERGENCE ANALYSIS AND IMPLEMENTATION DETAILS FOR MARKOV CHAINS GAMES a b a,∗ KRISTAL K. TREJO ,JULIO B. CLEMPNER ,ALEXANDER S. POZNYAK aDepartment of Automatic Control, Center for Research and Advanced Studies Av. IPN 2508, Col. San Pedro Zacatenco, 07360 Mexico City, Mexico e-mail: {apoznyak,ktrejo}@ctrl.cinvestav.mx bCenter for Economics, Management and Social Research, National Polytechnic Institute Lauro Aguirre 120, col. Agricultura, Del. Miguel Hidalgo, Mexico City, 11360, Mexico e-mail: [email protected] In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear pro- gramming problems implementing the Lagrange principle. In addition, Tikhonov’s regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the proximal format. We present a two-step iterated procedure for solving the extraproximal method: (a) the first step (the extra-proximal step) consists of a “prediction” which calculates the preliminary position approximation to the equilibrium point, and (b) the second step is designed to find a “basic adjustment” of the previous prediction. The procedure is called the “extraproximal method” because of the use of an extrapolation. Each equation in this system is an optimization problem for which the necessary and efficient condition for a minimum is solved using a quadratic programming method.
[Show full text]
Computation of Stackelberg Equilibria of Finite Sequential Games∗
Computation of Stackelberg Equilibria of Finite Sequential Games∗ Branislav Bosanskˇ yý Simina Branzeiˆ z Kristoffer Arnsfelt Hansenx Peter Bro Miltersen{ Troels Bjerre Sørensenk Abstract The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player 1 (the leader) first commits to a strategy that is publicly announced, then Player 2 (the follower) plays a best response to the leader’s choice. We study the problem of computing Stackelberg equilibria in finite sequential (i.e., extensive-form) games and provide new exact algorithms, approximate algorithms, and hardness results for finding equilibria for several classes of such two-player games. 1 Introduction The Stackelberg competition is a game theoretic model introduced by von Stackelberg [25] for studying market structures. The original formulation of a Stackelberg duopoly captures the scenario of two firms that compete by selling homogeneous products. One firm—the leader—first decides the quantity to sell and announces it publicly, while the second firm—the follower—decides its own production only after observing the announcement of the first firm. The leader firm must have commitment power (e.g., is the monopoly in an industry) and cannot undo its publicly announced strategy, while the follower firm (e.g., a new competitor) plays a best response to the leader’s chosen strategy. The Stackelberg competition has been an important model in economics ever since (see, e.g., [22, 15, 1, 24, 19, 11]), while the solution concept of a Stackelberg equilibrium has been studied in a rich body of literature in computer science, with a number of important real-world applications developed in the last decade [23].
[Show full text]
41 Professor Julio B. CLEMPNER, Phd E-Mail: [email protected]
Economic Computation and Economic Cybernetics Studies and Research, Issue 4/2016, Vol. 50 ________________________________________________________________________________ Professor Julio B. CLEMPNER, PhD E-mail: [email protected] Instituto Politécnico Nacional, Mexico Professor Alexander S. POZNYAK, PhD E-mail: [email protected] Center for Research and Advanced Studies ANALYZING AN OPTIMISTIC ATTITUDE FOR THE LEADER FIRM IN DUOPOLY MODELS: A STRONG STACKELBERG EQUILIBRIUM BASED ON A LYAPUNOV GAME THEORY APPROACH Abstract. This paper presents a novel game theory approach for representing the Stackelberg dynamic duopoly models. The problem is fitted into a class of ergodic controllable finite Markov chains game. It is consider the case where a strong Stackelberg equilibrium point is convenient for both firms. We first analyze the best-reply dynamics of the Stackelberg duopoly model such that each firm’s best-reply strategies set agree with the set of maximizers of the opponents’ strategies. Then, the classical Stackelberg duopoly game is transformed into a potential game in terms of the Lyapunov theory. As a result, a duopoly model has the benefit that the best-reply dynamics results in a natural implementation of the behavior of a Lyapunov-like function. In addition, the strong equilibrium point properties of Stackelberg and Lyapunov meet in potential games. We validate the proposed method theoretically by computing the complexity and by a numerical experiment related to the duopoly model. Keywords: Dynamic duopoly model, complexity, strong Stackelberg equilibrium, Lyapunov equilibrium, Stackelberg games, Lyapunov games, Markov decision process JEL Classification: C72, C73, D43, E37, C32 1. Introduction 1.1 Brief review Game theory is an increasingly important paradigm for reasoning about complex duopoly/oligopolies problems.
[Show full text]
Cournot Or Stackelberg Competition? a Survey on Experimental Evidence
Munich Personal RePEc Archive Cournot or Stackelberg competition? A survey on experimental evidence Hildenbrand, Andreas Department of Economics, Justus Liebig University Giessen 17 August 2010 Online at https://mpra.ub.uni-muenchen.de/24468/ MPRA Paper No. 24468, posted 18 Aug 2010 01:16 UTC Cournot or Stackelberg Competition? A Survey on Experimental Evidence Andreas Hildenbrand∗ August 17, 2010 ∗Department of Economics, Justus Liebig University Giessen, Licher Straße 66, 35394 Gießen, Germany. Telephone: +49 641 99-22203. Telefax: +49 641 99-22209. Electronic Mail: [email protected]. World Wide Web: wirtschaft.uni- giessen.de. Abstract In this survey, I look into experimental studies on duopolistic quantity competition with homogeneous products and duopolistic price competition with heterogeneous products. The focus is on the sequence of competition. That is, I summarize and analyze ex- perimental studies checking Cournot competition against Stackelberg competition. I ﬁnd that while Stackelberg equilibrium outcomes are seldom under quantity competi- tion, under price competition, the Stackelberg equilibrium prediction seems to be more appropriate. However, after discussing the experimental setups, I conclude that some methodological problems are present. Moreover, I make recommendations for further research. Keywords: Cournot competition, simultaneous competition, simultaneous play, Stackel- berg competition, sequential competition, sequential play, duopoly, homogeneous prod- ucts, heterogeneous products, experiemtal economics. Journal of Economic Literature Classiﬁcation Codes: C720, C910, D430, L130. 1 Introduction Although the Cournot model and the Stackelberg model of duopolistic quantity compe- tition with homogeneous products and duopolistic price competition with heterogeneous products are part and parcel of every textbook on industrial organization,1 only few ex- periments testing these models have been conducted yet.
[Show full text]
Markets, Competition, and Strategy LEC0101
ECO380H1S: Markets, Competition, and Strategy LEC0101 (Tue 10:00-13:00, MP202) LEC0201 (Tue 14:00-17:00, LM159) Instructor: Yao Luo Office: Max Gluskin House, 322 Email: [email protected] Office hours: Tue 13:00-14:00, or by appointment Head teaching assistant: LEC0101: Cheok in Fok, Email: [email protected] LEC0201: Alvaro Jose Pinzon Giraldo, Email: [email protected] TA office hours: TBA Objectives This course in applied microeconomics is concerned with the functioning of markets and the strategic behavior of firms. The focus is on strategic relationships between organizations, including competitive and cooperative relationships among firms. The first unit will cover basic models of imperfect competition and the impact of market structure. The second unit will focus on pricing strategies. The final unit will examine elements of firm competition that are not covered in the basic models. Prerequisite: ECO200Y1/ECO204Y1/ECO206Y1; ECO220Y1/ECO227Y1/(STA220H1, STA255H1)/(STA237H1, STA238H1)/(STA257H1, STA261H1) The Department of Economics checks whether students have the course prerequisites, and students are removed if they do not have them. It is the students’ responsibility to read the calendar. The instructor cannot waive prerequisites. Grading There will be three problem sets, one term test, and a final exam. Each problem set counts for 5%. The term test counts for 35%. The final exam counts for 50%. We use Crowdmark. Collaboration on the problem sets is encouraged. Collaborating students can choose to submit a single group answer (maximum group size: 3 students). You are encouraged to type your homework, but hand-written work will be accepted if it is clearly presented.
[Show full text]
Loss of Commitment? an Evolutionary Analysis of Bagwell's Example1
Loss of Commitment? An Evolutionary Analysis of Bagwells Example1 Jörg Oechssler Karl H. Schlag! Department of Economics Economic Theory III Humboldt University, Berlin University of Bonn April, 1997 We wish to thank Wolfgang Leininger for starting this project by asking us about the relevance of noise for evolutionary predictions, and Wieland Müller and Larry Samuelson for contributing valuable comments. Financial support by the Deutsche Forschungsgemeinschaft through SFBs 303 and 373 is gratefully acknowledged. Institut für Wirtschaftstheorie, Spandauer Str. 1, 10178 Berlin, Germany, FAX: +49302093-5619, Email: [email protected] ! Adenauerallee 24-26, 53113 Bonn, Germany, Email: [email protected] bonn.de Abstract In a recent paper Bagwell (1995) pointed out that only the Cournot outcome, but not the Stackelberg outcome, can be supported by a pure Nash equilib- rium when actions of the Stackelberg leader are observed with the slightest error. The Stackelberg outcome, however, remains close to the outcome of a mixed equilibrium. We compare the predictions in various classes of evolutionary and learning processes in this game. Only the continuous best response dynamic uniquely selects the Stackelberg outcome under noise. All other dynamics analyzed allow for the Cournot equilibrium to be selected. In typical cases Cournot is the unique long run outcome even for vanishing noise in the signal. JEL classi cation numbers: C72, C73. Key words: imperfectly observable commitment, evolution, imitation, learn- ing, equilibrium selection. 1 Introduction In a recent paper Bagwell (1995) pointed out that a rst mover advantage in games depends crucially on the fact that the action taken by the rst mover is perfectly observable.
[Show full text]
On the Efficiency of Local Electricity Markets Under Decentralized And
On the Efficiency of Local Electricity Markets Under Decentralized and Centralized Designs: A Multi-leader Stackelberg Game Analysis Hélène Le Cadre To cite this version: Hélène Le Cadre. On the Efficiency of Local Electricity Markets Under Decentralized and Centralized Designs: A Multi-leader Stackelberg Game Analysis . 2018. hal-01619885v2 HAL Id: hal-01619885 https://hal.archives-ouvertes.fr/hal-01619885v2 Preprint submitted on 4 Jan 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. On the Efficiency of Local Electricity Markets Under Decentralized and Centralized Designs: A Multi-leader Stackelberg Game Analysis∗ HélèneLe Cadrey Abstract In this paper, we analytically compare centralized and decentralized market designs involving a national and local market operators, strategic generators having market power and bidding sequentially in local mar- kets, to determine which design is more efficient for the procurement of energy. In the centralized design, used as benchmark, the national market operator optimizes the exchanges between local markets and the genera- tors' block bids. In the decentralized design, generators act as Stackelberg leaders, anticipating the local market prices and the flows on the trans- mission lines. Clearing of the local markets can be either simultaneous or sequential.
[Show full text]
Signaling in Bayesian Stackelberg Games
Signaling in Bayesian Stackelberg Games Haifeng Xu1, Rupert Freeman2, Vincent Conitzer2, Shaddin Dughmi1, Milind Tambe1 1University of Southern California, Los Angeles, CA 90007, USA {haifengx,shaddin,tambe}@usc.edu 2Duke University, Durham, NC 27708, USA {rupert,conitzer}@cs.duke.edu ABSTRACT that are correlated with the action she has chosen. This ability can Algorithms for solving Stackelberg games are used in an ever- of course never hurt the leader: she always has the choice of send- growing variety of real-world domains. Previous work has ex- ing an uninformative signal. In a two-player normal-form game, it tended this framework to allow the leader to commit not only to turns out that no beneﬁt can be had from sending an informative a distribution over actions, but also to a scheme for stochastically signal. This is because the expected leader utility conditioned on signaling information about these actions to the follower. This can each signal, which corresponds to a posterior belief of the leader’s result in higher utility for the leader. In this paper, we extend this action, is weakly dominated by the expected leader utility of com- methodology to Bayesian games, in which either the leader or the mitting to the optimal mixed strategy [4]. But this is no longer true follower has payoff-relevant private information or both. This leads in games with three or more players. Moreover, intriguingly, the to novel variants of the model, for example by imposing an incen- enriched problem with signaling can still be solved in polynomial tive compatibility constraint for each type to listen to the signal time in these games [4].
[Show full text]