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Chapter 12.V) ARTICLE IN PRESS Levels of Reasoning in Keynesian Beauty Contests: A Generative Framework✶ Felix Mauersberger∗, Rosemarie Nagel†,1 ∗Department of Economics and Business, Universitat Pompeu Fabra, Barcelona GSE, Barcelona, Spain †Department of Economics and Business, Universitat Pompeu Fabra, Barcelona GSE, ICREA, Barcelona, Spain 1Corresponding author: e-mail address: [email protected] CONTENTS 1 Introduction ....................................................................................... 543 2 An Overview of Experimental Economics ..................................................... 547 2.1 Experimental Economics Areas with Archetypal Games and Markets ....... 547 2.1.1 Public Good Provision ............................................................ 549 2.1.2 Bargaining .......................................................................... 550 2.1.3 Coordination Games .............................................................. 551 2.1.4 Industrial Organization ........................................................... 552 2.1.5 Asset Markets ...................................................................... 553 2.1.6 Auctions ............................................................................. 554 2.2 New Questions and Areas Since the Late 90s .................................. 557 2.3 Boundedly Rational Models........................................................ 559 3 The Keynesian Beauty Contest: A Generative Framework for Archetypal Games in Economics ......................................................................................... 562 3.1 The Beauty Contest as a Canonical Formulation ............................... 563 3.2 Continuous Strategy Space ........................................................ 567 3.2.1 Games of Strategic Substitutes ................................................. 568 3.2.2 Games of Strategic Complements.............................................. 569 ✶ We thank Larbi Alaoui, Jess Benhabib, Antoni Bosch, Pablo Brañas-Garza, Christoph Bühren, Antonio Cabrales, Gabriele Camera, John Duffy, Björn Frank, Willemien Kets, Anita Kopanyi-Peuker, Kiminori Matsuyama, Shabnam Mousavi, Mechthild Nagel, Antonio Penta, Michael Reiter, Ricardo Serrano-Padial, Edouard Schaal, Shyam Sunder, Michael Woodford, three anonymous referees, and the editor Cars Hommes for valuable comments. For financial support we both thank the Barcelona GSE; Felix Mauers- berger acknowledges the FPI grant from the Spanish Ministry of Science and Innovation and Rosemarie Nagel the grant MINECO-ECO2014-56154-R from the Spanish Ministry of Education. Handbook of Computational Economics, ISSN 1574-0021, https://doi.org/10.1016/bs.hescom.2018.05.002 Copyright © 2018 Elsevier B.V. All rights reserved. 541 ARTICLE IN PRESS 542 Levels of Reasoning in Keynesian Beauty Contests 3.2.3 Public and Private Information ................................................. 572 3.2.4 Other Games ....................................................................... 572 3.3 Discrete Strategy Space and Multiplicity ........................................ 573 3.3.1 Strategic Complements........................................................... 573 3.3.2 Strategic Substitutes .............................................................. 576 3.3.3 Matching ............................................................................ 577 3.3.4 Strategic Heterogeneity........................................................... 578 3.4 Other Dimensions ................................................................... 579 3.4.1 Game Structure .................................................................... 579 3.4.2 Experimental Implementation................................................... 581 4 Behavioral Regularities in BC-Experiments and Level-k ................................... 582 4.1 The Basic BC Experiment .......................................................... 583 4.1.1 First Period Choices............................................................... 583 4.1.2 The Level-k Model and Related Models ...................................... 583 4.1.3 Behavior over Time in the Basic BC Game ................................... 589 4.1.4 Heterogeneity of Subject Pools in Lab- and Field-BC Games ............ 590 4.1.5 Two Person Games................................................................ 592 4.1.6 Mixing Experienced with Inexperienced Subjects........................... 594 4.1.7 Strategic Substitutes vs. Strategic Complements............................ 595 4.2 De-Framing the Rules to (De-)Anchor Beliefs ................................... 595 4.2.1 Interior Equilibrium................................................................ 597 4.2.2 Public and Private Information – Anchoring Beliefs ........................ 598 4.2.3 Stochastic Common Shocks..................................................... 601 4.3 Multiple Equilibria (BC Game with b = 1) ....................................... 603 4.3.1 Minimum Effort Game ............................................................ 603 4.3.2 Public and Private Signals ....................................................... 604 4.3.3 Global Games ...................................................................... 605 4.3.4 Ultimatum Games (Played in Extensive Form) .............................. 607 4.4 Auction in the Laboratory and the Field ......................................... 609 4.5 Other Games with Discrete Strategy Spaces .................................... 610 4.5.1 A Ring Game – Spatial Reasoning ............................................. 610 4.5.2 Schelling Matching................................................................ 610 4.5.3 Mixed Equilibrium Games in Lab and Field .................................. 611 5 Elicitation Methods .............................................................................. 612 5.1 Strategy (Vector) Method ........................................................... 613 5.2 Response Time (RT)................................................................. 615 5.3 Mouselab, Eye-Tracking ............................................................ 616 5.4 Continuous Time Decision-Making................................................ 616 5.5 Written Comments, Chats, and Other Communication Tools, Team Decisions ............................................................................. 616 5.6 Asking for Guesses .................................................................. 617 5.7 Personal Characteristics and Training ........................................... 617 5.8 Neuroeconomics..................................................................... 618 6 Discussion ......................................................................................... 620 References............................................................................................ 623 ARTICLE IN PRESS 1 Introduction 543 “Because of the success of science, there is a kind of a pseudo-science. Social science is an example of a science which is not a science. They follow the forms. You gather data, you do so and so and so forth, but they don’t get any laws, they haven’t found out anything. They haven’t got anywhere – yet. Maybe someday they will, but it’s not very well developed.” (Richard Feynman, radio interview, 1981) “[This] is the principal problem of classical economics: how is the absolutely selfish ‘homo economicus’ going to act under given external circumstances?” (John von Neumann, 1932) 1 INTRODUCTION Aiming to improve the design of cockpits, US Air Force researchers in 1950 obtained body measures from 4063 pilots, containing 140 dimensions from size to thumb length. For every dimension, the “approximate average” was defined as 0.3 times the standard deviation above or below the sample mean. For the ten most vital di- mensions, between 990 (waist circumference) and 1713 (neck circumference) pilots belonged to the average defined this way. However, not a single pilot was “approx- imately average” with respect to all ten dimensions. Not only did the average pilot simply not exist, Daniels (1952) concluded that “the ‘average man’ is a misleading and illusory concept.” As prominently argued by Kirman (1992), the “reduction of the behavior of a group of heterogeneous agents even if they are all themselves utility maximizers, is not simply an analytical convenience as often explained, but is both unjustified and leads to conclusions which are usually misleading and often wrong.” This chapter shows that laboratory experiments can be used as an effective tool to uncover the usually rich heterogeneity of behavioral responses. For our context, we define heterogeneity as the existence of several distinct types which have to be described using various specifications with different parameters or even different functional forms. Homogeneity, in contrast, means that all agents can be defined by the same specification. It is important to distinguish between heterogeneity and ran- domness: heterogeneity points to systematic differences in a specification, so that at least one structural parameter differs across the population. A situation where the population can be described by the same specification and differences only come from random draws from a well-defined distribution may more accurately be de- scribed by randomness. We distinguish two dimensions of heterogeneity: firstly related to situations; and secondly related to behavior across games and within a game. While there is a myr- iad of different
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