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Persuasion by Strategic Obfuscation

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Persuasion by Strategic Obfuscation FUNDAÇÃO GETULIO VARGAS ESCOLA DE ECONOMIA DE SÃO PAULO LUIS HENRIQUE RIBEIRO LINHARES PERSUASION BY STRATEGIC OBFUSCATION São Paulo 2021 LUIS HENRIQUE RIBEIRO LINHARES PERSUASION BY STRATEGIC OBFUSCATION Dissertação apresentada à Escola de Econo- mia de São Paulo como pré-requisito à ob- tenção de título de mestre em Economia de Empresas. Orientador: Daniel Monte. São Paulo 2021 Linhares, Luis Henrique Ribeiro. Persuasion by strategic obfuscation / Luis Henrique Ribeiro Linhares. - 2021. 50f. Orientador: Daniel Monte. Dissertação (mestrado CMEE) – Fundação Getulio Vargas, Escola de Economia de São Paulo. 1. Persuasão (Retórica). 2. Teoria dos jogos. 3. Teoria bayesiana de decisão estatística. I. Monte, Daniel. II. Dissertação (mestrado CMEE) – Escola de Economia de São Paulo. III. Fundação Getulio Vargas. IV. Título. CDU 330.115 Ficha Catalográfica elaborada por: Raphael Figueiredo Xavier CRB SP-009987/O Biblioteca Karl A. Boedecker da Fundação Getulio Vargas - SP LUIS HENRIQUE RIBEIRO LINHARES PERSUASION BY STRATEGIC OBFUSCATION Dissertação apresentada à Escola de Econo- mia de São Paulo como pré-requisito à ob- tenção de título de mestre em Economia de Empresas. Data de aprovação: 02/06/2021 Banca examinadora: Prof. Dr. Daniel Monte FGV-EESP (Orientador) Prof. Dr. Henrique Roscoe de Oliveira FGV-EESP Prof. Dr. Lucas Jóver Maestri FGV-EPGE Agradecimentos Agradeço à minha família pelo apoio incondicional que me deram quando decidi mudar de direção na carreira e me jogar na vida do mestrado. Ao meus pais por sempre acreditarem em mim, à minha irmã por me ajudar a não desistir e ao Lucky por estar presente nas horas de estresse. Ao meu orientador, Prof. Daniel Monte, por ter tornado este trabalho possível e por sempre estar presente para me ajudar com as dúvidas e desafios que encontramos. Aos professores Henrique de Oliveira e Lucas Maestri por terem aceitado fazer parte da minha banca e darem conselhos valiosos. Aos professores Braz Camargo e Victor Filipe por terem me ajudado no processo de application. Ao pessoal da salinha. Ficamos juntos por menos tempo que deveríamos, mas vocês me mostraram que fazer o mestrado foi uma das melhores decisões que fiz na vida. Não é todo dia que se encontra um grupo que gosta de discutir modelos econômicos na frente de uma lousa. O presente trabalho foi realizado com apoio da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Código de Financiamento 001. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. Quaisquer falhas e omissões são de minha inteira responsabilidade. Resumo Nós estudamos um problema de persuasão em que um principal escolhe o quão custoso será para o agente obter e processar informações novas. Ofuscação ou transparência serão endógenas ao problema. Especificamente, nós combinamos um framework de inatenção racional com jogos de comunicação e problemas de persuasão bayesiana e mostramos que, sob algumas coindições, o custo ótimo induzido de processar informação é não-monotônico, isto é, o ótimo é confundir "só um pouco". Portanto, nosso modelo ajuda a explicar porque em alguns casos firmas escrevem contratos com tantas cláusulas, enquanto em outros contratos são simples e transparentes. O modelo também ajuda a explicar porque algumas empresas oferecem produtos com muitas características ou características diferentes das de seus concorrentes de modo a dificultar a escolha do produto. Obfuscação tem implicações para o bem-estar que legisladores devem levar em consideração. Palavras-chave: jogos de comunicação, design de informação, persuasão Bayesiana, inatenção racional, obfuscação estratégica. Abstract We study a persuasion problem in which the principal chooses how costly it will be for the agent to obtain and process new information. Obfuscation or transparency will be endogenous to the decision problem at hand. Specifically, we combine a rational inattention framework with communication games and Bayesian persuasion problems and we show that under some conditions the optimal induced cost of processing information is non-monotonic, that is, when it is optimal to confuse “just a little”. Thus, our model helps explain why in some environments firms write terms and conditions with so many clauses, whereas in other contexts, contracts might be simple and transparent. It also helps explain why some companies offer varying features that make choosing a product more difficult than it could be. Obfuscation has clear welfare implications that policy makers should bear in mind. Keywords: communication games, information design, bayesian persuasion, rational inattention. List of Figures Figure 1 – Example of Solution to the Receiver’s Problem.............. 21 Figure 2 – Expected Indirect Utility for the Informer ................ 22 Figure 3 – Expected Indirect Utility for the Receiver ................ 23 Figure 4 – Dynamics of an increase in k ........................ 24 Figure 5 – Expected payoffs for k > kˆ ......................... 24 Figure 6 – What happens when µ0 = µindf ...................... 26 Figure 7 – Payoffs as a function of beliefs for the Customer............. 29 Figure 8 – Payoffs as a function of k for the Customer................ 29 Figure 9 – The function the Receiver Maximizes................... 30 Figure 10 – The maximizing function and its concavication for the Customer for k = 1 and µ0 = 0.75............................. 31 Figure 11 – Customer’s maximizing function and solution. Left: Case for k = 0.5. Right: Case for k = 2. ........................... 31 Figure 12 – Producer’s indirect utility and the chosen split for k = 1. 32 Figure 13 – Producer’s indirect utility from k...................... 32 Figure 14 – Producer’s indirect utility from k for the new case in which c = 2. 33 Figure 15 – Payoffs as a function of beliefs for COM ................. 35 Figure 16 – Payoffs as a function of beliefs for MON ................. 36 Figure 17 – COM maximization function for k = 0.2 . 37 Figure 18 – MON expected payoffs from the split of posteriors induced by k = 0.2. 37 ˜ Figure 19 – Plot of V0.7.................................. 38 Figure 20 – Indirect utility for Informer with µ0 = 0.25 . 40 Figure 21 – Illustration of auxiliary variables...................... 47 Figure 22 – Example of a concave function....................... 49 List of Tables Table 1 – Payoffs table for the Better or Worse Product game............ 28 Table 2 – Payoffs table with numerical values. .................... 28 Table 3 – Payoffs table with new value of c. ..................... 32 Table 4 – Payoffs table for the Monopolist game.................... 35 Table 5 – Payoffs table for the Monopolist game with values for parameters. 35 Contents 1 INTRODUCTION............................ 10 2 RELATED LITERATURE........................ 14 3 THE MODEL .............................. 17 3.1 The Receiver’s Problem .......................... 19 3.2 The Informer’s Problem .......................... 22 4 PRACTICAL EXAMPLES........................ 27 4.1 Better or Worse Product ......................... 27 4.2 Monopoly .................................. 34 5 CLASSIFYING THE INFORMER’S PROBLEM ........... 39 6 CONCLUSIONS............................. 42 Bibliography ............................... 43 APPENDIX A – AUXILIARY PROOFS................ 47 10 1 Introduction During World War II, the 23rd Headquarters Special Troops was an American military unit with a different purpose than most: deception. A well kept secret until the 90’s, this "Ghost Unit" sowed confusion amongst the Axis troops through the use of inflatable tanks, fake radio messages and all sorts of clever tricks. Such diversionary tactics have been a staple of warfare for a long time, - even before Greeks pretended to go home and left a horse as a present for the Trojans - but this sort of behaviour is also more pervasive in our daily lives than we might think: opposing lawyers, when required to disclose evidence, may send not solely the pertinent documents, but many more, to make it harder to discern what is relevant and what is not; printers can be sold at a loss to attract consumers, while disguising ink sales that come with huge margins; and let he who has never blindingly agreed to those long terms and conditions cast the first stone. More recently, new research has shown that obfuscating (“making things less clear”) behaviour arises even in more traditional economic contexts. Contrary to what would be expected in a competitive market, papers document evidence of heterogeneous prices for similar products as firms engage in obfuscation to artificially create a difference in the eyes of the consumer. The mechanisms are numerous: by offering different product sizes and flavors (Richards et al., 2019), by making it more difficult to compare prices online (Ellison and Ellinson, 2009), or by hiding the price of add-ons (Ellison, 2005) are just a few examples. Other studies lay out how obfuscation may be sustained: Gabaix and Laibson(2006) illustrates cases in which firms don’t have an incentive to educate consumers about their competitors, and Jin et al.(2018) comments on how even companies with good products and services may try to confuse consumers as this induces systematic mistakes that they may exploit. No matter the method, agents seem to prey on customers’ inattention as if they were in opposing sides on a battlefield. On the other hand, there are situations in which agents are in agreement. A benign doctor wants their patient to choose the best possible
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