## ESRC Grant ProjectTheoretical Foundations and Design of Persuasion Mechanisms‣ Andy Zapechelnyuk (University of St Andrews)Research Team: ‣ Hisayuki Yoshimoto (University of Glasgow) ‣ Anton Kolotilin (UNSW Australia) ## Working Papers‣ Compromise, don't optimize: Generalizing perfect Bayesian equilibrium to games with ambiguity (with Karl Schlag) [Video][previously titled "Compromise, don't optimize: A prior-free alternative to perfect Bayesian equilibrium"]We introduce a solution concept for extensive-form games of incomplete information in which players need not assign likelihoods to what they do not know. This is embedded in a model in which players can hold a set of beliefs. Players make choices by looking for compromises that yield a good performance under each of their beliefs. Our solution concept is called perfect compromise equilibrium. It generalizes perfect Bayesian equilibrium. We show how it deals with uncertainty without using probabilities in Cournot and Bertrand markets, Spence's job market signaling, as well as in bilateral trade with common value. A sender designs how to disclose information about the state of the world to persuade a receiver to accept a proposal. The sender is ignorant about both the receiver's type and his risk attitude. The sender applies the principle of maximum entropy to resolve her ignorance. We show that the maximum-entropy utility is risk neutral if nothing is known about the agent's utility, and it is CARA if the average utility is known. Furthermore, the optimal signal is either fully revealing or completely uninformative if nothing is known about the distribution of the agent's type, or if its mean is known; the optimal signal is a censorship if the mean and variance are known. To derive our results, we propose a novel representation of preference over lotteries. ‣ Bargaining and trade without using priors (with Karl Schlag) We study bargaining under incomplete information, with applications to trade and to provision of public good. In our setting, agents not only agree on how they share their output, but also on how much output they produce. We are interested in bargaining rules that do not depend on priors. We find a unique rule that satisfies a set of axioms. Under this rule, the higher the surplus, the more output is produced. Moreover, the produced output is shared as in the Nash bargaining solution. We present a dynamic protocol that implements this rule for any priors. Heterogeneous discount factors and degrees of risk aversion can be included. We study the empirical relationship between hygiene conditions in restaurants and their food quality rated by professional reviewers. Using evidence from the UK, we show that this relationship is negative and statistically significant. So, a higher food quality rating is generally associated with a less sanitary kitchen. We find that 3% of Michelin starred restaurants in our dataset have poor hygiene conditions, while the same is true for only 2% of non-Michelin starred restaurants. Our findings illuminate potential channels through which the anticorrelation between food quality and hygiene could be mitigated, which can be helpful for hygiene inspection design. A principal can restrict an agent's information (the persuasion problem) or restrict an agent's discretion (the delegation problem). We show that these problems are generally equivalent — solving one solves the other. We use tools from the persuasion literature to generalize and extend many results in the delegation literature, as well as to address novel delegation problems, such as monopoly regulation with a participation constraint. [previously titled “Optimal persuasion with an application to media censorship”]A sender designs a signal about the state of the world to persuade a receiver. Under standard assumptions, an optimal signal censors states on one side of a cutoff and reveals all other states. This result holds in continuous and discrete environments with general and monotone partitional signals. The sender optimally censors more information if she is more biased, if she is more certain about the receiver's preferences, and if the receiver is easier to persuade. We apply our results to the problem of media censorship by a government. We study sequential search without priors. Our interest lies in decision rules that are close to being optimal under each prior and after each history. We call these rules robust. The search literature employs optimal rules based on cutoff strategies that are not robust. We derive robust rules and show that their performance exceeds 1/2 of the optimum against binary i.i.d. environments and 1/4 of the optimum against all i.i.d. environments. This performance improves substantially with the outside option value, for instance, it exceeds 2/3 of the optimum if the outside option exceeds 1/6 of the highest possible alternative. ‣ Value of information when searching for a secretary (with Karl Schlag) The secretary problem is the canonical model of search under ambiguity, in which secretaries are being interviewed in a random order. We assume that the number of secretaries is unknown and that one cares for the value of the secretary. We measure the value of information as a multiplier that describes how much better off one could have been had one known the distribution of secretaries' values. It is evaluated in the worst case, for all distributions and at all rounds of search. Under perfect recall, knowledge of the applicant pool size and their distribution can improve one's payoff at most 4 times. Knowledge that the values are i.i.d. does not improve one's payoff. ‣ Competing e-commerce intermediaries (with Alexander Matros) We consider a model where two e-commerce platforms, such as internet auctions, compete for sellers who are heterogeneous in their time preferences. Contrary to the literature which argues that if two platforms coexist in equilibrium, then the “law of one price” must hold, we demonstrate that two platforms may set different prices and have positive equilibrium profits by exploiting heterogeneity of sellers' time preferences. In such an equilibrium less patient sellers choose the more popular, but more expensive, platform, while more patient sellers prefer the less popular and cheaper one. ## PublicationsAmerican Economic Review: Insights (accepted) [doi]
Economic Theory Bulletin (accepted) [doi]
Econometrica 85 (2017), 1949-1964 [doi]
[earlier versions titled "Optimality of non-competitive allocation rules" and "Value of competition in allocation and search problems"]American Economic Review 107 (2017), 2666-2694 [doi]
[an earlier version titled “Decision making in environments without priors”]Journal of Economic Theory 169 (2017), 145-169 [doi] ‣ Eliciting information from a committee
Journal of Economic Theory 148 (2013), 2049-2067 [doi] ‣ Optimal arbitration (with Tymofiy Mylovanov) International Economic Review 54 (2013), 769-785 [doi] ‣ No-regret dynamics and fictitious play (with Yannick Viossat) Journal of Economic Theory 148 (2013), 825-842 [doi] ‣ Decision rules revealing commonly known events (with Tymofiy Mylovanov) Economics Letters 119 (2013), 8-10 [doi] ‣ On the impossibility of achieving no regrets in repeated games (with Karl Schlag), Journal of Economic Behavior and Organization 81 (2012), 153-158 [doi] ‣ Optimal mechanisms for an auction mediator (with Alexander Matros) International Journal of Industrial Organization 29 (2011), 426-431 [doi] ‣ Bargaining with a property rights owner (with Yair Tauman) Games and Economic Behavior 70 (2010), 132-145 [doi] ‣ On (non-) monotonicity of cooperative solutions (with Yair Tauman) International Journal of Game Theory 39 (2010), 171-175 [doi] ‣ Better-reply dynamics with bounded recall Mathematics of Operations Research 33 (2008), 869-879 [doi] ‣ Optimal fees in internet auctions (with Alexander Matros) Review of Economic Design 12 (2008), 155-163 [doi] ‣ Strategic complements and substitutes, and potential games (with Pradeep Dubey and Ori Haimanko) Games and Economic Behavior 54 (2006), 77-94 [doi] |