Bayesian Nash equilibrium is the classic solution concept for games with incomplete information. Yet choices may be very suboptimal when the players' priors do not reflect true likelihoods, when players look in hindsight at events that occurred, or when players must justify their choices in front of others with different priors. We propose an alternative solution concept, best compromise equilibrium, that involves making choices that are approximately optimal for all priors. It is simple to calculate and, unlike dominant strategy and ex post Nash equilibrium, it always exists. We provide examples, including bilateral trade, public good provision, bargaining with incomplete information, and Cournot games with uncertain costs. 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. We study the problem of media control by the government. For a large class of environments, the optimal media control policy is simple. It takes the form of an upper censorship, where the government censors all the media outlets whose editorial policies are more adversarial than a selected threshold. The model is an application of optimal Bayesian persuasion with a privately informed receiver. A searcher explores alternatives sequentially and is unaware of the distribution of values of unexplored alternatives. We are interested in decision rules that perform close to Bayesian optimal ones under any prior, at each point of time, and after each history of observations. We call such rules dynamically robust. Standard rules used in the search literature are based on cutoff strategies and are not dynamically robust. We uncover general principles that make this rich setting tractable. We derive a dynamically robust decision rule, which involves randomized behavior and can be approximated by a rule with a linear stopping probability. ‣ 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. ‣ Job search costs and incentives (with Ro'i Zultan) In labor markets with long-term wage contracts and moral hazard, policies aimed at reducing frictional unemployment such as unemployment benefits with eligibility constraints may lead to opposite results. A reduction in job search costs reduces the expected cost of losing one's job, and consequently leads to fewer employees willing to exert effort. With overall lower productivity, more individuals and firms opt to stay out of the labor market, resulting in lower employment and decreased welfare. Eventually, a reduction of jobs search costs below a certain level results in collapse of the labor market. ‣ 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. ## Publications‣ Persuasion of a privately informed receiver (with Anton Kolotilin, Tymofiy Mylovanov, and Ming Li)
Econometrica 85 (2017), 1949-1964 [doi]
‣ Optimal allocation with ex-post verification and limited penalties (with Tymofiy Mylovanov) + Online Appendix
[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] |