ESRC Grant Project

Theoretical Foundations and Design of Persuasion Mechanisms 

Research Team: 
    Andy Zapechelnyuk (University of St Andrews)
    Hisayuki Yoshimoto (University of Glasgow)
    Anton Kolotilin (UNSW Australia)

Working Papers

Compromise, don't optimize: A prior-free alternative to Bayesian Nash equilibrium (with Karl Schlag)

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.

 Optimal quality certification

Quality certification not only informs consumers, but also stimulates producers to supply better quality products. We study a problem of quality certification in a moral hazard setting. We show that, under standard assumptions, simple certification systems, such as quality assurance rule and pass-fail rule, are optimal. Our solution method involves interpreting the certification problem as a delegation problem.

 Persuasion meets delegation (with Anton Kolotilin)

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.

 Optimal media censorship (with Anton Kolotilin and Tymofiy Mylovanov)

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.

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 dynamically robust. The search literature employs optimal rules based on cutoff strategies that are not dynamically robust. We derive dynamically robust rules and show that their performance exceeds 1/2 of the optimum against binary environments and 1/4 of the optimum against all 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.

 Job search costs and incentives (with Ro'i Zultan)

We demonstrate that policies aimed at reducing frictional unemployment may lead to the opposite results. In a labor market with long-term wage contracts and moral hazard, any such policy reduces employees' opportunity costs of staying on a job. As employees are less worried about losing their job, a smaller share of employees is willing to exert effort, leading to a lower average productivity.

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

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] 

Economics Letters 132 (2015), 24-27 [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]