The Importance of Commitment Power in Games with Imperfect Evidence

Abstract

The literature initiated by Green and Laffont (1986) studies principal-agent models with hard evidence. Evidence is modeled by assuming that the message set of the agent is type dependent. In this setup, Glazer and Rubinstein (2004, 2006) and Sher (2011) show that when the agent’s utility function is type independent there is no advantage for the principal in having commitment power. This paper shows that this way of modeling evidence implicitly assumes it to be perfectly accurate and that the result that commitment power has no value is not robust to making the evidence imperfect. (JEL C70, D82)

Optimal assignment mechanisms with imperfect verification

“…Earlier work assumed that agents were able to provide “hard” evidence (Dye (1985), Green and Laffont (1986), Lipman and Seppi (1995), Glazer and Rubinstein (2004, 2006), Bull and Watson (2007), Deneckere and Severinov (2008), Sher (2011), Hart, Kremer, and Perry (2017), Ben‐Porath, Dekel, and Lipman (2019)). Recently, models of probabilistic verification have emerged, where the evidence provided by the agents may not be perfectly accurate (Caragiannis et al (2012), Ball and Kattwinkel (2019), Silva (2020)). Our model is similar to Ball and Kattwinkel (2019) and to Silva (2020) except that the technology to verify the agents' reports is independent of each agent's actions 8 .…”

“…Recently, models of probabilistic verification have emerged, where the evidence provided by the agents may not be perfectly accurate (Caragiannis et al (2012), Ball and Kattwinkel (2019), Silva (2020)). Our model is similar to Ball and Kattwinkel (2019) and to Silva (2020) except that the technology to verify the agents' reports is independent of each agent's actions 8 . We expand on these papers by characterizing optimal mechanisms (Ball and Kattwinkel (2019) focuses on discussing versions of the revelation principle, while Silva (2020), discusses the extent to which commitment power is important when disclosure is probabilistic).…”

“…1313 In line with the more recent models on probabilistic verification (e.g., Ball and Kattwinkel (2019) and Silva (2020)), the revelation principal applies. To see why that is, suppose that the agents play a game with the principal before signals are realized.…”

“…88 Specifically, it is as if (i) the set of tests (in Ball and Kattwinkel (2019)) and documents (in Silva (2020)) is a singleton and (ii) agents always have to exert effort. Conditions (i) and (ii) ensure that the distribution of the principal's signal only depends on the agents' type and not on their possible report (in particular, (ii) ensures that agents cannot have a “bad” signal on purpose).…”

Information transmission in persuasion models with imperfect verification

“…A general treatment of probabilistic verification can be found inSilva (2020) and inBall and Kattwinkel (2022).6 The same applies toBloch, Dutta, and Dziubinski (2023), who study a model with multiple agents.7 In Chen (2012), de Barreda (2013), andIshida and Shimizu (2016), it is the former, while in Ishida and Shimizu (2019) it is the latter.8 Watson (1996) also considers state-independent preferences but while I determine the distributions over signals for which some information is transmitted, Watson does a similar analysis to determine when all of the agent's information is transmitted.…”