Information Design in Insurance Markets: Selling Peaches in a Market for Lemons

Garcia, Daniel; Teper, Roee; Tsur, Matan

doi:10.2139/ssrn.3024500

“…Case 3. k 2 and G i ( ) is increasing in for every < 1 and every i 2 f1; :::; kg: 23 Using similar logic as in Section 4, one can show that the low- 22 Formally, G 1 ( ) is increasing when < 1 if, and only if, F 0 (1 )( 1 ) + F (1 ) 0. This reduces to 1 max f 2 : <1g f + F (1 ) F 0 (1 ) g. 23 A su¢ cient condition for this to happen is that 1 < max f 2 : <1g f + F (1 ) F 0 (1 ) g.…”

Section: Closed-form Solutions and Examplesmentioning

confidence: 82%

“…For more details, see the last paragraph in the proof of Lemma A-1 in the appendix 29. For a complete analysis of our model with a concave payo¤ function, see a follow-up paper byGarcia, Teper, and Tsur (2017).…”

mentioning

confidence: 99%

Stress Tests and Information Disclosure

Goldstein

¹

,

Leitner

²

2018

Working Paper (Federal Reserve Bank of Philadelphia)

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We study an optimal disclosure policy of a regulator that has information about banks (e.g., from conducting stress tests). In our model, disclosure can destroy risk-sharing opportunities for banks (the Hirshleifer e¤ect). Yet, in some cases, some level of disclosure is necessary for risk sharing to occur. We provide conditions under which optimal disclosure takes a simple form (e.g., full disclosure, no disclosure, or a cuto¤ rule). We also show that, in some cases, optimal disclosure takes a more complicated form (e.g., multiple cuto¤s or nonmonotone rules), which we characterize. We relate our results to the Bayesian persuasion literature.

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“…There is a group of works in static information disclosure which are more applied and aim to understand or improve real-world institutions via information design. Research in this strand includes applications to grading in schools [16], research procurement [79], medical testing [68], price discrimination [11], insurance [29], and routing software [18,45,74,78,81]. A through discussion of the literature on information design up until 2018 appears in [42].…”

Section: Static Information Design Problemsmentioning

confidence: 99%

Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

Farhadi

¹

,

Teneketzis

²

2021

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We study a dynamic information design problem in a finite-horizon setting consisting of two strategic and long-term optimizing agents, namely a principal (he) and a detector (she). The principal observes the evolution of a Markov chain that has two states, one “good” and one “bad” absorbing state, and has to decide how to sequentially disclose information to the detector. The detector’s only information consists of the messages she receives from the principal. The detector’s objective is to detect as accurately as possible the time of the jump from the good to the bad state. The principal’s objective is to delay the detector as much as possible from detecting the jump to the bad state. For this setting, we determine the optimal strategies of the principal and the detector. The detector’s optimal strategy is described by time-varying thresholds on her posterior belief of the good state. We prove that it is optimal for the principal to give no information to the detector before a time threshold, run a mixed strategy to confuse the detector at the threshold time, and reveal the true state afterward. We present an algorithm that determines both the optimal time threshold and the optimal mixed strategy that could be employed by the principal. We show, through numerical experiments, that this optimal sequential mechanism outperforms any other information disclosure strategy presented in the literature. We also show that our results can be extended to the infinite-horizon problem, to the problem where the matrix of transition probabilities of the Markov chain is time-varying, and to the case where the Markov chain has more than two states and one of the states is absorbing.

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“…There is a group of works in static information disclosure which are more applied and aim to understand or improve real-world institutions via information design. Research in this strand includes applications to grading in schools [15], research procurement [64], medical testing [54], price discrimination [9], insurance [26], and routing software [39,17,59,66,63]. A through discussion of the literature on information design up until 2018 appears in [37].…”

Section: Review Of Related Workmentioning

confidence: 99%

Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

Farhadi

¹

,

Teneketzis

²

2020

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We study a dynamic information design problem in a finite-horizon setting consisting of two strategic and long-term optimizing agents, namely a principal (he) and a detector (she). The principal observes the evolution of a Markov chain that has two states, one "good" and one "bad" absorbing state, and has to decide how to sequentially disclose information to the detector. The detector's only information consists of the messages she receives from the principal. The detector's objective is to detect as accurately as possible the time of the jump from the good to the bad state. The principal's objective is to delay the detector as much as possible from detective the jump to the bad state. For this setting, we determine the optimal strategies of the principal and the detector. The detector's optimal strategy is described by time-varying thresholds on her posterior belief of the good state. We prove that it is optimal for the principal to give no information to the detector before a time threshold, run a mixed strategy to confuse the detector at the threshold time, and reveal the true state afterwards. We present an algorithm that determines both the optimal time threshold and the optimal mixed strategy that could be employed by the principal. We show, through numerical experiments, that this optimal sequential mechanism significantly outperforms any other information disclosure strategy presented in literature.or subsidies) so as to align their strategic objectives (e.g. maximization of a strategic agent's utility) with his own objective (e.g. maximization of social welfare). In this situation, the system's information structure (who knows what and when) is fixed, and the coordinator's goal is to design a mechanism that incentivizes the strategic agents to reveal their information truthfully [48].2. Information Design. In this approach, the coordinator (e.g. a central control center in a metropolitan area) knows perfectly the evolution of the system's state (e.g. the evolution of traffic in the transportation network), but the decision making (e.g. route selection) is done by the strategic agents (e.g. drivers) who have incomplete/imperfect knowledge of the state (e.g. drivers only know the traffic in their immediate vicinity). To incentivize strategic agents to take actions that are desirable for the coordinator, he can provide, sequentially over time, information about the system's state to them (e.g. provide traffic updates to selfish drivers). The goal of information provision/disclosure is the alignment of each agent's objective (e.g. minimization of the average time to reach the destination) with the coordinator's objective (e.g. minimization of the traffic in the roads). In this situation, the game-form/mechanism is fixed but the system's information structure is not fixed. It has to be designed by the coordinator through the sequential disclosure/provision of information to the strategic agents so as to serve his goal [17,59].This paper addresses an information design problem. Information design problems are ...

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Information Design in Insurance Markets: Selling Peaches in a Market for Lemons

Cited by 4 publications

References 21 publications

Stress Tests and Information Disclosure

Stress Tests and Information Disclosure

Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

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