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Theory and Decision

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01.03.2017

Hard evidence and ambiguity aversion

verfasst von: Mehdi Ayouni, Frédéric Koessler

Erschienen in: Theory and Decision | Ausgabe 3/2017

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Abstract

This article shows that if an allocation rule can be implemented with unlimited information certification, then it can also be implemented with limited information certification if the designer can use ambiguous communication mechanisms, and if agents are averse to ambiguity in the sense of maxmin expected utility. The reverse implication is true if there is a single agent and a worst outcome.

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Section 5 discusses which of our results extend to multiple agents.

The certifiability structure defined above could be deduced from any arbitrary message correspondence \(\mathcal {M}(t)\), \(t\in T\), by letting \(\mathcal {C}(t) \equiv \{ \mathcal {M}^{-1}(m) : m\in \mathcal {M}(t)\}\). The number of messages in \(\mathcal {M}(t)\) may be larger than in \(\mathcal {C}(t)\) because several messages in \(\mathcal {M}(t)\) may certify the same event in \(\mathcal {C}(t)\), but since we consider mechanisms with arbitrary sets of additional cheap talk messages, taking the certifiability structure as a primitive of the model is without loss of generality.

This terminology is due to Bull and Watson (2007). The normality condition has also been called the full reports condition by Lipman and Seppi (1995) and the minimal closure condition by Forges and Koessler (2005).

We could also define the normalized certifiability structure of \(\mathcal {C}\) by the smallest set of events including \(\mathcal {C}\) which is closed under intersection without affecting any of the results below.

Similar examples appear in Glazer and Rubinstein (2001, (2004), Bull and Watson (2007) and Bull (2008).

As in Bose and Renou (2014), we assume prior-by-prior updating (full Bayesian updating), and that the agent is a consistent planner Siniscalchi (2011), i.e., at every information set he maximizes his minimal expected utility at this information set given the strategies he will actually follow.

This mechanism is constructed such that the agent faces ambiguity at the first stage (report) and a decision problem under certainty at the last stage (certification). Therefore, consistent plans consist in choosing a report that maximizes the minimal expected utility given the designer’s ambiguous communication strategy and his anticipated certification decisions.

Notice that, in general, a deviation to a nondeterministic strategy for an ambiguity averse player may be beneficial while no pure strategy is; however, it is readily observed that the strategy of the agent in the mechanism considered in the proof of the proposition is still optimal if he can use non-deterministic strategies.

Equivalently, agent 2 can first reveal his type to the designer, who then sends messages \(m_1\) and \(m_2\) to agent 1 according to the previous ambiguous communication strategy. Thus, the mechanism described here is consistent with our definition of ambiguous mechanisms.

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Titel: Hard evidence and ambiguity aversion
verfasst von: Mehdi Ayouni
Frédéric Koessler
Publikationsdatum: 01.03.2017
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 3/2017
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-016-9575-7

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