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Social Choice and Welfare

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03-03-2021 | Original Paper

Dynamic communication mechanism design

Author: Ryuji Sano

Published in: Social Choice and Welfare | Issue 1/2021

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Abstract

We consider dynamic communication mechanisms in a quasi-linear environment with single-dimensional types. The mechanism designer gradually identifies agents’ valuations by iteratively offering prices to agents at different stages. Agents pay the maximum price they accepted if their desirable decision is made. We show that within weakly tight mechanisms, if a communication mechanism is ex-post incentive compatible, then it is a monotone-price mechanism. English auctions are characterized as a class of mechanisms that satisfy ex-post incentive compatibility and efficiency.

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See Rothkopf et al. (1990) for example.

The strategic equivalence holds in a private value setting.

We use female pronoun for the mechanism designer and male pronoun for an agent.

Integer valuation is not crucial in our analysis. When valuation is bounded as we assume, it guarantees that the mechanism designer identifies the state of the world in finitely many steps.

We discuss the case in which \(X_i\) is private information of agent i in Sect. 3.4.

We will consider mechanisms such that \(V_i (h^t)\) is well defined and non-empty.

See Appendix A for a formal definition as an extensive form game.

We assume that a negative response against \(p_i\) implies a strict preference so that the mechanism designer can certainly identify \(v_i\).

We do not argue the formal notion of the simplicity of a transfer rule or the commitment issue. Akbarpour and Li (2019) show that the credibility of a mechanism induces the pay-as-bid transfer rule.

See Van Zandt (2007).

Note that subgame perfection is not required for DSIC or OSP.

The original “Ausubel auction” in Ausubel (2004) was not precisely ex-post perfect incentive compatible. Okamoto (2018) and Ausubel (2018) modify it to hold the property.

Ties are broken not randomly, but in an arbitrary predetermined way. The efficient allocation rule is not unique.

There is an exception when two or more agents respond yes at \(p_i^t={\bar{v}}\). In such cases, one agent is chosen as the winner and pays \({\bar{v}}\).

Due to the perfect information assumption, actions of agents are made sequentially.

Note that these mechanisms use more than two actions in a single round. Such auctions that iteratively offer prices and ask demands are common in dynamic multi-object auction designs. See Ausubel (2004, 2006), Ausubel and Milgrom (2002) and Mishra and Parkes (2007) for example.

For a general case of dichotomous preferences, Mishra and Roy (2013) characterize DSIC in terms of cutoff valuations.

See the main text for the conditions on p.

For any round \(s<t\) such that agent i is asked, he always responds yes and \(p_i^s \le v_i\).

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Title: Dynamic communication mechanism design
Author: Ryuji Sano
Publication date: 03-03-2021
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 1/2021
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-021-01309-y

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