Designing feedback mechanisms seems like a big area for market design where theory and experiments can go hand in hand, and where there are still lots of open questions.
Gary Bolton, Ben Greiner and Axel Ockenfels have a new paper "Engineering Trust - Reciprocity in the Production of Reputation Information" that is forthcoming in Management Science.
The abstract reads:
"Reciprocity in feedback giving distorts the production and content of reputation information in a market, hampering trust and trade efficiency. Guided by feedback patterns observed on eBay and other platforms we run laboratory experiments to investigate how reciprocity can be managed by changes in the way feedback information flows through the system, leading to more accurate reputation information, more trust and more efficient trade. We discuss the implications for theory building and for managing the redesign of market
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