Continuous actions space means choosing any value in a range (e.g. in the range $0-$10, as opposed to only $0 and only $10)
Although not a trust game, I think the following experiment by Todorova & Vogt seems to be ploughing the same furrow.
http://www.fww.ovgu.de/fww_media/femm/femm_2012/2012_22.pdf
Kim, thanks for the reference. I took a look, but I'm not seeing the connection.... Maybe you can help explain how you think that paper relates to my question?
Bikhchandani, Hirshleifer, & Welch 1992 cascades/herds are predicated on a binary action space. Todorova&Vogt 2012 show that this effect disappears when the action space granularity is increased from 2 to 1001. So with regard to information aggregation in an investment setting, the relevant transition in observable behavior occurs well before the infinite limit of a continuous action space is reached.
Kim, thanks very much for the clear summary of the connection. Yes, I think this seems to relate. And I expect that in the trust-based investment game setting something similar might be found. My colleagues Timothy Shilelds and Roman Sheremeta have looked at binary action space and continuous action space, finding interesting differences. But, i think if we also examined action space granularity >2 we would find difference when comparing to 2. Thanks again for the references!
I posted this question almost a couple months back because we were working on writing up a paper on this topic. We were motivated to do so because we felt it was an important but under-explored topic. Inquiries posted to other forums also yielded little. Here is a link to our working paper if anyone who has made it to the bottom of this thread is still interested:
2013. Limitations to signaling trust with all or nothing investments. with Sheremeta, R. Shields, T. (under review)
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2337733
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