Bad Reputation Under Bounded And Fading Memory

I relax the full memory assumption in Ely and Välimäki's (2003) mechanic game, where reputation is bad. Under bounded memory (only recent periods are observed), long memory still yields bad reputation due to an “echo” where bad signals cause future motorists to not hire, causing further lack of hiring, and so on. Short memory avoids bad reputation by making it “useless,” because consumers never learn enough information to change their decisions. No “happy middle” exists under bounded memory where consumers learn valuable information without tempting the mechanic into harmful signaling and thereby unraveling the market. By contrast, “fading memory” (past periods are randomly sampled with “fading” probabilities) achieves this happy middle by offering valuable information in a way that bounds the probabilities of these reputational echoes. Possible fading memory implementations (e.g., for review websites) are described and generalized to a broader class of games. (JEL C73, D8)