Does information efficiency require a perception of information inefficiency?

This paper examines the existence of significant differences in the expected returns to bets placed about identical outcomes in different sectors of a betting market. In an informationally efficient market, such differences should be arbitraged away. Evidence is presented here which suggests that this process actually occurs only in those situations where bettors are provided with a clear signal of some form of information efficiency in the market. The signal takes the form of a marked movement in bookmakers' odds. Where these signals are not present, unexploited opportunities for arbitrage persist. We suggest that actual information efficiency (in the sense of an absence of unexploited opportunities for arbitrage) requires a clear perception by market players of the existence of some form of information inefficiency in the market under consideration.