Elimination Tournament Design under Psychological Momentum

In multi-round elimination tournaments, players experience "psychological momentum". We re-consider the design of elimination tournament plan, by taking into account of various types of psychological momentum. The results show that if there is negative psychological momentum, either persistent or not, a double-elimination tournament elicits a higher total effort than a single-elimination tournament if and only if the negative psychological shocks from a player's failures in preceding rounds do not affect this player's mental status significantly in the following rounds. Similarly, if positive momentum is non-persistent, a double-elimination tournament elicits a higher total effort if and only if psychological shocks are not significant. However, if positive psychological momentum is persistent, then a double-elimination tournament always dominates a single-elimination tournament.