King of the hill: Positional dynamics in contests

In a contest with positional dynamics between an incumbent and a challenger i) inequality of power may magnify conflicts, ii) more severe conflicts can go together with lower turnover of incumbents, and iii) power can be self defeating as cost advantages can reduce pay-offs. These three propositions of our paper are contrary to the implications of static conflict models. They follow from incorporating positional dynamics into the standard static approach. Such positional dynamics are relevant for competition in battlefields, politics, and market places.