Dissipation in Rent-seeking Contests with Entry Costs

This paper considers the extent to which expenditure by contestants in imperfectly discriminating rent-seeking contests dissipates all or only part of the rent. In particular, we investigate strategic effects, technological effects and asymmetry under an assumption of diminishing returns to scale. Although asymmetry can reduce dissipation when there are few contestants, we show that this effect disappears in the Nash equilibria of large contests. Similarly, strategic effects are diminished if the cost of entry, which restricts the number of contestants, is fully taken into account. When individual entry costs fall to zero, the reduction in dissipation arising from technological factors is entirely eliminated in the limit. More generally, the dissipation-reducing properties of all three effects operating simultaneously disappear as individual entry fees fall to zero provided the aggregate cost of entry is added to the expenditure of entrants. These conclusions are robust to details of the entry process which can be sequential, in which case the ordering is irrelevant to the limiting results, or simultaneous. Our principal theoretical tool is the share function which expresses the probability of a player winning the contest as a function of aggregate expenditure. However, this methodology has independent interest as it can be applied in many other contexts (not formally analyzed here).