SUBSTITUTING COMPLEMENTS

The presence of multiple sellers in the provision of (nonsubstitutable)complementary goods leads to outcomes that are worse than thosegenerated by a monopoly (with a vertically integrated productionof complements), a problem known in the economic literatureas complementary oligopoly and recently popularized in the legalliterature as the tragedy of the anticommons. We ask the followingquestion: how many substitutes for each complement are necessaryto render the presence of multiple sellers preferable to a monopoly?Highlighting the asymmetries between Cournot (quantity) andBertrand (price) competition and their dual models, we showthat the results crucially depend on whether firms compete bycontrolling price or quantity. Two substitutes per componentare sufficient when firms choose price. However, when firmschoose quantity, the availability of substitutes, regardlessof their number, is ineffective. Considering more complex casesof multi-complementarity, we ask the related question of howmany complements need to be substitutable and offer commentson equilibrium prices and quantities under different scenarios.     

Seeking rents in the shadow of Coase

In this paper, we study a two-stage rent-seeking game. In the first stage, contestants compete à-la-Tullock; in the second stage, the winner can resell the rent à-la-Coase. We consider a complete information Tullock game in which the contestants have different valuations for the rent. The analysis focuses on the ex ante effects of a secondary market on efforts, payoffs, rent-dissipation and rent-misallocation. We show that the secondary market, while correcting possible misallocations, may exacerbate rent dissipation. In some situations, the increase in rent dissipation more than offsets the allocative advantage, so that a secondary market might reduce welfare. We further show how the effect of ex post tradeability on welfare depends on the parties’ bargaining power and valuations of the rent, also considering the case of endogenous bargaining power.     

Rents, dissipation and lost treasures: Rethinking Tullock's paradox

In this paper we revisit Tullock's paradox (Tullock, 1980) and consider a rent-seeking game in which parties face increasing returns to effort. We allow parties to randomize their strategies and give them an exit option. Given the mixed participation strategies of the parties, valuable rents may occasionally remain unexploited. We consider such a lost-treasure effect as an additional cost of rent seeking and examine how the expected value of such a lost rent varies with changes in the parameters of the problem.     

Crowding-out in productive and redistributive rent-seeking

This paper presents a general rent-seeking model in which participants decide on entry before choosing their levels of efforts. The conventional wisdom in the rent-seeking literature suggests that the rent dissipation increases with the number of potential participants and with their productivity of effort. In this paper, we show that this result of the rent-seeking literature is far from general and applies only when participants are relatively weak and enter the game with certainty. In the presence of strong competitors, the expected total dissipation actually decreases, since participation in the game is less frequent. We further consider the impact of competitors’ exit option, distinguishing between “redistributive rent-seeking” and “productive rent-seeking” situations. In redistributive rent-seeking, no social loss results from the fact that all competitors exit the race. In productive rent-seeking, instead, lack of participation creates a social loss (the “lost treasure” effect), since valuable rents are left unexploited. We show that the lost-treasure effect perfectly counterbalances the reduction in rent dissipation due to competitors’ exit. Hence, unlike redistributive rent-seeking, in productive rent-seeking the total social loss remains equal to the entire rent even when parties grow stronger or the number of players increases.     

Returns to effort in rent-seeking games

In the traditional formulation of rent-seeking games, increasing returns to effort are characterized by an exponent r>1. However, when the value of the rent is normalized to 1, the players’ effort levels A and B will typically be less than 1. Thus, when A<1 and r>1, the value of A ^r decreases as r increases, contradicting the interpretation of r>1 as representing increasing returns to effort. This apparent defect in the mathematization of the problem seems to suggest that a different interpretation of r is required whenever A<1, upsetting the uniformity and elegance of the model. In this short note, we demonstrate that the perceived problem is illusory, and that the usual interpretation of r is satisfactory for all values of A.     

Annullable bonuses and penalties

An annullable penalty is a sanction that is applied unless monitoring takes place and the agent is found non-shirking. An annullable bonus is a bonus that the agent receives unless he has been monitored and found shirking. Annullable penalties and bonuses stand in contrast with normal penalties and bonuses, which are only applied if monitoring has taken place. While real-life examples of annullable penalties are rare (an example is a sanction for which the burden of proof is reversed), there is a clear and oft-discussed example of annullable bonuses: efficiency wages. Under efficiency wages all employees receive a bonus (an overpayment), except for those who have been monitored and found shirking.This paper analyzes under what conditions annullable bonuses or penalties make economic sense. On the one hand, annullable bonuses and penalties have a degree of ineffectiveness that is absent in their normal counterparts: the penalty paid by or the bonus paid to non-monitored agents does not improve their incentives. Not only does this ineffective part make the expected sanction or bonus higher than necessary but it also creates an implicit tax on low monitoring levels and hence distorts monitoring choices. On the other hand, the annullable variants may change the ex post incentives of the agents (to come up with evidence) and the principal (to monitor as promised). As a result, annullable bonuses (such as efficiency wages) can be rational choices when the principal cannot credibly commit to paying bonuses with a certain probability, and annullable penalties can make sense when the agent needs an incentive to reveal information.     

The rise and fall of communal liability in ancient law

In ancient societies, rules of communal responsibility permitted the imposition of retaliatory sanctions on a wrongdoer's clan. These rules followed the collective ownership structure of early communities. Over time, notions of personal responsibility emerged, terminating the transfer of responsibility from one member to the whole clan. This paper intends to provide an economic explanation for this transition.