Normalized equilibrium in Tullock rent seeking game

International audienceGames with Common Coupled Constraints represent manyreal life situations. In these games, if one player fails tosatisfy its constraints common to other players, then theother players are also penalised. Therefore these games canbe viewed as being cooperative in goals related to meetingthe common constraints, and non cooperative in terms ofthe utilities. We study in this paper the Tullock rent seekinggame with additional common coupled constraints. We havesucceded in showing that the utilities satisfy the property ofdiagonal strict concavity (DSC), which can be viewed asan extention of concavity to a game setting. It not onlyguarantees the uniqueness of the Nash equilibrium but also of the normalized equilibrium

Rents, dissipation and lost treasures: comment

In an interesting recent paper, Dari-Mattiacci and Parisi (2005) extended Tullock.s (1980) rent-seeking game with an entry decision. The mixed strategies identified by Dari-Mattiacci and Parisi for the case of increasing returns in the contest success function (r > 2) do not constitute an equilibrium of the game they study. However, these strategies are an equilibrium if the strategy space of the game is restricted by a minimum expenditure requirement, and this minimum expenditure requirement is an element of a specific interval

Rents, dissipation and lost treasures: comment

In an interesting recent paper, Dari-Mattiacci and Parisi (2005) extended Tullock.s (1980) rent-seeking game with an entry decision. The mixed strategies identified by Dari-Mattiacci and Parisi for the case of increasing returns in the contest success function (r > 2) do not constitute an equilibrium of the game they study. However, these strategies are an equilibrium if the strategy space of the game is restricted by a minimum expenditure requirement, and this minimum expenditure requirement is an element of a specific interval.

Markets for Influence

We specify an oligopoly game, where firms choose quantity in order to maximise profits, that is strategically equivalent to a standard Tullock rent-seeking game. We then show that the Tullock game may be interpreted as an oligopsonistic market for influence.Alternative specifications of the strategic variable give rise to a range of Nash equilibria with varying levels of rent dissipation.Tullock contests, oligopoly

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 \textquotedblright redistributive rent-seeking\textquotedblright\ and \textquotedblright productive rent-seeking\textquotedblright\ 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 \textquotedblright lost treasure\textquotedblright\ 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.Rent-seeking; rent dissipation; Tullock's paradox

Markets for Influence

We specify an oligopoly game, where firms choose quantity in order to maximise profits, that is strategically equivalent to a standard Tullock rent- seeking game. We then show that the Tullock game may be interpreted as an oligopsonistic market for in?uence. Alternative specifications of the strategic variable give rise to a range of Nash equilibria with varying levels of rent dissipation

TULLOCK AND HIRSHLEIFER: A MEETING OF THE MINDS

We introduce the serial contest by building on the desirable properties of two prominent contest games. This family of contest games relies both on relative efforts (as Tullock's proposal) and on absolute effort differences (as difference-form contests). An additional desirable feature is that the serial contest is homogeneous of degree zero in contestant's efforts. The family is characterized by a parameter representing how sensitive the outcome is to contestants' efforts. It encompasses as polar cases the (fair) lottery and the (deterministic) all-pay auction. Equilibria have a close relationship to those of the (deterministic) all-pay auction and important properties of the latter hold for the serial contest, too.rent-seeking, (non-) deterministic contest, contest success function, all-pay auction, rent dissipation, exclusion principle, preemption effect, cap, campaign contributions.

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 pro- ductivity 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 unex- ploited. 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.Rent-seeking, rent dissipation, Tullock' s paradox.

Dynamic contests

Considering several main types of dynamic contests (the race, the tug-of-war, elimination contests and iterated incumbency fights) we identify a common pattern: the discouragement effect. This effect explains why the sum of rentseeking efforts often falls considerably short of the prize that is at stake. It may cause violent conflict in early rounds, but may also lead to long periods of peaceful interaction. -- Unter Berücksichtigung verschiedener Haupttypen dynamischer Wettbewerbe (das Wettrennen, das Tauziehen, Ausscheidungskämpfe und wiederholte Kämpfe um Amtszeiten) identifizieren die Autoren ein gemeinsames Muster: den Entmutigungseffekt. Dieser Effekt erklärt, wieso die Rent-seeking-Bemühungen in Summe oft deutlich nicht an den auf dem Spiel stehenden Preis heranreichen. Der Effekt kann heftige Kämpfe in den ersten Runden des Wettbewerbs auslösen, aber auch zu langen Perioden friedlichen Zusammenspiels führen.