Wolfgang Leininger

More efficient rent-seeking — A Münchhausen solution

In the by now standard Tullock model of rent-seeking (Tullock, 1980) fulfillment of the rent-dissipation hypothesis advanced by Tullock (1967) and Posner (1975) is rather the exception than the rule. Using a game-theoretic model, Tullock showed that in non-cooperative Cournot-Nash equilibrium the extent of rent-dissipation crucially depends on the (scale) returns to individual rent-seeking expenditures. His seminal work, in particular the ‘intellectual mire’ (Tullock, 1980) presented by increasing returns to such expenditure (which may lead to non-existence of Cournot-Nash equilibrium) has subsequently attracted considerable attention (see, e g, Hillman and Katz, 1984; Higgins, Shughart and Tollison, 1985; Corcoran and Karels, 1985; Michaels, 1988; and Allard, 1988). While all of these contributions have shed new light on the issue, they did not satisfactorily solve the basic modeling problem, which obstinately kept its status as an `intellectual swamp’ (Tullock, 1985). The present contribution is an attempt to point to a way out of this swamp by questioning the appropriateness of the Cournot-Nash solution concept for Tullock’s original problem. Equivalently, we question the modeling device of having rent seekers move simultaneously.

Equilibria of the Sealed- Bid Mechanism for Bargaining with Incomplete Information*, '

We study the Nash equilibria of the sealed-bid bargaining mechanism with incomplete information, a nonzero-sum game. For the case of uniform priors, we describe two uncountably numerous families of equilibria: the first has differentiable strategies; in the second the strategies are step-functions. The efficiencies of these equilibria range from “second best” to zero. For independent nonuniform priors, we show that a similar situation obtains. These results seem discouraging with regard to using the sealed-bid mechanism in practice. The mechanism might be salvaged, however, if bargainers turn out to confine themselves to linear-strategy equilibria.

Patent competition,rent dissipation and the persistence of monopoly: The role of research budgets

Abstract The paper investigates how patent rights can contribute to the persistence of monopoly. Patent competition is modelled as a dollar auction game between two firms, incumbent and entrant. Any bid (expenditure on R & D) in the game constitutes sunk cost, whose total amount is constrained by fixed (research) budgets. The explicit solution (subgame-perfect equilibrium) determines who wins the patent and how the winning expenditures depend on order of play and budgets of firms. The entrant can win if he moves first and has the higher budget. Rent may or may not be dissipated by the competition.

The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations

An intertemporal model of consumption and bequest behaviour is specified and analysed as a game between generations. The main feature of this game is that no a priori restrictions (like linearity) are placed on the strategy choice of generations. The paper gives an existence proof for perfect (Nash) equilibria in finite and infinite horizon versions of the model and determines characteristic properties of equilibrium strategies. The main result is to demonstrate existence of stationary perfect equilibrium if the time horizon is infinite.

Effort Maximization in Asymmetric N-Person Contest Games

This paper provides existence and characterization of the optimal contest success function under the condition that the objective of the contest designer is total effort maximization among n heterogeneous players. Heterogeneity of players makes active participation of a player in equilibrium endogenous with respect to the specific contest success function adopted by the contest designer. Hence, the aim of effort maximization implies the identification of those players who should be excluded from making positive efforts.We give a general proof for the existence of an optimal contest success function and provide an algorithm for the determination of the set of actively participating players.This is turn allows to determine optimal efforts in closed form.An important general feature of the solution is that maximization of total effort requires at least three players to be active.

On the Existence of Subgame-Perfect Equilibrium in Infinite-Action Games of Perfect Information

Abstract We study infinite-action games of perfect information with finitely or countably many players. It is assumed that payoff functions are continuous, strategy sets are compact, and constraint correspondences are continuous. Under these assumptions we prove the existence of subgame-perfect equilibria in pure strategies which are measurable functions. If for any date t , the subgame that is played from date t on depends on the history up to t only as this history affects some vector of “state” variables, then equilibrium strategies admit a “closed-loop” representation as measurable functions of the “state” trajectories.

Expected revenue of all-pay and first-price sealed-bid auctions with affiliated signals

In the general symmetric auction framework of Milgrom and Weber (1982) it is shown—as a new manifestation of thelinkage principle—that the all-pay sealed-bid auction yieldshigher expected revenue than the standard first-price sealed-bid auction. This raises the question why sealed-bid auctions of the standard first-price variety are observed in practice whereas the all-pay variety is not.

Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games

Abstract This paper relates infinite-action (continuous) games of perfect information to finite-action approximations of such games and thereby obtains a new existence proof for subgame-perfect equilibrium (SPE) in the infinite-action case. Accumulation points of SPE paths of approximating finite-action games are shown to be SPE paths of the limiting infinite-action game. However, no such upper hemi-continuity property holds for SPE strategies. The discontinuity in strategies corresponds to a need for forward induction in the SPE construction for the infinite-action game, thus conflicting with the Harsanyi-Selten principle of subgame-consistency.

Lottery Versus All-Pay Auction Contests – A Revenue Dominance Theorem

We allow a contest organizer to bias a contest in a discriminatory way; i.e., she can favor specific contestants by designing the contest rule in order to maximize total equilibrium effort (resp. revenue). The two predominant contest regimes are considered, all-pay auctions and lottery contests. For all-pay auctions the optimal bias is derived in closed form: It implies extreme competitive pressure among active contestants and low endogenous participation rates. Moreover, the exclusion principle advanced by Baye et al. (1993) becomes obsolete in this case. In contrast, the optimally biased lottery induces a higher number of actively participating contestants due to softer competition. Our main result regarding total revenue comparison under the optimal biases reveals that the all-pay auction revenue-dominates the lottery contest for all levels of heterogeneity among contestants. The incentive effect due to a strongly discriminating contest rule (all-pay auction) dominates the participation effect due to a weakly discriminating contest rule (lottery).

Rawls' Maximin Criterion and Time-Consistency: Further Results

The paper is concerned with the implications of a maximin welfare function for an intertemporal society which has a nonlinear technology at its disposal, but holds conflicting preferences over time. The complete solution given shows that time-consistency and optimality of plans may or may not be compatible. The time-consistent case is generalized to a very wide class of models. This leads to the partial invalidation of a result stated in the earlier literature on the subject.