Steven T. Tschantz

Post-Merger Product Repositioning

This paper analyzes the effects of mergers between firms competing by simultaneously choosing price and location. Products combined by a merger are repositioned away from each other to reduce cannibalization, and non-merging substitutes are, in response, repositioned between the merged products. This repositioning greatly reduces the merged firms incentive to raise prices and thus substantially mitigates the anticompetitive effects of the merger. Computation of, and selection among, equilibria is done with a novel technique known as the stochastic response dynamic, which does not require the computation of first-order conditions.

Effects of Assumed Demand Form on Simulated Postmerger Equilibria

This paper investigates the properties of four demand systems used to predict the effects of differentiated products mergers: the Almost Ideal Demand System (AIDS), logit, linear, and log-linear (constant elasticity). In Monte Carlo experiments, these demand systems yield significantly different predictions, although all are calibrated to the same the same, randomly generated, premerger relative quantities and demand elasticities. The predicted price increase is greatest with log-linear demand, followed by the AIDS. The linear and logit demand forms result in significantly lower postmerger prices. The results highlight the importance of the inherent higher-order properties of demand systems, i.e., their “curvature.”

The size of a hyperbolic Coxeter simplex

We determine the covolumes of all hyperbolic Coxeter simplex reflection groups. These groups exist up to dimension 9. the volume computations involve several different methods according to the parity of dimension, subgroup relations and arithmeticity properties.

The volume spectrum of hyperbolic 4-manifolds

We construct complete, open, hyperbolic 4-manifolds of smallest volume by gluing together the sides of a regular ideal 24-cell in hyperbolic 4-space. We also show that the volume spectrum of hyperbolic 4-manifolds is the set of all positive integral multiples of 47π2/3.

Tame Combings of Groups

In this paper, we introduce the idea of tame combings for finitely presented groups. If M is a closed irreducible 3-manifold and π1(M) is tame combable, then the universal cover of M is homeomorphic to R3. We show that all asynchronously automatic and all semihyperbolic groups are tame combable.

Mergers in Sealed versus Oral Auctions

In this paper, we study mergers in oral or second-price auctions and compare them to mergers in sealed-bid or first-price auctions. We use an adaptation of the logit qualitative choice model to characterize the underlying bidder value distributions. In second-price auctions, this model has a closed-form relationship between winning bids (prices) and the probabilities of winning (shares), and this relationship gives rise to a Herfindahl-like formula that predicts merger effects. We compare mergers in second-price auctions to mergers in first-price auctions. Despite their differences, sealed-bid merger effects are predicted by the oral Herfindahl-like formula.The source of this curious similarity is not apparent.

Bertrand competition with capacity constraints: mergers among parking lots

To analyze the e1ects of mergers among 2rms facing capacity constraints, we develop a numerical model of price-setting behavior among multi-product 2rms di1erentiated by location and capacity. We perform a number of computational experiments designed to inform merger policy, with speci2c reference to the Central Parking–Allright merger of 1999. The experiments show that capacity constraints on merging 2rms attenuate merger e1ects by much more than capacity constraints on non-merging 2rms amplify them. The experiments also highlight the dependence of merger welfare e1ects on parking demand. In preparation for further industry consolidation, we propose estimators of parking demand to more precisely estimate the costs and bene2ts of future mergers. c 2002 Elsevier Science B.V. All rights reserved. JEL classi)cation: L41; C63; C35

Visual decompositions of Coxeter groups

A Coxeter system is an ordered pair .W;S/ where S is the generating set in a particular type of presentation for the Coxeter groupW . A subgroup ofW is called special if it is generated by a subset ofS. Amalgamated product decompositions of a Coxeter group having special factors and special amalgamated subgroup are easily recognized from the presentation of the Coxeter group. If a Coxeter group is a subgroup of the fundamental group of a given graph of groups, then the Coxeter group is also the fundamental group of a graph of special subgroups, where each vertex and edge group is a subgroup of a conjugate of a vertex or edge group of the given graph of groups. A vertex group of an arbitrary graph of groups decomposition of a Coxeter group is shown to split into parts conjugate to special groups and parts that are subgroups of edge groups of the given decomposition. Several applications of the main theorem are produced, including the classification of maximal FA subgroups of a finitely generated Coxeter group as all conjugates of certain special subgroups. Mathematics Subject Classification (2000). 20F55, 20E08, 20E28.

Commensurability classes of hyperbolic Coxeter groups

In this paper, we classify all the hyperbolic Coxeter n-simplex reflection groups up to widecommensurability for all n 3. We also determine all the subgroup relationships among the groups.

One relator groups are semistable at infinity

IN THIS paper, we show that all finitely generated one relator groups satisfy a homotopy property. For a connected CW-complex Y proper rays r, s: [0, cc) -+ Y converge to the same end of Y if for any compact set C E Y there is an integer N such that r([N, ~0)) and s([N, co)) are contained in the same component of Y C. The space Y is semistable at infinity if any two proper rays converging to the same end of Y are properly homotopic. A finitely presented group G is semistable at infinity if for some (equivalently any) finite complex X with n,(X) = G the universal cover of X is semistable at infinity. Our main result is