Assessing the structural change of strategic mobility: determinants under hypercompetitive environments

The primary purpose of this exploratory empirical study is to examine the structural stability of a limited number of alternative explanatory factors of strategic change. On the basis of theoretical arguments and prior empirical evidence from two traditional perspectives, we propose an original empirical framework to analyse whether these potential explanatory factors have remained stable over time in a highly turbulent environment. This original question is explored in a particular setting: the population of Spanish private banks. The firms of this industry have experienced a high level of strategic mobility as a consequence of fundamental changes undergone in their environmental conditions over the last two decades (mainly changes related to the new banking and financial regulation process). Our results consistently support that the effect of most explanatory factors of strategic mobility considered did not remain stable over the whole period of analysis. From this point of view, the study sheds new light on major debates and dilemmas in the field of strategy regarding why firms change their competitive patterns over time and, hence, to what extent the "contextdependency" of alternative views of strategic change as their relative validation can vary over time for a given population. Methodologically, this research makes two major contributions to the study of potential determinants of strategic change. First, the definition and measurement of strategic change employing a new grouping method, the Model-based Cluster Method or MCLUST. Second, in order to asses the possible effect of determinants of strategic mobility we have controlled the non-observable heterogeneity using logistic regression models for panel data.

The unbounded dead-end depth propertie is not a group invariant

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Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.