Inter-group conflict and intra-group punishment in an experimental contest game

We study how conflict in a contest game is influenced by rival parties being groups and by group members being able to punish each other. Our main motivation stems from the analysis of socio-political conflict. The relevant theoretical prediction in our setting is that conflict expenditures are independent of group size and independent of whether punishment is available or not. We find, first, that our results contradict the independence of group-size prediction: conflict expenditures of groups are substantially larger than those of individuals, and both are substantially above equilibrium. Towards the end of the experiment material losses in groups are 257% of the predicted level. There is, however, substantial heterogeneity in the investment behaviour of individual group members. Second, allowing group members to punish each other after individual contributions to the contest effort are revealed leads to even larger conflict expenditures. Now material losses are 869% of the equilibrium level and there is much less heterogeneity in individual group members' investments. These results contrast strongly with those from public goods experiments where punishment enhances efficiency and leads to higher material payoffs.

The Measurement of social polarization in a multi-group context

Polarization indices presented up to now have only focused their attention on the distribution of income/wealth. However, in many circumstances income is not the only relevant dimension that might be the cause of social conflict, so it is very important to have a social polarization index able to cope with alternative dimensions. In this paper we present an axiomatic characterization of one of such indices: it has been obtained as an extension of the (income) polarization measure introduced in Duclos, Esteban and Ray (2004) to a wider domain. It turns out that the axiomatic structure introduced in that paper alone is not appropriate to obtain a fully satisfactory characterization of our measure, so additional axioms are proposed. As a byproduct, we present an alternative axiomatization of the aforementioned income polarization measure.

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Individual versus group strategy-proofness: when do they coincide?

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on the

Dynamics in Thompson's group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

Strong exceptional sequences of vector bundles on certain Fano varieties

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Persistent bundles over a two dimensional compact set

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On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

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The loop group and the cobar construction

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Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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An irreducibility criterion for group representations, with arithmetic applications

We prove a criterion for the irreducibility of an integral group representation p over the fraction field of a noetherian domain R in terms of suitably defined reductions of p at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.

Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results

We define different concepts of group strategy-proofness for social choice functions. We discuss the connections between the defined concepts under different assumptions on their domains of definition. We characterize the social choice functions that satisfy each one of them and whose ranges consist of two alternatives, in terms of two types of basic properties.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.