Geometric aspects of the symmetric inverse M-matrix problem

We investigate the symmetric inverse M-matrix problem from a geometric perspective. The central question in this geometric context is, which conditions on the k-dimensional facets of an n-simplex S guarantee that S has no obtuse dihedral angles. First we study the properties of an n-simplex S whose k-facets are all nonobtuse, and generalize some classical results by Fiedler. We prove that if all (n-1)-facets of an n-simplex S are nonobtuse, each makes at most one obtuse dihedral angle with another facet. This helps to identify a special type of tetrahedron, which we will call sub-orthocentric, with the property that if all tetrahedral facets of S are sub-orthocentric, then S is nonobtuse. Rephrased in the language of linear algebra, this constitutes a purely geometric proof of the fact that each symmetric ultrametric matrix is the inverse of a weakly diagonally dominant M-matrix. Review papers support our belief that the linear algebraic perspective on the inverse M-matrix problem dominates the literature. The geometric perspective however connects sign properties of entries of inverses of a symmetric positive definite matrix to the dihedral angle properties of an underlying simplex, and enables an explicit visualization of how these angles and signs can be manipulated. This will serve to formulate purely geometric conditions on the k-facets of an n-simplex S that may render S nonobtuse also for k>3. For this, we generalize the class of sub-orthocentric tetrahedra that gives rise to the class of ultrametric matrices, to sub-orthocentric simplices that define symmetric positive definite matrices A with special types of k x k principal submatrices for k>3. Each sub-orthocentric simplices is nonobtuse, and we conjecture that any simplex with sub-orthocentric facets only, is sub-orthocentric itself.Comment: 42 pages, 20 figure

Factorization of CP-rank-3 completely positive matrices

A symmetric positive semi-definite matrix A is called completely positive if there exists a matrix B with nonnegative entries such that A=BB^T. If B is such a matrix with a minimal number p of columns, then p is called the cp-rank of A. In this paper we develop a finite and exact algorithm to factorize any matrix A of cp-rank 3. Failure of this algorithm implies that A does not have cp-rank 3. Our motivation stems from the question if there exist three nonnegative polynomials of degree at most four that vanish at the boundary of an interval and are orthonormal with respect to a certain inner product.Comment: 13 pages, 10 figure

Political Autonomy and Independence: Theory and Experimental Evidence

We study the process by which subordinated regions of a country can obtain a more favourable political status. In our theoretical model a dominant and a dominated region first interact through a voting process that can lead to different degrees of autonomy. If this process fails then both regions engage in a costly political conflict which can only lead to the maintenance of the initial subordination of the region in question or to its complete independence. In the subgame-perfect equilibrium the voting process always leads to an intermediate rrangement acceptable for both parts. Hence, the costly political struggle never occurs. In contrast, in our experiments we observe a large amount of fighting involving high material losses, even in a case in which the possibilities for an arrangement without conflict are very salient. In our experimental environment intermediate solutions are feasible and stable, but purely emotional elements prevent them from being reached.secession, collective action, independence movements, laboratory experiments, rent-seeking.

Political Autonomy and Independence: Theory and Experimental Evidence

We study the process by which subordinated regions of a country can obtain a more favourable political status. In our theoretical model a dominant and a dominated region first interact through a voting process that can lead to different degrees of autonomy. If this process fails then both regions engage in a costly political conflict which can only lead to the maintenance of the initial subordination of the region in question or to its complete independence. In the subgame-perfect equilibrium the voting process always leads to an intermediate arrangement acceptable for both parts. Hence, the costly political struggle never occurs. In contrast, in our experiments we observe a large amount of fighting involving high material losses, even in a case in which the possibilities for an arrangement without conflict are very salient. In our experimental environment intermediate solutions are feasible and stable, but purely emotional elements prevent them from being reached.Secession, collective action, independence movements, laboratory experiments, rent-seeking

The Puzzle of Social Preferences

We present a brief overview of the experimental economics literature on social preferences. In numerous experiments, economically incentivized subjects are willing to sacrifice part of their material earnings to compensate the kind behavior of others, or will be willing to reciprocate at a non-negligible cost, or even pay a positive price for punishing the behavior of selfish individuals. All these actions are labeled as social in economics because there is no apparent way to reconcile them with any reasonable form of pure self-interest. We focus on social dilemma games and want to communicate two main messages. First, research in experimental economics has produced abundant evidence that illustrates the social components of people’s preferences. Second, social sanctions of different types play an important role in facilitating cooperative behavior.

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We study the relation between the number of firms and market power in experimental oligopolies. Price competition under decreasing returns involves a wide interval of pure strategy equilibrium prices. We present results of an experiment in which two, three and four identical firms repeatedly interact in this environment. Less collusion with more firms leads to lower average prices. With more than two firms, the predominant market price is 24. A simple imitation model captures this phenomenon. For the long run, the model predicts that prices converge to the Walrasian outcome, but for the intermediate term the modal price is 24Laboratory experiments, industrial organisation, oligopoly, price competition, co-ordination games, learning

Personal Relations and their Effect on Behavior in an Organizational Setting: An Experimental Study

We study how personal relations affect performance in organizations. In the experimental game we use a manager has to assign different degrees of decision power to two employees. These two employees then have to make distributive decisions which affect themselves and the manager. Our focus is on the effects on managers' assignment of decision power and on employees' distributive decisions of one of the employees and the manager knowing each other personally. Our evidence shows that managers tend to favor employees that they personally know and that these employees tend, more than other employees, to favor the manager in their distributive decisions. However, this behavior does not affect the performance of the employees that do not know the manager. All these effects are independent of whether the employees that know the manager are more or less productive than those who do not know the manager. The results shed light on discrimination and nepotism and its consequences for the performance of family firms and other organizations.Family firms, nepotism, corporate governance, procedural fairness, experiments

ART Versus Reinsurance: The Disciplining Effect of Information Insensitivity

We provide a novel benefit of "Alternative Risk Transfer" (ART) products with parametric or index triggers. When a reinsurer has private information about his client's risk, outside reinsurers will price their reinsurance offer less aggressively. Outsiders are subject to adverse selection as only a high-risk insurer might find it optimal to change reinsurers. This creates a hold-up problem that allows the incumbent to extract an information rent. An information-insensitive ART product with a parametric or index trigger is not subject to adverse selection. It can therefore be used to compete against an informed reinsurer, thereby reducing the premium that a low-risk insurer has to pay for the indemnity contract. However, ART products exhibit an interesting fate in our model as they are useful, but not used in equilibrium because of basis-risk.Cat Bonds, Risk Transfer, Index Trigger, Adverse Selection