A Survey of Best Monotone Degree Conditions for Graph Properties

We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 page

Informal Insurance in Social Networks

This paper studies informal insurance across networks of individuals. Two characteristics are fundamental to the model developed here: First, informal insurance is a bilateral activity, and rarely involves explicit arrangements across several people. Second, insurance is a social activity, and transfers are often based on norms. In the model studied here, only directly linked agents make transfers to each other, although they are aware of the (aggregate) transfers each makes to third parties. An insurance scheme for the network as a whole is an equilibrium of several interacting bilateral arrangements. This model serves as a starting point for investigating stable insurance networks, in which all agents actually have private incentives to abide by the ongoing insurance arrangement. The resulting analysis shows that network links have two distinct and possibly conflicting roles to play. First, they act as conduits for transfers, and in this way this make better insurance possible. Second, they act as conduits for information, and in this sense they affect the severity of punishments for noncompliance with the scheme. A principal task of this paper is to describe how these two forces interact, and in the process characterize stable networks. The concept of "sparse" networks, in which the removal of certain links increases the number of network components, is crucial in this characterization. As corollaries, we found that both "thickly connected" networks(such as the complete graph) and "thinly connected" networks (such as trees) are likely to be stable, whereas intermediate degrees of connectedness jeopardize stability. Finally, we study in more detail the notion of networks as conduits for transfers, by simply assuming a punishment structure (such as autarky) that is independent of the precise architecture of the tree. This allows us to isolate a bottleneck effect: the presence of certain key agents who act as bridges for several transfers. Bottlenecks are captured well in a feature of trees that we call decomposability, and we show that all decomposable networks have the same stability properties and that these are the least likely to be stable.social networks, informal insurance

Banks versus venture capital when the venture capitalist values private benefits of control

If control of their firms allows entrepreneurs to derive private benefits, it also allows other controlling parties. Private benefits are especially relevant for venture capitalists, who typically get considerable control in their portfolio firms, but not for banks, which are passive loan providers. We incorporate this difference between banks and venture capital and analyze entrepreneurs' financing strategy between the two. We find that, in all strict Nash Equilibria, entrepreneurs who value private benefits more choose banks while the rest choose venture capital. Thus, bank-financed entrepreneurs allocate more resources to tasks that yield private benefits while VC-backed entrepreneurs have higher profitability

Informal Insurance in Social Networks

social networks, informal insurance.

Knowledge Accumulation within an Organization

We develop a simple model of task allocation for knowledge workers over their career within an organization. The human capital theory initiated by Becker (1962, 1964) has o¤ered a rich analysis of an individuals life cycle investment in human capital. One of the main result of this literature states that human capital investments are undertaken at the early stage of the career because workers have then a longer period of time over which they can bene…t from the return of their investments. In this paper, we consider a knowledge accumulation problem within an organization that cannot prevent the worker from quitting and using the knowledge outside the organization. In the …rst best situation, we show a similar result as in the human capital theory, i.e. the share of time allocated to knowledge creation tasks decreases over time. We then ask how this pattern is a¤ected when the knowledge worker can leave the organization and bene…t from this knowledge outside the organization. In this case, we obtain the novel result that the time path of the fraction of working time allocated to knowledge creation tasks is non-monotone. This fraction is highest at the early career stage, falls gradually, then rises again, before falling …nally toward zero. We also show that an increase in the …rm-speci…city of knowledge can increase or decrease the life-time income of the knowledge worker.

Optimal Collusion with Limited Liability and Policy Implications

Collusion sustainability depends on firms’ aptitude to impose sufficiently severe punishments in case of deviation from the collusive rule. We characterize the ability of oligopolistic firms to implement a collusive strategy when their ability to punish deviations over one or several periods is limited by a severity constraint. It captures all situations in which either structural conditions (the form of payoff functions), institutional circumstances (a regulation), or financial considerations (profitability requirements) set a lower bound to firms’ losses. The model specifications encompass the structural assumptions (A1-A3) in Abreu (1986) [Journal of Economic Theory, 39, 191-225]. The optimal punishment scheme is characterized, and the expression of the lowest discount factor for which collusion can be sustained is computed, that both depend on the status of the severity constraint. This extends received results from the literature to a large class of models that include a severity constraint, and uncovers the role of structural parameters that facilitate collusion by relaxing the constraint.

Optimal Collusion with Limited Liability and Policy Implications

Collusion sustainability depends on firms’ aptitude to impose sufficiently severe punishments in case of deviation from the collusive rule. We characterize the ability of oligopolistic firms to implement a collusive strategy when their ability to punish deviations over one or several periods is limited by a severity constraint. It captures all situations in which either structural conditions (the form of payoff functions), institutional circumstances (a regulation), or financial considerations (profitability requirements) set a lower bound to firms’ losses. The model specifications encompass the structural assumptions (A1-A3) in Abreu (1986) [Journal of Economic Theory, 39, 191-225]. The optimal punishment scheme is characterized, and the expression of the lowest discount factor for which collusion can be sustained is computed, that both depend on the status of the severity constraint. This extends received results from the literature to a large class of models that include a severity constraint, and uncovers the role of structural parameters that facilitate collusion by relaxing the constraint.

Learning and Hysteresis in a Dynamic Coordination Game

This paper introduces a dynamic coordination game with incomplete information defined by a state variable that evolves stochastically. Incomplete information enables us to use iterated dominance argument in order to resolve the indeterminacy issues. The key endogenous variable is the belief that each agent holds about the state of the world. We show that as agents update their heterogeneous beliefs through learning sequentially, they adjust their beliefs to justify the status quo. This effect induces equilibrium actions that support the status quo, a property we call hysteresis.dynamic coordination game, hysteresis, global games

Systems biology approaches to the dynamics of gene expression and chemical reactions

Systems biology is an emergent interdisciplinary field of study whose main goal is to understand the global properties and functions of a biological system by investigating its structure and dynamics [74]. This high-level knowledge can be reached only with a coordinated approach involving researchers with different backgrounds in molecular biology, the various omics (like genomics, proteomics, metabolomics), computer science and dynamical systems theory. The history of systems biology as a distinct discipline began in the 1960s, and saw an impressive growth since year 2000, originated by the increased accumulation of biological information, the development of high-throughput experimental techniques, the use of powerful computer systems for calculations and database hosting, and the spread of Internet as the standard medium for information diffusion [77]. In the last few years, our research group tried to tackle a set of systems biology problems which look quite diverse, but share some topics like biological networks and system dynamics, which are of our interest and clearly fundamental for this field. In fact, the first issue we studied (covered in Part I) was the reverse engineering of large-scale gene regulatory networks. Inferring a gene network is the process of identifying interactions among genes from experimental data (tipically microarray expression profiles) using computational methods [6]. Our aim was to compare some of the most popular association network algorithms (the only ones applicable at a genome-wide level) in different conditions. In particular we verified the predictive power of similarity measures both of direct type (like correlations and mutual information) and of conditional type (partial correlations and conditional mutual information) applied on different kinds of experiments (like data taken at equilibrium or time courses) and on both synthetic and real microarray data (for E. coli and S. cerevisiae). In our simulations we saw that all network inference algorithms obtain better performances from data produced with \u201cstructural\u201d perturbations (like gene knockouts at steady state) than with just dynamical perturbations (like time course measurements or changes of the initial expression levels). Moreover, our analysis showed differences in the performances of the algorithms: direct methods are more robust in detecting stable relationships (like belonging to the same protein complex), while conditional methods are better at causal interactions (e.g. transcription factor\u2013binding site interactions), especially in presence of combinatorial transcriptional regulation. Even if time course microarray experiments are not particularly useful for inferring gene networks, they can instead give a great amount of information about the dynamical evolution of a biological process, provided that the measurements have a good time resolution. Recently, such a dataset has been published [119] for the yeast metabolic cycle, a well-known process where yeast cells synchronize with respect to oxidative and reductive functions. In that paper, the long-period respiratory oscillations were shown to be reflected in genome-wide periodic patterns in gene expression. As explained in Part II, we analyzed these time series in order to elucidate the dynamical role of post-transcriptional regulation (in particular mRNA stability) in the coordination of the cycle. We found that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates. Moreover, the cascade of events which occurs during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses or stimuli. The concepts of network and of systems dynamics return also as major arguments of Part III. In fact, there we present a study of some dynamical properties of the so-called chemical reaction networks, which are sets of chemical species among which a certain number of reactions can occur. These networks can be modeled as systems of ordinary differential equations for the species concentrations, and the dynamical evolution of these systems has been theoretically studied since the 1970s [47, 65]. Over time, several independent conditions have been proved concerning the capacity of a reaction network, regardless of the (often poorly known) reaction parameters, to exhibit multiple equilibria. This is a particularly interesting characteristic for biological systems, since it is required for the switch-like behavior observed during processes like intracellular signaling and cell differentiation. Inspired by those works, we developed a new open source software package for MATLAB, called ERNEST, which, by checking these various criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results of this analysis can be used, for example, for model discrimination: if for a multistable biological process there are multiple candidate reaction models, it is possible to eliminate some of them by proving that they are always monostationary. Finally, we considered the related property of monotonicity for a reaction network. Monotone dynamical systems have the tendency to converge to an equilibrium and do not present chaotic behaviors. Most biological systems have the same features, and are therefore considered to be monotone or near-monotone [85, 116]. Using the notion of fundamental cycles from graph theory, we proved some theoretical results in order to determine how distant is a given biological network from being monotone. In particular, we showed that the distance to monotonicity of a network is equal to the minimal number of negative fundamental cycles of the corresponding J-graph, a signed multigraph which can be univocally associated to a dynamical system