Jigsaw percolation on random hypergraphs

The jigsaw percolation process on graphs was introduced by Brummitt, Chatterjee, Dey, and Sivakoff as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of two graphs on a common vertex set. Our aim is to extend a result of Bollob\'as, Riordan, Slivken, and Smith concerning this process to hypergraphs for a variety of possible definitions of connectedness. In particular, we determine the asymptotic order of the critical threshold probability for percolation when both hypergraphs are chosen binomially at random.Comment: 17 page

On the Distribution of Random Geometric Graphs

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy as a measure of the graph's topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution of the $n(n-1)/2$ distances between $n$ nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in $\mathbb{R}^2$. This enables the calculation of the probability distribution and entropy of a three-node graph. For arbitrary $n$, we derive a series of upper bounds on the graph entropy; in particular, the bound involving the entropy of a three-node graph is tighter than the existing bound which assumes distances are independent. Finally, we provide numerical results on graph connectedness and the tightness of the derived entropy bounds.Comment: submitted to the IEEE International Symposium on Information Theory 201

A non-differentiable approach to revenue equivalence

We give a sufficient condition on the type space for revenue equivalence when the set of social alternatives consists of probability distributions over a finite set. Types are identified with real-valued functions that assign valuations to elements of this finite set, and the type space is equipped with the Euclidean topology. Our sufficient condition is stronger than connectedness but weaker than smooth arcwise connectedness. Our result generalizes all existing revenue equivalence theorems when the set of social alternatives consists of probability distributions over a finite set. When the set of social alternatives is finite, we provide a necessary and sufficient condition. This condition is similar to, but slightly weaker than, connectedness.Revenue equivalence, mechanism design, incentive compatibility, non-differentiable approach, connected type space

Nash Networks with Heterogeneous Agents

A non-cooperative model of network formation is developed. Agents form links with others based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents with- out their consent, provided the agent forming the link makes the appropriate investment. Information flw is two-way. The model builds on the work of Bala and Goyal, but allows for agent heterogeneity. Whereas they permit links to fail with a certain common probability, in our model the probability of failure can be different for different links. We investigate Nash networks that exhibit connectedness and super-connectedness. We provide an explicit characterization of certain star networks. Efficiency and Pareto-optimality issues are discussed through examples. We explore alternative model specifications to address potential shortcomings.

Differences in school connectedness and learned helplessness among undergraduates in a public and private university in Osun State, Nigeria

This study examined differences in school connectedness and learned helplessness among students of a private (Redeemer’s University, Ede) and public university (Obafemi Awolowo University, Ile-Ife) in Osun state, south-west Nigeria. The study utilized an exploratory cross-sectional survey design.278 under-graduate university students were purposively sampled from both universities using a non-probability sampling method. Instruments include, the Learned Helplessness Scale (r = 0.86) and Measurement of School Connectedness (MOSC) questionnaire (r = 0.72).Results show that OAU students had a significantly higher mean score on learned helplessness as opposed to RUN students. OAU students likewise, had significantly lower mean scores on three of the four domains of school connectedness: belonging, communication and connectedness with teachers than RUN students. However, no significant relationship was found between learned helplessness and school connectedness. Further research is recommended to extensively study the variables.Keywords: Learned helplessness, school climate, school connectedness, students, 1Universit

Estimating Private Incentives for Wildfire Risk Mitigation: Determinants of Demands for Different Fire-Safe Actions

In this article we develop a general conceptual model of a property-owner’s decision to implement actions to protect his property against wildfire threat. Assuming a prospective-utility maximizing decision maker, we derive a system of demand functions for fire-safe actions that characterizes factors affecting individual decision making. We then empirically estimate the demands for various fire-safe actions functions using survey data of property owners facing a wildfire threat in Nevada. We find that the probability of individuals implementing some fire-safe action increases with value of the residence, previous experience with wildfire, the property being used as the primary residence, positive attitude towards wildfire management methods on public lands, and connectedness of community members. A lower probability of implementing fire-safe actions is found for those who value pristine nature and privacy that nature provides.Risk and Uncertainty,