Counting and Enumerating Crossing-free Geometric Graphs

We describe a framework for counting and enumerating various types of crossing-free geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and Seidel, who used them to count triangulations in time $O(2^nn^2)$ where $n$ is the number of points. The main idea is to reduce the problem of counting geometric graphs to counting source-sink paths in a directed acyclic graph. The following new results will emerge. The number of all crossing-free geometric graphs can be computed in time $O(c^nn^4)$ for some $c < 2.83929$. The number of crossing-free convex partitions can be computed in time $O(2^nn^4)$. The number of crossing-free perfect matchings can be computed in time $O(2^nn^4)$. The number of convex subdivisions can be computed in time $O(2^nn^4)$. The number of crossing-free spanning trees can be computed in time $O(c^nn^4)$ for some $c < 7.04313$. The number of crossing-free spanning cycles can be computed in time $O(c^nn^4)$ for some $c < 5.61804$. With the same bounds on the running time we can construct data structures which allow fast enumeration of the respective classes. For example, after $O(2^nn^4)$ time of preprocessing we can enumerate the set of all crossing-free perfect matchings using polynomial time per enumerated object. For crossing-free perfect matchings and convex partitions we further obtain enumeration algorithms where the time delay for each (in particular, the first) output is bounded by a polynomial in $n$. All described algorithms are comparatively simple, both in terms of their analysis and implementation

A Case For Negative & General Facts

In this paper I take a closer look at Bertrand Russell's ontology of facts, pro- posed in his 1918 lectures on "The Philosophy of Logical Atomism". Part II is devoted to the question what Russell considered facts to be, and what kinds of facts he assumed. In part III, the controversy over two kinds of facts Russell postulates is described; the opinions of Raphael Demos and Keith Halbasch are considered for this purpose. Following this discussion, part IV investigates the question as to what kind of analysis Russell is conducting that leads him to negative and general facts. Finally, in part V, my conclusions drawn from the combined information of parts II to IV are elaborated; the main claim being, that due to the kind of analysis Russell is conducting, he is not making a mis- take when he assumes negative and general facts

The Optimal Design of Rewards in Contests

Using contests to generate innovation has and is widely used. Such contests often involve offering a prize that depends upon the accomplishment (effort). Using an all-pay auction as a model of a contest, we determine the optimal reward for inducing innovation. In a symmetric environment, we find that the reward should be set to c(x)/c′(x) where c is the cost of producing an innovation of level x. In an asymmetric environment with two firms, we find that it is optimal to set different rewards for each firm. There are cases where this can be replicated by a single reward that depends upon accomplishments of both contestants.contests; innovation; mechanism design

Implementing Cooperative Solution Concepts: A Generalized Bidding Approach

This paper provides a framework for implementing and comparing several solution concepts for transferable utility cooperative games.We construct bidding mechanisms where players bid for the role of the proposer.The mechanisms differ in the power awarded to the proposer.The Shapley, consensus and equal surplus values are implemented in subgame perfect equilibrium outcomes as power shifts away from the proposer to the rest of the players.Moreover, an alternative informational structure where these solution concepts can be implemented without imposing any conditions of the transferable utility game is discussed as well.implementation;bidding mechanism;Shapley value;consensus value;equal surplus value

What are ‘true’ loyal consumers in the food sector? Insights from an empirical study

Because loyal consumers are less likely to switch to competitors and because they are more tolerant to increases in price than non-loyal consumers, one of the main aims of firms is the “generation” of loyal consumers. But what is consumer loyalty? The marketing literature emphasises that for “true loyalty” it is important to consider both consumers' purchasing pattern (i.e. repurchases) as well as the underlying attitudes of the consumers. Thus, true loyalty includes both a behavioural (purchase) component, which results in repeated purchases, and an attitudinal component, which results in a dispositional commitment to a product, a brand, or a company, and associates a unique value to it. However, considering the characteristics of food products and the sector the question arises whether the above mentioned strict definition of true consumer loyalty is realistic in the food sector. The aim of our paper is to empirically test this question. In order to test our research question we conduct 30 semi-structured in-death interviews with regular customers of an organic retail shop in March / April 2009. Each interview lasts for roughly thirty minutes.Consumer loyalty, food sector, survey, organic products, Agricultural and Food Policy,

Implementation of the Ordinal Shapley Value for a three-agent economy

We propose a simple mechanism that implements the Ordinal Shapley Value (Pérez-Castrillo and Wettstein 2005) for economies with three or less agents.

Implementation of the Ordinal Shapley Value for a three-agent economy

We propose a simple mechanism that implements the Ordinal Shapley Value (Pérez-Castrillo and Wettstein [2005]) for economies with three or less agents.Ordinal Shapley Value, implementation, mechanism design

In whose backyard? A generalized bidding approach

We analyze situations in which a group of agents (and possibly a designer) have to reach a decision that will affect all the agents. Examples of such scenarios are the location of a nuclear reactor or the siting of a major sport event. To address the problem of reaching a decision, we propose a one-stage multi-bidding mechanism where agents compete for the project by submitting bids. All Nash equilibria of this mechanism are efficient. Moreover, the payoffs attained in equilibrium by the agents satisfy intuitively appealing lower bounds..externalities, bidding, implementation

An Ordinal Shapley Value for Economic Environments (Revised Version)

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.Non-Transferable utility games, Shapley value, Ordinal Shapley value, consistency, fairness.