A Belief-based Approach to Network Formation

In this paper we consider four different game-theoretic approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider Jackson-Wolinsky’s concept of pairwise stability. Next, we introduce a stronger version of this concept based on linking decisions by nodes, denoted as strict pairwise stability. Third, we consider Myerson’s consent game and its Nash equilibria. Fourth, within the context of Myerson’s consent game, we consider self-confirming equilibria based on simple myopic belief systems. We provide an exhaustive comparison of the classes of equilibrium networks that result from each of these four approaches. We determine the conditions under which there is equivalence of pairwise stability and strict pairwise stability. Second, we show that the Nash equilibria of Myerson’s consent game form a super set of the class of pairwise stable networks, while strict pairwise stability and monadic stability are fully equivalent.

Generosity

We develop a simple model of generous behavior. It is based on the premise that some people are generous, but everyone wants to appear generous. Although non-monetary donations are always inefficient, our model predicts donors to favor non-monetary donations when the inefficiency is relatively small and when the recipient is sufficiently rich. The model helps to explain the prevalence of volunteering, the nature of Christmas gifts, and the taboo against paying cash in return for friendly favors. The model also explains why it is socially more acceptable to ask for favors than for money.Altruism; Non-monetary gifts; Volunteering

Strategic Interaction in the Sex Market

There have been few attempts to empirically explain the pursuit of short term relationships and sex in a formal context. Previous work has lamented the paucity of empirical studies which utilize incentive driven behavior to draw conclusions and recommend policy. We develop a model of social network formation through sexual matching, provide an empirical approach derived from the model and apply it to a population of high interest. Specifically, we apply the approach to a population of sexually active men who have sex with men (MSM) in a large metropolitan area and derive qualitative conclusions regarding how individuals behave in the marketplace for sex

Players with limited memory

This paper studies a model of memory. The model takes into account that memory capacity is limited and imperfect. We study how agents with such memory limitations, who have very little information about their choice environment, play games. We introduce the notion of a Limited Memory Equilibrium (LME) and show that play converges to an LME in every generic normal form game. Our characterization of the set of LME suggests that players with limited memory do (weakly) better in games than in decision problems. We also show that agents can do quite well even with severely limited memory, although severe limitations tend to make them behave cautiously

Statistical Mechanics of maximal independent sets

The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints. It is known that finding minimum and maximum-density maximal independent sets are hard optimization problems. In this paper, we use cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs. We obtain the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks, shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms. This is of particular relevance for the application to the study of strategic interactions in social and economic networks, where maximal independent sets correspond to pure Nash equilibria of a graphical game of public goods allocation

Uncertainty and the management of multi-state ecosystems : an apparently rational route to collapse

environmental policy;ecology;management;decision making

The Role of Beliefs and Confidence in Building Social Networks

We examine the process of building social relationships in a non-cooperative game where such link formation is costly and requires mutual consent. We provide a noncooperative foundation for several link-based network stability concepts that have been studied in the literature on network formation. In our model players form myopic beliefs about the feasibility of building direct relationships with their acquaintances. These beliefs represent how each neighbor of a player is expected to respond to the initiation of a link by that player. We introduce a stability concept called “monadic stability” where agents play a best response to their formed myopic beliefs such that these beliefs are self-confirming. The resulting equilibrium networks form a class of networks that are shown to have some very appealing properties.