Richard Baron

Control costs and potential functions for spatial games

AbstractVan Damme and Weibull (1998, 2002) model the noise in games as endogenously determined tremble probabilities, by assuming that with some effort players can control the probability of implementing the intended strategy. Following their methodology, we derive logit-like adjustment rules for games played on quasi-symmetric weighted graphs and explore the properties of the ensuing Markov chain.

Complexity and stochastic evolution of dyadic networks

A strategic model of network formation is developed which permits unreliable links and organizational costs. Finding a connected Nash network which guarantees a given payoff to each player proves to be an NP-hard problem. For the associated evolutionary game with asynchronous updating and logit updating rules, the stochastically stable networks are characterized.The organization of agents into networks has an important role in the communication of information within a spatial structure. One goal is to understand how such networks form and evolve over time. Our agents are endowed with some information which can be accessed by other agents forming links with them. Link formation is costly and communication not fully reliable. We model the process of network formation as a non-cooperative game, and we then focus on Nash networks. But, showing existence of a Nash network with particular properties and computing one are two different tasks. The aim of this paper is to show that computing a connected Nash network is a computationally demanding optimization problem. The question then arises what outcomes might be chosen by agents who would like to form a connected Nash network but fail to achieve their goal because of computational limitations. We propose a stochastic evolutionary model. By solving a companion global optimization problem, this model selects a subset of Nash networks referred to as the set of stochastically stable networks.

Stochastic Evolutionary Game Theory

This chapter first gives an overview of some developments in the area of adaptive learning in games. Next, we present a general framework to model adaptive learning processes with persistent noise, and define the notion of stochastic stability. We provide several leading examples.

A Geometric Examination of Majorities Based on Difference in Support

Reciprocal preferences have been introduced in the literature of social choice theory in order to deal with preference intensities. They allow individuals to show preference intensities in the unit interval among each pair of options. In this framework, majority based on difference in support can be used as a method of aggregation of individual preferences into a collective preference: option a is preferred to option b if the sum of the intensities for a exceeds the aggregated intensity of b in a threshold given by a real number located between 0 and the total number of voters. Based on a three dimensional geometric approach, we provide a geometric analysis of the non transitivity of the collective preference relations obtained by majority rule based on difference in support. This aspect is studied by assuming that each individual reciprocal preference satisfies a g-stochastic transitivity property, which is stronger than the usual notion of transitivity