2,088 research outputs found
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
A survey of random processes with reinforcement
The models surveyed include generalized P\'{o}lya urns, reinforced random
walks, interacting urn models, and continuous reinforced processes. Emphasis is
on methods and results, with sketches provided of some proofs. Applications are
discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A cognitive hierarchy theory of one-shot games: Some preliminary results
Strategic thinking, best-response, and mutual consistency (equilibrium) are three
key modelling principles in noncooperative game theory. This paper relaxes mutual
consistency to predict how players are likely to behave in in one-shot games before they
can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model
to predict behavior in one-shot games, and initial conditions in repeated games. The CH
approach assumes that players use k steps of reasoning with frequency f (k). Zero-step
players randomize. Players using k (≥ 1) steps best respond given partially rational
expectations about what players doing 0 through k - 1 steps actually choose. A simple
axiom which expresses the intuition that steps of thinking are increasingly constrained by
working memory, implies that f (k) has a Poisson distribution (characterized by a mean
number of thinking steps Ď„ ). The CH model converges to dominance-solvable equilibria
when Ď„ is large, predicts monotonic entry in binary entry games for Ď„ < 1:25, and predicts
effects of group size which are not predicted by Nash equilibrium. Best-fitting values of
Ď„ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental
samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable
p-beauty contests. The CH model also has economic value because subjects would have
raised their earnings substantially if they had best-responded to model forecasts instead
of making the choices they did
Where do mistakes lead? A survey of games with incompetent players
Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings
Modeling the Psychology of Consumer and Firm Behavior with Behavioral Economics
Marketing is an applied science that tries to explain and influence how firms and
consumers actually behave in markets. Marketing models are usually applications of
economic theories. These theories are general and produce precise predictions, but they
rely on strong assumptions of rationality of consumers and firms. Theories based on
rationality limits could prove similarly general and precise, while grounding theories in
psychological plausibility and explaining facts which are puzzles for the standard
approach.
Behavioral economics explores the implications of limits of rationality. The goal is to
make economic theories more plausible while maintaining formal power and accurate
prediction of field data. This review focuses selectively on six types of models used in
behavioral economics that can be applied to marketing.
Three of the models generalize consumer preference to allow (1) sensitivity to reference
points (and loss-aversion); (2) social preferences toward outcomes of others; and (3)
preference for instant gratification (quasi-hyperbolic discounting). The three models are
applied to industrial channel bargaining, salesforce compensation, and pricing of virtuous
goods such as gym memberships. The other three models generalize the concept of gametheoretic
equilibrium, allowing decision makers to make mistakes (quantal response
equilibrium), encounter limits on the depth of strategic thinking (cognitive hierarchy),
and equilibrate by learning from feedback (self-tuning EWA). These are applied to
marketing strategy problems involving differentiated products, competitive entry into
large and small markets, and low-price guarantees.
The main goal of this selected review is to encourage marketing researchers of all kinds
to apply these tools to marketing. Understanding the models and applying them is a
technical challenge for marketing modelers, which also requires thoughtful input from
psychologists studying details of consumer behavior. As a result, models like these could
create a common language for modelers who prize formality and psychologists who prize
realism
Generalized asset integrity games
Generalized assets represent a class of multi-scale adaptive state-transition systems with domain-oblivious performance criteria. The governance of such assets must proceed without exact specifications, objectives, or constraints. Decision making must rapidly scale in the presence of uncertainty, complexity, and intelligent adversaries.
This thesis formulates an architecture for generalized asset planning. Assets are modelled as dynamical graph structures which admit topological performance indicators, such as dependability, resilience, and efficiency. These metrics are used to construct robust model configurations. A normalized compression distance (NCD) is computed between a given active/live asset model and a reference configuration to produce an integrity score. The utility derived from the asset is monotonically proportional to this integrity score, which represents the proximity to ideal conditions. The present work considers the situation between an asset manager and an intelligent adversary, who act within a stochastic environment to control the integrity state of the asset. A generalized asset integrity game engine (GAIGE) is developed, which implements anytime algorithms to solve a stochastically perturbed two-player zero-sum game. The resulting planning strategies seek to stabilize deviations from minimax trajectories of the integrity score.
Results demonstrate the performance and scalability of the GAIGE. This approach represents a first-step towards domain-oblivious architectures for complex asset governance and anytime planning
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