8,859 research outputs found
Aspiration Dynamics of Multi-player Games in Finite Populations
Studying strategy update rules in the framework of evolutionary game theory,
one can differentiate between imitation processes and aspiration-driven
dynamics. In the former case, individuals imitate the strategy of a more
successful peer. In the latter case, individuals adjust their strategies based
on a comparison of their payoffs from the evolutionary game to a value they
aspire, called the level of aspiration. Unlike imitation processes of pairwise
comparison, aspiration-driven updates do not require additional information
about the strategic environment and can thus be interpreted as being more
spontaneous. Recent work has mainly focused on understanding how aspiration
dynamics alter the evolutionary outcome in structured populations. However, the
baseline case for understanding strategy selection is the well-mixed population
case, which is still lacking sufficient understanding. We explore how
aspiration-driven strategy-update dynamics under imperfect rationality
influence the average abundance of a strategy in multi-player evolutionary
games with two strategies. We analytically derive a condition under which a
strategy is more abundant than the other in the weak selection limiting case.
This approach has a long standing history in evolutionary game and is mostly
applied for its mathematical approachability. Hence, we also explore strong
selection numerically, which shows that our weak selection condition is a
robust predictor of the average abundance of a strategy. The condition turns
out to differ from that of a wide class of imitation dynamics, as long as the
game is not dyadic. Therefore a strategy favored under imitation dynamics can
be disfavored under aspiration dynamics. This does not require any population
structure thus highlights the intrinsic difference between imitation and
aspiration dynamics
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
Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out
This paper investigates the evolution of strategic play where players drawn
from a finite well-mixed population are offered the opportunity to play in a
public goods game. All players accept the offer. However, due to the
possibility of unforeseen circumstances, each player has a fixed probability of
being unable to participate in the game, unlike similar models which assume
voluntary participation. We first study how prescribed stochastic opting-out
affects cooperation in finite populations. Moreover, in the model, cooperation
is favored by natural selection over both neutral drift and defection if return
on investment exceeds a threshold value defined solely by the population size,
game size, and a player's probability of opting-out. Ultimately, increasing the
probability that each player is unable to fulfill her promise of participating
in the public goods game facilitates natural selection of cooperators. We also
use adaptive dynamics to study the coevolution of cooperation and opting-out
behavior. However, given rare mutations minutely different from the original
population, an analysis based on adaptive dynamics suggests that the over time
the population will tend towards complete defection and non-participation, and
subsequently, from there, participating cooperators will stand a chance to
emerge by neutral drift. Nevertheless, increasing the probability of
non-participation decreases the rate at which the population tends towards
defection when participating. Our work sheds light on understanding how
stochastic opting-out emerges in the first place and its role in the evolution
of cooperation.Comment: 30 pages, 4 figures. This is one of the student project papers arsing
from the Mathematics REU program at Dartmouth 2017 Summer. See
https://math.dartmouth.edu/~reu/ for more info. Comments are always welcom
Evolutionary Multiplayer Games
Evolutionary game theory has become one of the most diverse and far reaching
theories in biology. Applications of this theory range from cell dynamics to
social evolution. However, many applications make it clear that inherent
non-linearities of natural systems need to be taken into account. One way of
introducing such non-linearities into evolutionary games is by the inclusion of
multiple players. An example is of social dilemmas, where group benefits could
e.g.\ increase less than linear with the number of cooperators. Such
multiplayer games can be introduced in all the fields where evolutionary game
theory is already well established. However, the inclusion of non-linearities
can help to advance the analysis of systems which are known to be complex, e.g.
in the case of non-Mendelian inheritance. We review the diachronic theory and
applications of multiplayer evolutionary games and present the current state of
the field. Our aim is a summary of the theoretical results from well-mixed
populations in infinite as well as finite populations. We also discuss examples
from three fields where the theory has been successfully applied, ecology,
social sciences and population genetics. In closing, we probe certain future
directions which can be explored using the complexity of multiplayer games
while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape
Statics and dynamics of selfish interactions in distributed service systems
We study a class of games which model the competition among agents to access
some service provided by distributed service units and which exhibit congestion
and frustration phenomena when service units have limited capacity. We propose
a technique, based on the cavity method of statistical physics, to characterize
the full spectrum of Nash equilibria of the game. The analysis reveals a large
variety of equilibria, with very different statistical properties. Natural
selfish dynamics, such as best-response, usually tend to large-utility
equilibria, even though those of smaller utility are exponentially more
numerous. Interestingly, the latter actually can be reached by selecting the
initial conditions of the best-response dynamics close to the saturation limit
of the service unit capacities. We also study a more realistic stochastic
variant of the game by means of a simple and effective approximation of the
average over the random parameters, showing that the properties of the
average-case Nash equilibria are qualitatively similar to the deterministic
ones.Comment: 30 pages, 10 figure
Interbank lending with benchmark rates: Pareto optima for a class of singular control games
We analyze a class of stochastic differential games of singular control,
motivated by the study of a dynamic model of interbank lending with benchmark
rates. We describe Pareto optima for this game and show how they may be
achieved through the intervention of a regulator, whose policy is a solution to
a singular stochastic control problem. Pareto optima are characterized in terms
of the solutions to a new class of Skorokhod problems with piecewise-continuous
free boundary.
Pareto optimal policies are shown to correspond to the enforcement of
endogenous bounds on interbank lending rates. Analytical comparison between
Pareto optima and Nash equilibria provides insight into the impact of
regulatory intervention on the stability of interbank rates.Comment: 31 pages; 1 figur
Ramsey monetary policy and international relative prices
We analyze welfare maximizing monetary policy in a dynamic two-country model with price stickiness and imperfect competition. In this context, a typical terms of trade externality affects policy interaction between independent monetary authorities. Unlike the existing literature, we remain consistent to a public finance approach by an explicit consideration of all the distortions that are relevant to the Ramsey planner. This strategy entails two main advantages. First, it allows an accurate characterization of optimal policy in an economy that evolves around a steady-state which is not necessarily efficient. Second, it allows to describe a full range of alternative dynamic equilibria when price setters in both countries are completely forward-looking and households' preferences are not restricted. In this context, we study optimal policy both in the long-run and along a dynamic path, and we compare optimal commitment policy under Nash competition and under cooperation. By deriving a second order accurate solution to the policy functions, we also characterize the welfare gains from international policy cooperation. Klassifikation: E52, F41 . This version: January, 2004. First draft: October 2003
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