2,629 research outputs found
Static Stability in Games
Static stability of equilibrium in strategic games differs from dynamic stability in not being linked to any particular dynamical system. In other words, it does not make any assumptions about off-equilibrium behavior. Examples of static notions of stability include evolutionarily stable strategy (ESS) and continuously stable strategy (CSS), both of which are meaningful or justifiable only for particular classes of games, namely, symmetric multilinear games or symmetric games with a unidimensional strategy space, respectively. This paper presents a general notion of local static stability, of which the above two are essentially special cases. It is applicable to virtually all n-person strategic games, both symmetric and asymmetric, with non-discrete strategy spaces.Stability of equilibrium, static stability
Evolutionary Stability of First Price Auctions
This paper studies the evolutionary stability of the unique Nash equilibrium of a first price sealed bid auction. It is shown that the Nash equilibrium is not asymptotically stable under payoff monotonic dynamics for arbitrary initial popu- lations. In contrast, when the initial population includes a continuum of strategies around the equilibrium, the replicator dynamic does converge to the Nash equilibrium. Simulations are presented for the replicator and Brown-von Neumann-Nash dynamics. They suggest that the convergence for the replicator dynamic is slow compared to the Brown-von Neumann-Nash dynamics.
On the Stability of CSS under the Replicator Dynamic
This paper considers a two-player game with a one-dimensional continuous strategy. We study the asymptotic stability of equilibria under the replicator dynamic when the support of the initial population is an interval. We find that, under strategic complementarities, Continuously Stable Strategy (CSS) have the desired convergence properties using an iterated dominance argument. For general games, however, CSS can be unstable even for populations that have a continuous support. We present a sufficient condition for convergence based on elimination of iteratively dominated strategies. This condition is more restrictive than CSS in general but equivalent in the case of strategic complementarities. Finally, we offer several economic applications of our results.
Benefits of tolerance in public goods games
Leaving the joint enterprise when defection is unveiled is always a viable
option to avoid being exploited. Although loner strategy helps the population
not to be trapped into the tragedy of the commons state, it could offer only a
modest income for non-participants. In this paper we demonstrate that showing
some tolerance toward defectors could not only save cooperation in harsh
environments, but in fact results in a surprisingly high average payoff for
group members in public goods games. Phase diagrams and the underlying spatial
patterns reveal the high complexity of evolving states where cyclic dominant
strategies or two-strategy alliances can characterize the final state of
evolution. We identify microscopic mechanisms which are responsible for the
superiority of global solutions containing tolerant players. This phenomenon is
robust and can be observed both in well-mixed and in structured populations
highlighting the importance of tolerance in our everyday life.Comment: 10 two-column pages, 8 figures; accepted for publication in Physical
Review
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
Evolutionary establishment of moral and double moral standards through spatial interactions
Situations where individuals have to contribute to joint efforts or share
scarce resources are ubiquitous. Yet, without proper mechanisms to ensure
cooperation, the evolutionary pressure to maximize individual success tends to
create a tragedy of the commons (such as over-fishing or the destruction of our
environment). This contribution addresses a number of related puzzles of human
behavior with an evolutionary game theoretical approach as it has been
successfully used to explain the behavior of other biological species many
times, from bacteria to vertebrates. Our agent-based model distinguishes
individuals applying four different behavioral strategies: non-cooperative
individuals ("defectors"), cooperative individuals abstaining from punishment
efforts (called "cooperators" or "second-order free-riders"), cooperators who
punish non-cooperative behavior ("moralists"), and defectors, who punish other
defectors despite being non-cooperative themselves ("immoralists"). By
considering spatial interactions with neighboring individuals, our model
reveals several interesting effects: First, moralists can fully eliminate
cooperators. This spreading of punishing behavior requires a segregation of
behavioral strategies and solves the "second-order free-rider problem". Second,
the system behavior changes its character significantly even after very long
times ("who laughs last laughs best effect"). Third, the presence of a number
of defectors can largely accelerate the victory of moralists over non-punishing
cooperators. Forth, in order to succeed, moralists may profit from immoralists
in a way that appears like an "unholy collaboration". Our findings suggest that
the consideration of punishment strategies allows to understand the
establishment and spreading of "moral behavior" by means of game-theoretical
concepts. This demonstrates that quantitative biological modeling approaches
are powerful even in domains that have been addressed with non-mathematical
concepts so far. The complex dynamics of certain social behaviors becomes
understandable as result of an evolutionary competition between different
behavioral strategies.Comment: 15 pages, 5 figures; accepted for publication in PLoS Computational
Biology [supplementary material available at
http://www.soms.ethz.ch/research/secondorder-freeriders/ and
http://www.matjazperc.com/plos/moral.html
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