30,907 research outputs found
Common Knowledge and Interactive Behaviors: A Survey
This paper surveys the notion of common knowledge taken from game theory and computer science. It studies and illustrates more generally the effects of interactive knowledge in economic and social problems. First of all, common knowledge is shown to be a central concept and often a necessary condition for coordination, equilibrium achievement, agreement, and consensus. We present how common knowledge can be practically generated, for example, by particular advertisements or leadership. Secondly, we prove that common knowledge can be harmful, essentially in various cooperation and negotiation problems, and more generally when there are con icts of interest. Finally, in some asymmetric relationships, common knowledge is shown to be preferable for some players, but not for all. The ambiguous welfare effects of higher-order knowledge on interactive behaviors leads us to analyze the role of decentralized communication in order to deal with dynamic or endogenous information structures.Interactive knowledge, common knowledge, information structure, communication.
On the beliefs off the path: equilibrium refinement due to quantal response and level-k
This paper studies the relevance of equilibrium and nonequilibrium explanations of behavior, with respects to equilibrium refinement, as players gain experience. We investigate this experimentally using an incomplete information sequential move game with heterogeneous preferences and multiple perfect equilibria. Only the limit point of quantal response (the limiting logit equilibrium), and alternatively that of level-k reasoning (extensive form rationalizability), restricts beliefs off the equilibrium path. Both concepts converge to the same unique equilibrium, but the predictions differ prior to convergence. We show that with experience of repeated play in relatively constant environments, subjects approach equilibrium via the quantal response learning path. With experience spanning also across relatively novel environments, though, level-k reasoning tends to dominate
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
Collaboration in Social Networks
The very notion of social network implies that linked individuals interact
repeatedly with each other. This allows them not only to learn successful
strategies and adapt to them, but also to condition their own behavior on the
behavior of others, in a strategic forward looking manner. Game theory of
repeated games shows that these circumstances are conducive to the emergence of
collaboration in simple games of two players. We investigate the extension of
this concept to the case where players are engaged in a local contribution game
and show that rationality and credibility of threats identify a class of Nash
equilibria -- that we call "collaborative equilibria" -- that have a precise
interpretation in terms of sub-graphs of the social network. For large network
games, the number of such equilibria is exponentially large in the number of
players. When incentives to defect are small, equilibria are supported by local
structures whereas when incentives exceed a threshold they acquire a non-local
nature, which requires a "critical mass" of more than a given fraction of the
players to collaborate. Therefore, when incentives are high, an individual
deviation typically causes the collapse of collaboration across the whole
system. At the same time, higher incentives to defect typically support
equilibria with a higher density of collaborators. The resulting picture
conforms with several results in sociology and in the experimental literature
on game theory, such as the prevalence of collaboration in denser groups and in
the structural hubs of sparse networks
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