zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The evolution of conventions. (English) Zbl 0773.90101
Summary: Consider an $n$-person game that is played repeatedly, but by different agents. In each period, $n$ players are drawn at random from a large finite population. Each player chooses an optimal strategy based on a sample of information about what others players have done in the past. The sampling defines a stochastic process that, for a large class of games that includes coordination games and common interest games, converges almost surely to a pure strategy Nash equilibrium. Such an equilibrium can be interpreted as the “conventional” way of playing the game. If, in addition, the players sometimes experiment or make mistakes, then society occasionally switches from one convention to another. As the likelihood of mistakes goes to zero, only some conventions (equilibria) have positive probability in the limit. These are known as stochastically stable equilibria. They are essentially the same as the risk dominant equilibria in $2\times 2$ games, but for general games the two concepts differ. The stochastically stable equilibria are computed by finding a path of least resistance from every equilibrium to every other, and then finding the equilibrium that has lowest overall resistance. This is a special case of a general theorem on perturbed Markov processes that characterizes their stochastically stable states graph-theoretically.

91A15Stochastic games
91A20Multistage and repeated games
92D15Problems related to evolution
Full Text: DOI