Name
Abstract | ||
|---|---|---|
In evolutionary game theory, repeated two-player games are used to study
strategy evolution in a population under natural selection. As the evolution
greatly depends on the interaction structure, there has been growing interests
in studying the games on graphs. In this setting, players occupy the vertices
of a graph and play the game only with their immediate neighbours. Various
evolutionary dynamics have been studied in this setting for different games.
Due to the complexity of the analysis, however, most of the work in this area
is experimental. This paper aims to contribute to a more complete
understanding, by providing rigorous analysis. We study the imitation dynamics
on two classes of graph: cycles and complete graphs. We focus on three well
known social dilemmas, namely the Prisoner's Dilemma, the Stag Hunt and the
Snowdrift Game. We also consider, for completeness, the so-called Harmony Game.
Our analysis shows that, on the cycle, all four games converge fast, either to
total cooperation or total defection. On the complete graph, all but the
Snowdrift game converge fast, either to cooperation or defection. The Snowdrift
game reaches a metastable state fast, where cooperators and defectors coexist.
It will converge to cooperation or defection only after spending time in this
state which is exponential in the size, n, of the graph. In exceptional cases,
it will remain in this state indefinitely. Our theoretical results are
supported by experimental investigations. |
Year | Venue | Keywords |
|---|---|---|
2011 | Clinical Orthopaedics and Related Research | natural selection,social dilemma,evolutionary dynamics,game theory,prisoner s dilemma,complete graph,metastable state,evolutionary game theory |
Field | DocType | Volume |
Combinatorial game theory,Mathematical economics,Repeated game,Game theory,Symmetric game,Normal-form game,Sequential game,Non-cooperative game,Game tree,Mathematics | Journal | abs/1102.3 |
Citations | PageRank | References |
1 | 0.35 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Colin Cooper | 1 | 287 | 30.73 |
| Martin E. Dyer | 2 | 529 | 116.66 |
| Velumailum Mohanaraj | 3 | 4 | 1.12 |