Stability of strategies in payoff-driven evolutionary games on networks

Chaos

Volumn 21, Issue 3, 2011, Pages

  Sorrentino, Francesco ^a,b   Mecholsky, Nicholas ^b  

^a UNIVERSITY OF NAPLES PARTHENOPE   (Italy)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER SIMULATION; COOPERATION; EVOLUTION; GAME; HUMAN; THEORETICAL MODEL;

BIOLOGICAL EVOLUTION; COMPUTER SIMULATION; COOPERATIVE BEHAVIOR; GAME THEORY; HUMANS; MODELS, THEORETICAL;

EID: 80053388568     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3613924     Document Type: Article

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42. A classical model of this type involves replicator dynamics, which describes the time-evolution of frequencies of players who adopt given strategies in a large population. In general, such a macroscopic description is appropriate when the underlying social network is characterized by a mean-field type interaction and the number of agents is very large. The case of finite-size populations has been studied, e.g., in Ref. 37. The effects of departure from the well-mixed population assumption on the evolution of cooperation have been studied in Refs. 20, 21, and 38394041.
43. Answering this question is nontrivial, as we are putting ourselves in a typical situation characterized by limited information. In this paper, we focus on situations in which agents have to make decisions in the absence of information on their neighbors' strategies. Therefore, this kind of questions represents a motivation for our study. Moreover, we note that the fact that there is not an obvious answer to this question makes it an interesting subject of investigation.
44. In Appendix we show that the matrix B has at least one zero eigenvalue. Therefore, there is at least one eigenvector in the null subspace of the matrix B, other than the null vector ō.
45. Here, the location of a node in the network is identified by the nodes it is connected to.