Abstract
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for the prisoner’s dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 597-628 |
| Number of pages | 32 |
| Journal | SIAM Journal on Applied Dynamical Systems |
| Volume | 18 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 2019 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Modeling and Simulation
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Consensus and information cascades in game-theoretic imitation dynamics with static and dynamic network topologies. / Griffin, Christopher; Rajtmajer, Sarah; Squicciarini, Anna; Belmonte, Andrew.
In: SIAM Journal on Applied Dynamical Systems, Vol. 18, No. 2, 01.01.2019, p. 597-628.Research output: Contribution to journal › Article
TY - JOUR
T1 - Consensus and information cascades in game-theoretic imitation dynamics with static and dynamic network topologies
AU - Griffin, Christopher
AU - Rajtmajer, Sarah
AU - Squicciarini, Anna
AU - Belmonte, Andrew
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for the prisoner’s dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.
AB - We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for the prisoner’s dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.
UR - http://www.scopus.com/inward/record.url?scp=85065781321&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065781321&partnerID=8YFLogxK
U2 - 10.1137/16M109675X
DO - 10.1137/16M109675X
M3 - Article
AN - SCOPUS:85065781321
VL - 18
SP - 597
EP - 628
JO - SIAM Journal on Applied Dynamical Systems
JF - SIAM Journal on Applied Dynamical Systems
SN - 1536-0040
IS - 2
ER -