Document Type


Publication Date


Publication Title

New Journal of Physics


Department of Mathematics

Additional Department

Geisel School of Medicine


In some scenarios ('anti-coordination games'), individuals are better off choosing different actions than their neighbors while in other scenarios ('coordination games'), it is beneficial for individuals to choose the same strategy as their neighbors. Despite having different incentives and resulting population dynamics, it is largely unknown which collective outcome, anti-coordination or coordination, is easier to achieve. To address this issue, we focus on the distributed graph coloring problem on bipartite graphs.We show that with only two strategies, anti-coordination games (two-colorings) and coordination games (uniform colorings) are dual problems that are equally difficult to solve. To prove this, we construct an isomorphism between the Markov chains arising from the corresponding anti-coordination and coordination games under certain specific individual stochastic decision-making rules. Our results provide novel insights into solving collective action problems on networks.



Original Citation

Matthew I Jones et al 2021 New J. Phys. 23 113018