On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Eigenvalues and expansion of regular graphs
Journal of the ACM (JACM)
On the emergence of social conventions: modeling, analysis, and simulations
Artificial Intelligence - Special issue on economic principles of multi-agent systems
Glauber Dynamics onTrees and Hyperbolic Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Convergence of the Iterated Prisoner's Dilemma Game
Combinatorics, Probability and Computing
On the Dynamics of Social Balance on General Networks (with an application to XOR-SAT)
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Theoretical Computer Science
On the Dynamics of Social Balance on General Networks (with an application to XOR-SAT)
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Adversarial scheduling in discrete models of social dynamics
Mathematical Structures in Computer Science
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We consider a group of agents on a graph who repeatedly play the prisoner's dilemma game against their neighbors. The players adapt their actions to the past behavior of their opponents by applying the win-stay lose-shift strategy. On a finite connected graph, it is easy to see that the system learns to cooperate by converging to the all-cooperate state in a finite time. We analyze the rate of convergence in terms of the size and structure of the graph. Dyer et al. (2002) showed that the system converges rapidly on the cycle, but that it takes a time exponential in the size of the graph to converge to cooperation on the complete graph. We show that the emergence of cooperation is exponentially slow in some expander graphs. More surprisingly, we show that it is also exponentially slow in bounded-degree trees, where many other dynamics are known to converge rapidly.