Technical supplement to “Population Games and Deterministic Evolutionary Dynamics”
نویسنده
چکیده
After 3.3: Ordinary differential equations . . . . . . . . . . . . . . . . . . . . . . 2 Before 5.1.3: Extinction and invariance under imitative dynamics . . . . . . . . . 3 With 5.1.3: Monotone percentage growth rates and positive correlation . . . . . . 3 With 5.1.3: Rest points and restricted equilibria . . . . . . . . . . . . . . . . . . . . 5 With 5.2.2: Construction of solutions of the best response dynamic . . . . . . . . . 5 With 5.2.3: More on perturbed best response dynamics . . . . . . . . . . . . . . . 6 With 5.3.1: Characterization of Nash equilibrium via excess payoffs . . . . . . . . 8 With 5.3.2: Analysis of pairwise comparison dynamics . . . . . . . . . . . . . . . 9 With 5.3.2: Multiple revision protocols and hybrid dynamics . . . . . . . . . . . . 11 With 6.3: Efficiency in homogeneous full potential games . . . . . . . . . . . . . . 11 After 6.4: Inefficiency and inefficiency bounds in congestion games . . . . . . . . 12 Before 6.5: Stability and recurrence for flows . . . . . . . . . . . . . . . . . . . . . 13 Before 6.5: Lyapunov functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 With 6.5: Global convergence and local stability in potential games . . . . . . . . 16 With 6.6: Local stability of strict equilibrium . . . . . . . . . . . . . . . . . . . . . 17 With 7.2: Differential characterization of contractive games . . . . . . . . . . . . . 18 After 7.4: Existence of Nash equilibrium in contractive games . . . . . . . . . . . 19 After 7.5: Linear differential equations . . . . . . . . . . . . . . . . . . . . . . . . 20 After 7.5: Linearization of nonlinear differential equations . . . . . . . . . . . . 22 After 7.5: Local stability of ESS via linearization . . . . . . . . . . . . . . . . . . . 23 With 7.5: More on global convergence in contractive games . . . . . . . . . . . . . 26 With 7.5: Local stability of ESS via Lyapunov functions . . . . . . . . . . . . . . . 30 With 8.1: More on strict dominance and imitative dynamics . . . . . . . . . . . . 31 With 8.3: More on iterated p-dominance and sampling best response dynamics . 32 With 8.3: A transitivity theorem for asymptotic stability . . . . . . . . . . . . . . 34 With 9.1: More on games with nonconvergent dynamics . . . . . . . . . . . . . . 34 With 9.1: Attractors and continuation . . . . . . . . . . . . . . . . . . . . . . . . . 38 With 9.1: The Poincaré-Bendixson theorem . . . . . . . . . . . . . . . . . . . . . . 38 With 9.2: More on survival of dominated strategies . . . . . . . . . . . . . . . . . 39
منابع مشابه
Population Games and Deterministic Evolutionary Dynamics
Population games describe strategic interactions among large numbers of small, anonymous agents. Behavior in these games is typically modeled dynamically, with agents occasionally receiving opportunities to switch strategies, basing their choices on simple myopic rules called revision protocols. Over finite time spans the evolution of aggregate behavior is well approximated by the solution of a...
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