Population Games And Evolutionary Dynamics

By William H. Sandholm. 2010

1,578 citations recorded by the source corpus.

Subfields: Game & Decision Theory, Evolutionary Computation

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Citations in the corpus

OpenSpiel: A Framework for Reinforcement Learning in Games (2019, methodology): “This is equivalent to updating the policy of a parameterized replicator dynamics from evolutionary game theory [27, 61] using an Euler discretization.”
Sampling best response dynamics and deterministic equilibrium selection (2015, methodology): “See Sandholm (2010b) for accounts of these and other examples.”
Cycles in adversarial regularized learning (2017, background): “The resulting FoReL dynamics enjoy a particularly strong O(t−1) regret minimization rate and they capture as a special case the replicator dynamics [38, 44, 45] and the projection dynamics [12, 24, 36], arguably the most widely studied game dynamics in biology, evolutionary game theory and transport”
On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning (2017, background): “Let x = σ ( z ) , then we have, We note that this is precisely the matrix term appearing in the replicator dynamics [2, p. 229], [45], that is, where x ∈ ∆ n − 1 is a mixed strategy and u ∈ n is a payoff vector .”
Unity in Diversity? How Intergroup Contact Can Foster Nation Building (2019, positive): “The probability of revisions is proportional to the difference between K and their current payoff (Sandholm, 2010). (4)Note that a slightly different setup would consider the revision timing to reflect a birth and death process. Instead of living forever, individuals have survival probabilities of t”
The Interface Theory of Perception (2009, neutral): “Evolution by natural selection can be studied using mathematical tools such as evolutionary game theory, evolutionary graph theory, and genetic algorithms (Hofbauer and Sigmund 1998; Mitchell 1998; Lieberman et al. 2005; Nowak 2006; Samuelson 1997; Sandholm 2007).”
The replicator equation and other game dynamics (2014, background): “Following Sandholm (10), it is a strictly stable game and so has a unique ESS p* which is globally asymptotically stable under the replicator equation (as well as many other game dynamics).”
α-Rank: Multi-Agent Evaluation by Evolution (2019, background): “Since solutions in the neighborhood of an asymptotically stable set, all approach the set, volume is contracted in this neighborhood, however, replicator dynamics is volume preserving in the interior of the state space [44, 106, 107]; the formal argument works by transforming the system induces by t”
Evolutionary game dynamics (2011, background): “The dynamic describes how the strategy distribution in a large population of players changes over time, due to selection, imitation or other kinds of adaptation [4,5,7,8].”
Actor-Critic Policy Optimization in Partially Observable Multiagent Environments (2018, background): “In Figure 1, we see the similarity of the regret dynamics to replicator dynamics [88, 75].”
Re-evaluating evaluation (2018, background): “Perturbed best response converges to a more stable approximation to Nash [65,66] that unfortunately is not invariant.”
Opinion Dynamics and Learning in Social Networks (2011, background): “In replicator dynamics, just as in genetic evolution, particular actions or beliefs that have performed better in the past are more likely to replicate and their fraction in the population increases (e.g., [79, 80 , 92]).”
Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling (2020, background): “Perhaps the most prominent of these failures is the appearance of cycles [4, 6, 7, 20, 21] and, potentially, the transition to aperiodic orbits and chaos [3, 8, 28, 29, 31].”
Human strategy updating in evolutionary games (2010, methodology): “In our case with two strategies only, this is equivalent to the multinomial logit model [35, 36].”
What Can Be Learned from Spatial Economics? (2019, positive): “Such games always have a Nash equilibrium in pure strategies and display convenient properties (Sandholm 2010). the role of transport networks.”