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Average Case Performance of Replicator Dynamics in Potential Games via Computing Regions of Attraction [article]

Ioannis Panageas, Georgios Piliouras
2016 arXiv   pre-print
Computing regions of attraction: Given point-wise convergence can we compute the region of asymptotic stability of each equilibrium (e.g., estimate its volume, geometry)?  ...  The golden standard typically is the behavior of learning dynamics in potential games, where many evolutionary dynamics, e.g., replicator, are known to converge to sets of equilibria.  ...  Acknowledgments The authors would like to thank Iosif Pinelis for the proof of Claim 8.8.  ... 
arXiv:1403.3885v6 fatcat:7su2bhez7zevlaebpnwr7lqisq

Ordinal Imitative Dynamics [article]

George Loginov
2019 arXiv   pre-print
In other cases, the IBR dynamics exhibits behaviors that are impossible under the replicator dynamics.  ...  In Rock-Paper-Scissors games we conjecture that both dynamics exhibit the same types of behavior, but the partitions of the game set do not coincide.  ...  We also conjecture that they generate the same types of behavior in Rock-Paper-Scissors games. In other cases, the IBR dynamics can generate behavior that is impossible under the replicator dynamics.  ... 
arXiv:1907.04272v1 fatcat:ndxto42dwretxmaf3ut4oq3ezy

Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory [article]

Stefanos Leonardos, Georgios Piliouras
2020 arXiv   pre-print
to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents.  ...  In our main task, we then turn to measure the effect of exploration in collective system performance.  ...  Bounded Regret in All Games and Convergence in Weighted Potential Games Our first observation is that the SQL dynamics in (1) can be considered as replicator dynamics in a modified game with the same sets  ... 
arXiv:2012.03083v2 fatcat:4gf4oayirjaofcswgkr5vxzbeu

Evolutionary Game Theory [chapter]

William H. Sandholm
2012 Computational Complexity  
Glossary 2 I Definition and Importance 3 * The figures in Sections VII and IX were created using Dynamo [184] and VirtualLabs [92], respectively.  ...  Thus, in potential games, very mild conditions on agents' adjustment rules are sufficient to justify the prediction of Nash equilibrium play. In the case of the replicator dynamic, one can say more.  ...  Figure 4 :Figure 5 : 45 Solutions of the Smith dynamic in (i) the potential game F 0 ; (ii) the perturbed potential game F ε , Chaotic behavior under the replicator dynamic.  ... 
doi:10.1007/978-1-4614-1800-9_63 fatcat:bekfkq5dhbc3zfvix63yokxyfm

Population Games and Deterministic Evolutionary Dynamics [chapter]

William H. Sandholm
2015 Handbook of Game Theory with Economic Applications  
Combining these streams, we consider classes of population games in which members of these families of dynamics converge to equilibrium; these classes include potential games, contractive games, games  ...  In this chapter, we provide an overview of the theory of population games and deterministic evolutionary dynamics.  ...  In words, the augmented gameF is a full potential game, and its full potential function is the average payoff function of the original game F.  ... 
doi:10.1016/b978-0-444-53766-9.00013-6 fatcat:tgrp7uklrzechcdohflynznvoa

Complex dynamics in learning complicated games

Tobias Galla, J. Doyne Farmer
2013 Proceedings of the National Academy of Sciences of the United States of America  
In case (iii), the dimension of the chaotic attractors can be very high, implying that the learning dynamics are effectively random.  ...  We investigate two-person games in which the players learn based on a type of reinforcement learning called experience-weighted attraction (EWA).  ...  For example, in SI Appendix, see our discussion of 2 × 2 games under replicator dynamics (SI Appendix, section II).  ... 
doi:10.1073/pnas.1109672110 pmid:23297213 pmcid:PMC3557065 fatcat:upcygztnvjejpahxuxhdfi2m7i

The route to chaos in routing games: When is Price of Anarchy too optimistic? [article]

Thiparat Chotibut, Fryderyk Falniowski, Michał Misiurewicz, Georgios Piliouras
2019 arXiv   pre-print
In this work, we perform a stress test for these classic results by studying the ubiquitous dynamics, Multiplicative Weights Update, in different classes of congestion games, uncovering intricate non-equilibrium  ...  As the system demand increases, the learning dynamics go through period-doubling bifurcations, leading to instabilities, chaos and large inefficiencies even in the simplest case of non-atomic routing games  ...  [79] showed analytically by computing the Lyapunov exponents of the system that even in a simple two-player game of rock-paper-scissor, replicator dynamics (the continuous-time analogue of MWU) can  ... 
arXiv:1906.02486v2 fatcat:tbsgjgv57fhbletfa7hopzof3e

Dynamics of service selection and provider pricing game in heterogeneous cloud market

Cuong T. Do, Nguyen H. Tran, Eui-Nam Huh, Choong Seon Hong, Dusit Niyato, Zhu Han
2016 Journal of Network and Computer Applications  
Furthermore, we use the Wardrop equilibrium and replicator dynamics to determine the equilibrium and its convergence properties of the service selection game.  ...  Numerical results illustrate that our game models can provide comprehensive understanding of the heterogeneous CSPs market and service selection in cloud computing.  ...  We used the Wardrop equilibrium concept and replicator dynamics to compute the equilibrium and characterized its convergence properties in the service selection game.  ... 
doi:10.1016/j.jnca.2016.04.012 fatcat:cditcbzpj5bpxjmyo56tpfeqbm

Stochastic evolution in populations of ideas

Robin Nicole, Peter Sollich, Tobias Galla
2017 Scientific Reports  
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas.  ...  We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.  ...  Stochastic dynamics in finite populations: the case of symmetric games Birth-death dynamics.  ... 
doi:10.1038/srep40580 pmid:28098244 pmcid:PMC5241820 fatcat:kvgxcyi5ezf7fcvcwzbxual5ly

Optimal Price Strategy Selection for MVNOs in Spectrum Sharing: An Evolutionary Game Approach

Shasha Zhao
2012 KSII Transactions on Internet and Information Systems  
The behavior dynamics and the evolutionary stable strategy (ESS) of the operators are derived via replicated dynamics.  ...  The evolutionary game theory (EGT) is employed to model the dynamic price strategy selection of the MVNOs taking into account the response of the secondary users.  ...  We consider the case that the two MVNOs lease the temporarily unused wireless spectrum and then dynamically compete via price strategy to serve the potential secondary users.  ... 
doi:10.3837/tiis.2012.12.006 fatcat:ska3uzovavhmtgzt4xiuvyz6qa

Evolutionary dynamics, intrinsic noise, and cycles of cooperation

Alex J. Bladon, Tobias Galla, Alan J. McKane
2010 Physical Review E  
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma  ...  game.  ...  Canonical replicator-mutator equation Within the standard replicator dynamics of evolutionary game theory the time evolution of the concentration of a strategy i is given by ͓28͔ ẋ i = x i ͑f i ϱ − ϱ ͒  ... 
doi:10.1103/physreve.81.066122 pmid:20866493 fatcat:dwg73xn5h5hv5ph7ezyf2z4uq4

Escalation of Coevolutionary Arms Races

Kyle Harrington
2016 Figshare  
In a signaling game from evolutionary game theory we show how parameters of evolutionary dynamics influence the reachability of evolutionary equilibria.  ...  S, (2014) "Escalation of Coevolutionary Arms Races". In Department of Computer Science, Brandeis University.  ...  We showed that GA-based finite population models can fail to capture the dynamics of hybrid equilibria , one of the most attractive dynamics of the SPS game.  ... 
doi:10.6084/m9.figshare.3146824.v1 fatcat:ahpantix6nf6fbzsxyc66kqukm

A decision support system for coordinated disaster relief distribution

Christian Fikar, Manfred Gronalt, Patrick Hirsch
2016 Expert systems with applications  
Results show a significant reduction in average lead times when coordinating last-mile distribution during disasters.  ...  In particular, the impact of road closures on supply and optimal transfer points is analysed by considering road, off-road and air transportation.  ...  ACKNOWLEDGMENTS Financial support of the program KIRAS (project number 840 897) provided by the Austrian Federal Ministry for Transport, Innovation and Technology, is gratefully acknowledged.  ... 
doi:10.1016/j.eswa.2016.03.039 fatcat:stzu5437ofcydi4mg2fmjwtk5u

A Dynamic Resource Allocation Framework for Synchronizing Metaverse with IoT Service and Data [article]

Yue Han, Dusit Niyato, Cyril Leung, Chunyan Miao, Dong In Kim
2021 arXiv   pre-print
A key enabler of such virtual service is the digital twin, i.e., a digital replication of real-world entities in the Metaverse, e.g., city twin, avatars, etc.  ...  In this paper, we consider the scenario in which a group of IoT devices are employed by the Metaverse platform to collect such data on behalf of virtual service providers (VSPs).  ...  As such, the topic of Metaverse has attracted a lot of research attention, for its potential in service offerings in retailing [10] , gaming [11] , education [12] , and socialnetworking [1] .  ... 
arXiv:2111.00431v1 fatcat:antpbqfiz5btbefb55rpfaevvu

α-Rank: Multi-Agent Evaluation by Evolution [article]

Shayegan Omidshafiei, Christos Papadimitriou, Georgios Piliouras, Karl Tuyls, Mark Rowland, Jean-Baptiste Lespiau, Wojciech M. Czarnecki, Marc Lanctot, Julien Perolat, Remi Munos
2019 arXiv   pre-print
We introduce α-Rank, a principled evolutionary dynamics methodology for the evaluation and ranking of agents in large-scale multi-agent interactions, grounded in a novel dynamical game-theoretic solution  ...  profiles, whereas computing a Nash equilibrium for a general-sum game is known to be intractable.  ...  But unfortunately, this "convergence" is typically considered in the sense of time average; time averages can be useful for establishing performance bounds for games, but tell us little about actual system  ... 
arXiv:1903.01373v4 fatcat:p7qcpsvqsrctlhnocr5shaxfse
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