Serving by local consensus in the public service location game

Sun, Yifan; Zhou, Haijun

doi:10.1038/srep32502

Cited by 4 publications

(5 citation statements)

References 39 publications

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“…In agreement with the Edwards hypothesis, we use statistical-mechanics methods to evaluate the flat-measure statistical properties of Nash equilibria, even though this approach has to be combined with more proper characterizations that could take into account the effects of dynamical equilibrium selection as well. The cavity method was successfully used to study optimisation problems in finiteconnectivity graphs [29,115] and it was then employed to investigate the properties of Nash equilibria on networks for random games [140], public goods [44,159], cooperation problems [43] and congestion games [3].…”

Section: The Equilibrium Landscapementioning

confidence: 99%

Coordination problems on networks revisited: statics and dynamics

Dall'Asta

2021

Preprint

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Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of large-scale coordination events taking place abruptly, in the form of a cascade process, as a consequence of small perturbations of an apparently stable state. The conditions for the occurrence of cascade instabilities have been largely analysed in the literature, however for the same coordination models no sufficient attention was given to the relation between structural properties of (Nash) equilibria and possible outcomes of dynamical equilibrium selection. Using methods from the statistical physics of disordered systems, the present work investigates both analytically and numerically, the statistical properties of such Nash equilibria on networks, focusing mostly on random graphs. We provide an accurate description of these properties, which is then exploited to shed light on the mechanisms behind the onset of coordination/miscoordination on large networks. This is done studying the most common processes of dynamical equilibrium selection, such as best response, bounded-rational dynamics and learning processes. In particular, we show that well beyond the instability region, full coordination is still globally stochastically stable, however equilibrium selection processes with low stochasticity (e.g. best response) or strong memory effects (e.g. reinforcement learning) can be prevented from achieving full coordination by being trapped into a large (exponentially in number of agents) set of locally stable Nash equilibria at low/medium coordination (inefficient equilibria). These results should be useful to allow a better understanding of general coordination problems on complex networks. CONTENTS I. IntroductionII. A coordination model with heterogeneous payoffs III. Monotone decision processes A. Message-passing equations for minimal equilibria and global cascade condition B. Properties of the maximal equilibria IV. The equilibrium landscape A. Cavity method for Nash equilibria B. Results for random regular graphs C. Results on non-regular random graphs V. Dynamical equilibrium selection A. Best-response dynamics B. Stochastic stability C. Learning dynamics D. Comparative Statics: emergence of coordination on general random networks E. Payoff dominance vs. risk dominance VI. Conclusions

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Section: The Equilibrium Landscapementioning

confidence: 99%

Coordination problems on networks revisited: statics and dynamics

Dall'Asta

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In agreement with the Edwards hypothesis, we use statistical-mechanics methods to evaluate the flat-measure statistical properties of Nash equilibria, even though this approach has to be combined with more proper characterizations that could take into account the effects of dynamical equilibrium selection as well. The cavity method was successfully used to study optimisation problems in finite-connectivity graphs [40,41] and it was then employed to investigate the properties of Nash equilibria on networks for random games [42], public goods [43,44], cooperation problems [45] and congestion games [46].…”

Section: The Equilibrium Landscapementioning

confidence: 99%

Coordination problems on networks revisited: statics and dynamics

Dall’Asta¹

2021

J. Stat. Mech.

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Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of large-scale coordination events taking place abruptly, in the form of a cascade process, as a consequence of small perturbations of an apparently stable state. The conditions for the occurrence of cascade instabilities have been largely analysed in the literature, however for the same coordination models no sufficient attention was given to the relation between structural properties of (Nash) equilibria and possible outcomes of dynamical equilibrium selection. Using methods from the statistical physics of disordered systems, the present work investigates both analytically and numerically, the statistical properties of such Nash equilibria on networks, focussing mostly on random graphs. We provide an accurate description of these properties, which is then exploited to shed light on the mechanisms behind the onset of coordination/miscoordination on large networks. This is done studying the most common processes of dynamical equilibrium selection, such as best response, bounded-rational dynamics and learning processes. In particular, we show that well beyond the instability region, full coordination is still globally stochastically stable, however equilibrium selection processes with low stochasticity (e.g. best response) or strong memory effects (e.g. reinforcement learning) can be prevented from achieving full coordination by being trapped into a large (exponentially in number of agents) set of locally stable Nash equilibria at low/medium coordination (inefficient equilibria). These results should be useful to allow a better understanding of general coordination problems on complex networks.

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“…We consider two local algorithms, the greedy algorithm and the local-consensus algorithm, which have been shown to have comparative satisfactory performances in solving the MDS problem on both random-generated networks and real-world networks [16,17]. We generalize these two algorithms to the t-MDS problem.…”

Section: Local Algorithmsmentioning

confidence: 99%

“…To solve this problem, we need a decentralized algorithm. For the MDS problem, the first author and a collaborator proposed a decentralized local-consensus algorithm, which can lead to a DS with size approaching the smallest possible value for both random networks and real-world networks [17].…”

Section: Local-consensus Algorithmmentioning

confidence: 99%

“…The fields of mathematics and theoretical computer science focus on constructing various bounds on the size of the MDS and quantifying the complexity of solving MDS problem [14,15]. The field of physics, instead, pays more attention to analyzing the statistical properties of the MDS on various networks and designing heuristic algorithms to search for a near-optimal solution [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

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