Truthful Transaction Protocol for E-Commerce Networks Based on Double Auction

Sun, Jiachen; Ge, Ning; Chen, Xu; Feng, Wei; Lu, Jianhua

doi:10.1109/tnse.2022.3218642

Cited by 1 publication

(1 citation statement)

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“…In the absence of mathematical tools for evolutionary graph theory in multi-strategy multiplayer games, recent studies have attempted to bypass this challenge by incorporating the third strategy within the existing two strategies. For instance, punishing or rewarding behaviors have been added to the existing cooperation strategy in the traditional two-strategy system 55 , 56 . This approach allows for the examination of additional mechanisms like punishment and reward within the two-strategy system’s framework.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary dynamics of any multiplayer game on regular graphs

Wang,

Perc,

Szolnoki

2024

Nat Commun

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Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs.

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Section: Introductionmentioning

confidence: 99%