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In our model, $n$ traders interact with each other and with a central bank; they are taxed on the money they make, some of which is dissipated away by corruption. A generic feature of our model is that the richest trader always wins by consuming all the others: another is the existence of a threshold wealth, below which all traders go bankrupt. The two-trader case is examined in detail,in the socialist and capitalist limits, which generalise easily to $n>2$. In its mean-field incarnation, our model exhibits a two-time-scale glassy dynamics, as well as an astonishing universality.When preference is given to local interactions in finite neighbourhoods,a novel feature emerges: instead of at most one overall winner in the system,finite numbers of winners emerge, each one the overlord of a particular region.The patterns formed by such winners (metastable states) are very much a consequence of initial conditions, so that the fate of the marketplace is ruled by its past history; hysteresis is thus also manifested.
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Proof-of-Work (PoW) is the most widely adopted incentive model in current blockchain systems, which unfortunately is energy inefficient. Proof-of-Stake (PoS) is then proposed to tackle the energy issue. The rich-get-richer concern of PoS has been heavily debated in the blockchain community. The debate is centered around the argument that whether rich miners possessing more stakes will obtain higher staking rewards and further increase their potential income in the future. In this paper, we define two types of fairness, i.e., expectational fairness and robust fairness, that are useful for answering this question. In particular, expectational fairness illustrates that the expected income of a miner is proportional to her initial investment, indicating that the expected return on investment is a constant. To better capture the uncertainty of mining outcomes, robust fairness is proposed to characterize whether the return on investment concentrates to a constant with high probability as time evolves. Our analysis shows that the classical PoW mechanism can always preserve both types of fairness as long as the mining game runs for a sufficiently long time. Furthermore, we observe that current PoS blockchains implement various incentive models and discuss three representatives, namely ML-PoS, SL-PoS and C-PoS. We find that (i) ML-PoS (e.g., Qtum and Blackcoin) preserves expectational fairness but may not achieve robust fairness, (ii) SL-PoS (e.g., NXT) does not protect any type of fairness, and (iii) C-PoS (e.g., Ethereum 2.0) outperforms ML-PoS in terms of robust fairness while still maintaining expectational fairness. Finally, massive experiments on real blockchain systems and extensive numerical simulations are performed to validate our analysis.
The rich-get-richer mechanism (agents increase their ``wealth randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree distribution of growing scale free nets. We use two different analytical approaches, as well as numerical simulations, to study the case where the number of agents is fixed and finite (but large), and the rich-get-richer mechanism is invoked a fraction r of the time (the remainder of the time wealth is disbursed by a homogeneous process). At short times, we recover the Pareto law observed for an unbounded number of agents. In later times, the (moving) distribution can be scaled to reveal a phase transition with a Gaussian asymptotic form for r < 1/2 and a Pareto-like tail (on the positive side) and a novel stretched exponential decay (on the negative side) for r > 1/2.
Standard economic theory, starting with Adam Smiths invisible hand, holds that those who trade for their own selfish motives of maximizing their private preferences may contribute more to the public wealth than those who claim altruistic motives. Under restrictive conditions, this has been shown to result from a self-organizing mechanism acting at the global system level, which ensures that optimal allocation of resources derives from competition within the rule of law. In a nutshell, according to this view, being competitively selfish adds value for all. But to what degree can doing good add competitive value to products and services? We propose the creation of the Donation-Payment card as a solution to the legal and moral issues plaguing the emerging anonymous, direct-to-consumer, stored-value prepaid (SVP) card market. Our proposal to redirect millions of dollars whose status is in conflict not only improves society and empowers people, but also represents the best free-market solution to the SVP-Cards industry. The Donation-Payment card kills two birds with one stone by marrying business interests with societal benefits. In addition, think of the state of mind of a grand-parent giving a SVP-card to a grand-child, who also feels like killing two birds with one stone or should we say more aptly feels like giving twice with one card.
Under preferential attachment (PA) network growth models late arrivals are at a disadvantage with regard to their final degrees. Previous extensions of PA have addressed this deficiency by either adding the notion of node fitness to PA, usually drawn from some fitness score distributions, or by using fitness alone to control attachment. Here we introduce a new dynamical approach to address late arrivals by adding a recent-degree-change bias to PA so that nodes with higher relative degree change in temporal proximity to an arriving node get an attachment probability boost. In other words, if PA describes a rich-get-richer mechanism, and fitness-based approaches describe good-get-richer mechanisms, then our model can be characterized as a hot-get-richer mechanism, where hotness is determined by the rate of degree change over some recent past. The proposed model produces much later high-ranking nodes than the PA model and, under certain parameters, produces networks with structure similar to PA networks.
This paper studies the structure of the Japanese production network, which includes one million firms and five million supplier-customer links. This study finds that this network forms a tightly-knit structure with a core giant strongly connected component (GSCC) surrounded by IN and OUT components constituting two half-shells of the GSCC, which we call atextit{walnut} structure because of its shape. The hierarchical structure of the communities is studied by the Infomap method, and most of the irreducible communities are found to be at the second level. The composition of some of the major communities, including overexpressions regarding their industrial or regional nature, and the connections that exist between the communities are studied in detail. The findings obtained here cause us to question the validity and accuracy of using the conventional input-output analysis, which is expected to be useful when firms in the same sectors are highly connected to each other.
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