Wealth concentration in systems with unbiased binary exchanges

Taxes, Inequality, and Equal Opportunities

“…As we stressed before, numerical and analytical studies with the Yard-Sale model, as well as its variations, consistently lead to condensation. Recently, we have given a general proof that all models following a fair principle, including the Yard-Sale, inevitably lead to condensation [10,11]. To overcome this fate, different rules of interaction have been applied, for example increasing the probability of favoring the poorer agent in a transaction [19,20] or introducing a cut-off that avoids interactions between agents below and above this cut-off [29].…”

“…Even simple exchange models used in econophysics to simulate trade and economic exchanges demonstrate this phenomenon. In two recent papers [ 10 , 11 ], we have demonstrated that exchange models considered fair , where agents participating in trade have equal chances of earning money, inevitably lead to the total concentration of wealth in the hands of a single individual or a select few. Moreover, most microscopic models of exchange among economic agents exhibit this behavior (see ref.…”

Study of taxes, regulations and inequality using machine learning algorithms

“…It is relevant to know how successful is the solution found by the trained agents. For this purpose, we compare in figure 9 the average wealth obtained at every time-step for both, the trained and the untrained groups and for two distinct cases: in figure 9 a , the irrational agents behave randomly, changing their risk at every time-step, according to the model proposed in [16]. In figure 9 b , the irrational group comprises agents with fixed risks that were randomly chosen at the start of the simulation, as proposed in [13].…”

“…This rule is also called fair because the amount of wealth exchanged is the minimum of the amounts risked by the two agents, so it is the same regardless of who wins [14]. Also, the model is fair because the probability of winning is 50normal% for both agents, therefore the expected gain is the same for each of them [14,16]. However, numerical [11,15] and analytical [16–18] results obtained with the Yard–Sale rule (or variations thereof) confirm that the asymptotic state of the model is condensation, i.e.…”

“…Also, the model is fair because the probability of winning is 50normal% for both agents, therefore the expected gain is the same for each of them [14,16]. However, numerical [11,15] and analytical [16–18] results obtained with the Yard–Sale rule (or variations thereof) confirm that the asymptotic state of the model is condensation, i.e. all the wealth ends up in the hands of one or a very few agents.…”