In this work we consider an agent based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the mean strategy of the population satisfies an equation close to the classical replicator equation.
Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. If the equilibrium is a pure strategy, the wealth distribution is fixed after some transient time, and those players which are close to optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coefficients of the game matrix. We compute theoretically their second moment in this case.
The accumulation of individual fitness or wealth is modelled as a population game in which pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a constant background resource, and their fitness or wealth depreciates over time. For brevity we focus on the well-known Hawk-Dove game. In the base-line model, the probability of winning a fight (that is, when both play Hawk) is the same for both parties. In an extended version, the individual with higher current fitness or wealth has a higher probability of winni…
In a social dilemma game group members are allowed to decide if they contribute to the joint venture or not. As a consequence, defectors, who do not invest but only enjoy the mutual benefit, prevail and the system evolves onto the tragedy of the common state. This unfortunate scenario can be avoided if participation is not obligatory but only happens with a given probability. But what if we also consider a player's individual wealth when to decide about participation? To address this issue we propose a model in which the probabilistic participation in the public goods game is combined with a c…
A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payof…
We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale which defines the random fluctuations. Players with higher bank values are thus less likely to change strategy than players with lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or …
Public Goods Games represent one of the most useful tools to study group interactions between individuals. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not able to reproduce some key features observed in social and economical interactions. The typical shape of wealth distribution - known as Pareto Law - and the microscopic organization of wealth production are two of them. Here, we introduce a modification to the classical formulation of Public Goods Games that allows for the emergence of both of these features …
Modern economies evolved from simpler human exchanges into very convoluted systems. Today, a multitude of aspects can be regulated, tampered with, or left to chance; these are economic {\em degrees of freedom} which together shape the flow of wealth. Economic actors can exploit them, at a cost, and bend that flow in their favor. If intervention becomes widespread, microeconomic strategies of different actors can collide or resonate, building into macroeconomic effects. How viable is a `rigged' economy, and how is this viability affected by growing economic complexity and wealth? Here we captur…
We study the wealth distribution of UK households through a detailed analysis of data from wealth surveys and rich lists, and propose a non-linear Kesten process to model the dynamics of household wealth. The main features of our model are that we focus on wealth growth and disregard exchange, and that the rate of return on wealth is increasing with wealth. The linear case with wealth-independent return rate has been well studied, leading to a log-normal wealth distribution in the long time limit which is essentially independent of initial conditions. We find through theoretical analysis and s…
A Unified Framework for the Pareto Law and Matthew Effect using Scale-Free Networks
我们采用进化博弈的方式研究了无标度网络中的累积财富分布。该系统自组织到一个临界帕累托分布（1897）的财富$P(m)\sim m^{-(v+1)}$与$1.6 < v <2.0$（这是在协议与美国或日本）。特别是，代理人的个人财富与其联系人数量成正比这种现象与社会、经济、科学等领域中存在的马太效应相吻合。虽然我们的模型比较简单，但它很好地代表了经济中的合作和利润积累行为，它将网络理论与经济物理学相结合。
A Fokker-Planck approach to a stochastic multiplicative wealth model with taxation and redistribution
Universidade Federal de Viçosa (UFV)（维索萨联邦大学）；Ibitipoca Institute of Physics (IbitiPhys)（伊比蒂波卡物理研究所）；Pontifícia Universidade Católica do Rio de Janeiro (PUC–Rio)（里约热内卢天主教大学）
We consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring. All other sources of wealth are neglected. We consider different societies characterized by a different offspring probability distribution. We find that, if the population remains constant, the society reaches a stationary wealth distribution. We show that inequality emerges every time the number of children per family is not always the same. For realistic …
Families form the basis of society, and anthropologists have characterised various family systems. This study developed a multi-level evolutionary model of pre-industrial agricultural societies to simulate the evolution of family systems and determine how each of them adapts to environmental conditions and forms a characteristic socio-economic structure. In the model, competing societies evolve, which themselves comprise multiple evolving families that grow through family labour. Each family has two strategy parameters: the time children leave the parental home and the distribution of inherita…
In the present paper, we identify several distributions from Physics and study their applicability to phenomena such as distribution of income, wealth, and expenditure. Firstly, we apply logistic distribution to these data and we find that it fits very well the annual data for the entire income interval including for upper income segment of population. Secondly, we apply Fermi-Dirac distribution to these data. We seek to explain possible correlations and analogies between economic systems and statistical thermodynamics systems. We try to explain their behavior and properties when we correlate …
