We propose an oligopoly model where players can choose between two kinds of behaviors, denoted as cooperative and aggressive, respectively. Each cooperative agent chooses the quantity to produce in order to maximize her own profit as well as the profits of other agents (at least partially), whereas an aggressive player decides the quantity to produce by maximizing his own profit while damaging (at least partially) competitors’ profits. At each discrete time, players face a binary choice to select the kind of behavior to adopt, according to a proportional imitation rule, expressed by a replicator equation based on a comparison between accumulated profits. This means that the behavioral decisions are driven by an evolutionary process where fitness is measured in terms of current profits as well as a weighted sum of past gains. The model proposed is expressed by a nonlinear two-dimensional iterated map, whose asymptotic behavior describes the long-run population distribution of cooperative and aggressive agents. We show under which conditions one of the following long-run behaviors prevails: (i) all players choose the same strategy; (ii) both behaviors coexist according to a mixed stationary equilibrium; and (iii) a self-sustained (i.e. endogenous) oscillatory (periodic or chaotic) time pattern occurs. The influence of memory and that of the levels of cooperative/aggressive attitudes on the dynamics are analyzed as well.

我们提出了一种寡头垄断模型，参与者可以在两种行为之间进行选择，分别表示为合作行为和进取行为。每个合作社代理人选择生产数量以最大化自己的利润以及其他代理人的利润（至少部分），而积极进取的参与者通过在损害（至少部分）的同时最大化自身利润来决定生产数量。竞争对手的利润。在每个离散的时间，参与者面对一个二进制选择，以根据比例模仿规则选择一种行为类型，该行为由复制者方程式表示，该方程式基于累积利润之间的比较。这意味着行为决策是由进化过程驱动的，在进化过程中，适合度是根据当前利润以及过去收益的加权总和来衡量的。提出的模型由非线性二维迭代图表示，该图的渐近行为描述了协作和攻击性代理的长期种群分布。我们显示在以下条件下盛行的下列长期行为之一：（i）所有参与者都选择相同的策略；（ii）两种行为根据混合平稳平衡共存；（iii）出现了自我维持的（即内生的）振荡（周期性或混沌）时间模式。还分析了记忆以及合作/攻击态度水平对动力学的影响。（i）所有参与者都选择相同的策略；（ii）两种行为根据混合平稳平衡共存；（iii）出现了自我维持的（即内生的）振荡（周期性或混沌）时间模式。还分析了记忆以及合作/攻击态度水平对动力学的影响。（i）所有参与者都选择相同的策略；（ii）两种行为根据混合平稳平衡共存；（iii）出现了自我维持的（即内生的）振荡（周期性或混沌）时间模式。还分析了记忆以及合作/攻击态度水平对动力学的影响。