AI 中文总结
研究资源稀缺与丰富对行为的影响，开发随机最后通牒博弈框架，发现恶意和公平的出现依赖资源增长率，高增长率时公平占优，低增长率时恶意驱动资源反馈循环促进公平。
AI 中文摘要
资源稀缺会从根本上助长反社会行为，而资源丰富则能促进公平行为。实验证据表明稀缺会引发恶意行为，反复互动会增强公平性。然而，现有博弈 - 环境反馈系统研究大多局限于合作演化，忽视了资源、恶意和公平之间的相互作用。为填补这一空白，我们开发了一个随机最后通牒博弈框架，其中提议者和接受者反复互动以协商对提议者拥有的可再生资源的开发利用。成功协议会消耗资源，失败协议则抑制开发并促进补充。突变 - 选择驱动的双物种随机进化动力学表明，恶意和公平的出现强烈依赖于资源增长率。高增长率资源中公平占主导。有趣的是，低资源增长率会引发由恶意驱动的资源反馈循环：恶意行为在资源耗尽状态占主导，促使资源状态转变为充足状态，进而通过反复互动促进公平。
英文摘要
Resource scarcity can fundamentally encourage antisocial behaviour, whereas resource abundance can promote fair behaviour. Experimental evidence indeed suggests that scarcity induces spiteful behaviour, while repeated interactions enhance fairness. However, existing studies of game--environment feedback systems are largely confined to the evolution of cooperation and they overlook the interplay between resources, spite, and fairness. To address this lacuna, we develop a stochastic ultimatum game framework in which an offerer and an accepter repeatedly interact to negotiate exploitation of a self-renewable resource under the ownership of the offerer. Successful agreements deplete the resource, whereas unsuccessful agreements inhibit exploitation and facilitate replenishment. The mutation--selection driven two-species stochastic evolutionary dynamics reveal that the emergence of spite and fairness strongly depends on the resource growth rate. Fairness predominantly prevails for resources with high growth rates. Intriguingly, low resource growth rates give rise to a resource feedback loop driven by spite: spiteful behaviour dominates in the depleted state, facilitating transition of the resource state to replete state which, in turn, promotes fairness through repeated interactions.
