Stability of dining clubs in the Kolkata Paise Restaurant Problem with and without cheating
Stability of dining clubs in the Kolkata Paise Restaurant Problem with and without cheating
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DOI：
10.1016/j.physa.2023.128767
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发表时间：
2023-02
期刊：
影响因子：
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通讯作者：
Akshat Harlalka;A. Belmonte;C. Griffin
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文献类型：
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作者：
Akshat Harlalka;A. Belmonte;C. Griffin
我们将餐饮俱乐部的理念引入到加尔各答Paise餐厅问题中。在这个问题中，N个智能体在N家餐馆中（随机）选择，但如果多个智能体选择同一家餐馆，只有一个会吃。餐饮俱乐部中的代理会协调他们的餐厅选择，避免选择冲突，增加他们的用餐概率。我们将是否加入餐饮俱乐部的问题建模为一个进化博弈，并证明了加入餐饮俱乐部的策略是进化稳定的。然后，我们向就餐俱乐部的个人引入了一种优化的会员税，用于为那些因与非就餐俱乐部成员发生碰撞而不吃饭的团体成员提供安全网。当非用餐俱乐部成员被允许在用餐俱乐部内欺骗和分享公共食物时，我们表明在动态中出现了一个新的不稳定不动点。在这种情况下执行分岔分析。为了总结我们的理论研究，我们引入了作弊群体的进化动力学，并研究了这些动力学。数值实验说明了该系统在多个餐饮俱乐部中的行为，并显示了未来研究的几个潜在领域。
We introduce the idea of a dining club to the Kolkata Paise Restaurant Problem. In this problem, N agents choose (randomly) among N restaurants, but if multiple agents choose the same restaurant, only one will eat. Agents in the dining club will coordinate their restaurant choice to avoid choice collision and increase their probability of eating. We model the problem of deciding whether to join the dining club as an evolutionary game and show that the strategy of joining the dining club is evolutionarily stable. We then introduce an optimized member tax to those individuals in the dining club, which is used to provide a safety net for those group members who do not eat because of collision with a non-dining club member. When non-dining club members are allowed to cheat and share communal food within the dining club, we show that a new unstable fixed point emerges in the dynamics. A bifurcation analysis is performed in this case. To conclude our theoretical study, we then introduce evolutionary dynamics for the cheater population and study these dynamics. Numerical experiments illustrate the behaviour of the system with more than one dining club and show several potential areas for future research.