The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the agents all share the same subset of the cake which must be chosen subject to a length constraint. We focus on the design of truthful and fair mechanisms in the presence of strategic agents who have piecewise uniform utilities over the cake. On the one hand, we show that the leximin solution is truthful and moreover maximizes an egalitarian welfare measure among all truthful and position oblivious mechanisms. On the other hand, we demonstrate that the maximum Nash welfare solution is truthful for two agents but not in general. Our results assume that mechanisms can block each agent from accessing parts that the agent does not claim to desire; we provide an impossibility result when blocking is not allowed.

翻译：典型的蛋糕切除问题涉及在感兴趣的代理人之间公平分配不同资源的问题。 在本文中,我们研究了这一问题的公益物变种,在这种变种中,代理人不为蛋糕而相互竞争,而是都分享蛋糕中必须经过长时间限制才能选择的同一部分。我们侧重于设计真实和公平的机制,在战略代理人面前,他们拥有对蛋糕的零碎统一设施。一方面,我们表明法理解决办法是真实的,而且最大限度地在所有诚实和立场不明的机制中实现平等福利措施。另一方面,我们证明纳什的最大福利办法对两个代理人来说是真实的,而不是一般而言。我们的结果假定,机制可以阻止每个代理人接触代理人并不声称想要的部件;我们提出在不允许阻塞的情况下不可能实现的结果。