Coalitional games are mathematical models suited to study payoff distribution problems in cooperative scenarios. In abstract terms, a coalitional game can be specified by explicitly listing all possible—in fact, exponentially many—coalitions with their associated distributions. This naïve representation, however, quickly becomes infeasible over games involving many agents, thereby calling for suitable compact representations, that is, encoding mechanisms that (on some specific classes of games of interest) take an amount of space that grows polynomially with the number of agents. To date, a plethora of compact encodings have been already introduced and analyzed from the algorithm and computational viewpoints. Despite their specific technical differences, these encodings typically share the assumption that the utility associated with a coalition can be freely transferred among agents. Indeed, designing encoding mechanisms for the non-transferable utility (NTU) setting is a research issue that has been largely unexplored so far.

The paper addresses this issue by proposing a compact encoding for representing and reasoning about the outcomes of NTU coalitional games founding on answer set programming. By exploiting the expressiveness of this well-known knowledge representation formalism, it is shown that the proposed representation can succinctly encode several games of interest within a wide range of application domains. Computational issues arising in the setting have been studied too, by addressing questions related to certain payoff distributions enjoying desirable stability properties. Eventually, a prototype system supporting the proposed framework has been implemented by leveraging a state-of-the-art answer set engine, and results of a thorough experimental activity conducted on top of it have been discussed.

联盟博弈是适合研究合作场景中收益分配问题的数学模型。抽象地说，可以通过明确列出所有可能的（实际上是指数级的）联盟及其相关分布来指定联盟博弈。然而，这种朴素的表示在涉及许多代理的游戏中很快变得不可行，因此需要合适的紧凑表示，即编码机制（在某些特定的感兴趣的游戏类别上）占用的空间量随着代理的数量呈多项式增长。迄今为止，已经从算法和计算的角度引入和分析了大量的紧凑编码。尽管存在特定的技术差异，但这些编码通常都假设与联盟相关的效用可以在代理之间自由转移。事实上，为不可转移效用 (NTU)设置设计编码机制是一个迄今为止尚未探索的研究问题。

本文通过提出一种紧凑的编码来解决这个问题，用于表示和推理基于答案集编程的 NTU 联盟游戏的结果。通过利用这种众所周知的知识表示形式的表现力，表明所提出的表示可以在广泛的应用领域内简洁地编码几个感兴趣的游戏。通过解决与某些具有理想稳定性属性的收益分布相关的问题，也研究了设置中出现的计算问题。最终，通过利用最先进的答案集引擎实现了支持所提出框架的原型系统，并讨论了在其之上进行的彻底实验活动的结果。