大联盟会形成吗？嵌套绑定协议动态过程中的持续性、到达性与分享规则的作用
Does the grand coalition form? Persistence, arrival, and the role of the sharing rule in a dynamic process of nested binding agreements
中文总结 AI 辅助
该研究在嵌套绑定协议动态过程中，证明大状态与吸收态的等价性，给出大状态几乎必然形成的三种情况，构造反例表明4参与者下大联盟未必形成，相关问题可判定且部分仍待研究。
中文摘要 AI 辅助
我们研究了Konishi和Ray（2003）传统下的动态联盟形成过程：参与者反复形成和解散绑定协议，通过贴现长期期望收益评估状态，并对该过程持有自我确认信念。状态与收益分配遵循Heitzig和Kornek（2018）的设定：状态是嵌套协议的层级结构；协议通过合并现有顶层联盟形成，且会与所有包含它们的协议一同终止；新协议的成员按该协议产生的剩余进行分配，剩余以无该协议时的状态为基准衡量。所有收益假设均为结构性假设。我们证明，对于任意贴现因子，所有达到过的大状态都是吸收态，且所有吸收态都是大状态。在三种情况下，大状态几乎必然会被达到：贴现因子较小；参与者数量为3；以及对于任意参与者数量和所有贴现因子，当每个参与者在静态收益中都偏好所有大状态甚于所有非大状态时，比如当分配利益小于每个参与者在效率收益中的份额时。否则，该过程可能仅在非大状态间无限循环而无法达到大状态。我们给出了此类循环的精确必要条件，并表明对于固定的候选循环，这些条件可简化为静态收益的有限线性不等式系统，因此该问题是可判定的。求解该问题得到一个反例：在4个参与者、贴现因子为1/2的情况下，无论采用哪种终止规则，都存在一个无限循环的均衡，因此大联盟未必形成。该例子在一种更具远见的分享规则变体下仍然成立，该变体下合并会提高每个参与者的贴现长期收益，而非仅静态收益；此时合并被纯粹因某个子组可获得更好的行动所阻碍。当贴现因子趋近于1时，到达性是否会失效仍有待研究。
英文摘要
We study a dynamic coalition-formation process in the tradition of Konishi and Ray (2003): players repeatedly form and dissolve binding agreements, evaluate states by discounted long-term expected payoffs, and hold self-confirming beliefs about the process. States and payoff sharing follow Heitzig and Kornek (2018): a state is a hierarchy of nested agreements, and the members of a new agreement share the surplus it generates, measured against the state without that agreement. All payoff assumptions are structural. We prove that every grand state ever reached is absorbing, and that every absorbing state is grand, for every discount factor. A grand state is actually reached, almost surely, for small discount factors, for three players, and, at every discount factor, whenever distributional stakes are smaller than each player s share of the efficiency gain. Otherwise the process can fail only by cycling for ever among non-grand states. We give exact necessary conditions on such a cycle, decidable for a fixed candidate cycle by linear programming, and exhibit, under an earlier and weaker notion of profitability, a four-player payoff structure whose only closed class is a cycle of two pairs forming and dissolving alternately. Under the present definition, and under either termination rule, no equilibrium traverses a cycle on a fixed schedule: somebody always reaches a state they would rather not leave, and the axioms give them the floor. Whether arrival can fail by cycling at random is open. The axioms are not merely postulated: we exhibit a bargaining game proposal, amendment by substitutes voted on by their own signatories, final unanimity, and an arbitrarily small delay on failure whose equilibria satisfy them as the delay vanishes, and which settles each period in its first round.
