在受互联网交换点（IXP）启发的群体形成游戏中形成更好的稳定解决方案
Forming better stable solutions in Group Formation Games inspired by Internet Exchange Points (IXPs)
摘要：
我们研究了一个由互联网交换点（IXPs）形成的协调博弈，代理选择加入哪些设施。加入与您通信的其他代理相同的设施有好处，但不同的设施对每个代理有不同的成本。因此，玩家希望加入与他们的“朋友”相同的设施，但这是通过他们不想支付加入设施的费用来平衡的。我们首先证明了这个博弈的稳定价格（$PoS$）最多为2，更一般地说，总是存在一个$α$-近似均衡，成本最多为最优的$\frac{2}α$。然后，我们专注于如何形成更好的稳定解决方案。如果我们允许代理支付他们的邻居，以防止他们偏离（即，玩家$i$自愿支付另一玩家$j$，使得$j$加入相同的设施），那么我们提供一种支付方案，其以最小的社会成本$s^*$稳定解决方案，即PoS为1。在我们的主要技术结果中，我们考虑了为了形成良好的稳定解决方案，中央协调器必须支付玩家多少钱。令$Δ$表示为了稳定$s^*$而需要支付给玩家的支付总额，即，如果玩家改变了他们在$s^*$中的策略，那么这些支付将失去。我们证明了$Δ$和稳定的代价：$\fracΔ{cost(s^*)} \le 1 - \frac{2}{5} PoS$之间存在一个折衷。因此，当不存在良好的稳定解时，仅需要少量的额外支付来稳定$s^*$;并且当良好的稳定解已经存在时（即，$PoS$很小），那么我们应该对这些解决方案感到满意。最后，我们考虑了求解最优解$s^*$的计算复杂性，设计了一个多项式时间的$O(\log n)$近似算法。
英文摘要：
We study a coordination game motivated by the formation of Internet Exchange Points (IXPs), in which agents choose which facilities to join. Joining the same facility as other agents you communicate with has benefits, but different facilities have different costs for each agent. Thus, the players wish to join the same facilities as their "friends", but this is balanced by them not wanting to pay the cost of joining a facility. We first show that the Price of Stability ($PoS$) of this game is at most 2, and more generally there always exists an $α$-approximate equilibrium with cost at most $\frac{2}α$ of optimum. We then focus on how better stable solutions can be formed. If we allow agents to pay their neighbors to prevent them from deviating (i.e., a player $i$ voluntarily pays another player $j$ so that $j$ joins the same facility), then we provide a payment scheme which stabilizes the solution with minimum social cost $s^*$, i.e. PoS is 1. In our main technical result, we consider how much a central coordinator would have to pay the players in order to form good stable solutions. Let $Δ$ denote the total amount of payments needed to be paid to the players in order to stabilize $s^*$, i.e., these are payments that a player would lose if they changed their strategy from the one in $s^*$. We prove that there is a tradeoff between $Δ$ and the Price of Stability: $\fracΔ{cost(s^*)} \le 1 - \frac{2}{5} PoS$. Thus when there are no good stable solutions, only a small amount of extra payment is needed to stabilize $s^*$; and when good stable solutions already exist (i.e., $PoS$ is small), then we should be happy with those solutions instead. Finally, we consider the computational complexity of finding the optimum solution $s^*$, and design a polynomial time $O(\log n)$ approximation algorithm for this problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
