凹按比例游戏
Concave Pro-rata Games
摘要：
在本文中，我们介绍了一个家庭的游戏称为凹比例游戏。在这样的游戏中，玩家将他们的资产放入池中，池支付放入其中的所有资产的凹函数。然后每个玩家按比例获得支付份额;即，每个玩家收到与他们在池中放置的量成比例的量。这种游戏出现在许多实际场景中，包括作为批量分散交易所的简化版本，例如Penumbra提出的那些。我们表明，这个游戏有一些有趣的属性，包括一个对称的纯平衡，这是唯一的平衡，这个游戏，我们证明了它的无政府代价是$Ω(n)$的球员的数量。我们还展示了一些数值结果，在迭代设置这表明，球员很快收敛到一个平衡，在迭代播放。
英文摘要：
In this paper, we introduce a family of games called concave pro-rata games. In such a game, players place their assets into a pool, and the pool pays out some concave function of all assets placed into it. Each player then receives a pro-rata share of the payout; i.e., each player receives an amount proportional to how much they placed in the pool. Such games appear in a number of practical scenarios, including as a simplified version of batched decentralized exchanges, such as those proposed by Penumbra. We show that this game has a number of interesting properties, including a symmetric pure equilibrium that is the unique equilibrium of this game, and we prove that its price of anarchy is $Ω(n)$ in the number of players. We also show some numerical results in the iterated setting which suggest that players quickly converge to an equilibrium in iterated play.
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。
