发表机构
The Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev（内盖夫本古里安大学斯坦计算机与信息科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带奖励的离散穷汉竞价博弈（DPBGr）因配置图无限带来的挑战，引入消除次优插入序列的技术，通过近似连续竞价博弈求解，还讨论了保证可达性玩家获胜的策略子类，其成员归属属NP问题。
AI 中文摘要
竞价博弈是一种图博弈，其中代币被放置在一个顶点上，每个玩家都有初始预算，同时进行的拍卖决定哪个玩家移动代币；随后玩家的预算会相应更新。受资源分配系统等场景的启发，在这类场景中，智能体在争夺控制权时会获得周期性奖励（如信用点、能量），我们引入并研究带奖励的竞价博弈，在该博弈中，玩家在每个顶点都可能获得额外预算，以激励期望的行为。我们聚焦于带奖励的离散穷汉竞价博弈（DPBGr）的可达性问题。与无奖励的离散竞价博弈相比，主要挑战在于配置图是无限的。为此，我们引入一种新技术来消除具有次优插入序列的博弈过程，这使得我们可以将注意力集中在无限配置图的有限部分，以便通过近似连续竞价博弈来求解该博弈，整体复杂度为指数时间（EXP）。最后，我们讨论了一种新型策略，可用于DPBGr的一个子类，该策略能为可达性玩家保证获胜策略，且该子类的成员归属问题属于NP问题。
英文摘要
Bidding games are graph games in which a token is placed on a vertex, each player starts with an initial budget, and a simultaneous auction determines which player moves the token; the players' budgets are then updated accordingly. Motivated by scenarios such as resource-allocation systems in which agents receive periodic rewards (e.g., credits, energy) while competing for control, we introduce and study bidding games with rewards, in which, at each vertex, players may receive additional budget, incentivizing desired behaviors. We focus on reachability discrete poorman bidding games with rewards (DPBGr). The main challenge when compared to discrete bidding games without rewards is that the configuration graph is infinite. To this end we introduce a novel technique to eliminate plays with suboptimal infixes. This enables focusing on a finite part of the infinite configuration graph in order to solve the game via approximation to continuous bidding games with overall complexity in EXP. Finally, we discuss a new type of strategy, usable on a subclass of DPBGr, which guarantee a winning strategy for the reachability player. Membership in this subclass is shown to be in NP.
