摘要翻译:
在两人零和图游戏中,玩家在图中移动令牌以产生无限路径,这决定了游戏的赢家或收益。传统上,玩家轮流移动令牌。然而,在{\em竞标游戏}中,玩家有预算,在每一轮中,我们举行一次“拍卖”(竞标)来确定哪个玩家移动代币:两个玩家同时提交出价,出价较高的玩家移动代币。投标机制的付款方式不同。竞标博弈主要研究了{\em第一价格}竞标的变体,在这种变体中,只有较高的出价者支付他的出价。我们专注于{\em全付}出价,其中双方玩家支付他们的出价。研究了有限持续时间的全薪竞标游戏,并表明比第一价格竞标游戏在技术上更具挑战性。我们首次研究了无限时长全付费竞标游戏。我们最有趣的结果是关于{\em均值-回报}目标:我们刻画了强连通图上博弈的完整图像。我们研究了纯(确定性)和混合(概率)策略,并完全刻画了参与者可以分别保证的最优肯定和几乎肯定(概率$1$)收益。我们证明了全报酬竞价下的平均报酬博弈表现出其第一价格对应方的有趣的数学性质;也就是说,与{\em随机回合游戏}等价,在每一回合中,移动的玩家是根据(有偏差的)掷硬币来选择的。全薪竞标的等价物比一价竞标更复杂,也更出乎意料。
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英文标题:
《Infinite-Duration All-Pay Bidding Games》
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作者:
Guy Avni, Isma\"el Jecker, {\DJ}or{\dj}e \v{Z}ikeli\'c
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最新提交年份:
2020
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分类信息:
一级分类:Economics 经济学
二级分类:Theoretical Economics 理论经济学
分类描述:Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类:Computer Science 计算机科学
二级分类:Computer Science and Game Theory 计算机科学与博弈论
分类描述:Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面,包括机制设计的工作,游戏中的学习(可能与学习重叠),游戏中的agent建模的基础(可能与多agent系统重叠),非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类:Computer Science 计算机科学
二级分类:Logic in Computer Science 计算机科学中的逻辑
分类描述:Covers all aspects of logic in computer science, including finite model theory, logics of programs, modal logic, and program verification. Programming language semantics should have Programming Languages as the primary subject area. Roughly includes material in ACM Subject Classes D.2.4, F.3.1, F.4.0, F.4.1, and F.4.2; some material in F.4.3 (formal languages) may also be appropriate here, although Computational Complexity is typically the more appropriate subject area.
涵盖计算机科学中逻辑的所有方面,包括有限模型理论,程序逻辑,模态逻辑和程序验证。程序设计语言语义学应该把程序设计语言作为主要的学科领域。大致包括ACM学科类D.2.4、F.3.1、F.4.0、F.4.1和F.4.2中的材料;F.4.3(形式语言)中的一些材料在这里也可能是合适的,尽管计算复杂性通常是更合适的主题领域。
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英文摘要:
In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In {\em bidding games}, however, the players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token: both players simultaneously submit bids and the higher bidder moves the token. The bidding mechanisms differ in their payment schemes. Bidding games were largely studied with variants of {\em first-price} bidding in which only the higher bidder pays his bid. We focus on {\em all-pay} bidding, where both players pay their bids. Finite-duration all-pay bidding games were studied and shown to be technically more challenging than their first-price counterparts. We study for the first time, infinite-duration all-pay bidding games. Our most interesting results are for {\em mean-payoff} objectives: we portray a complete picture for games played on strongly-connected graphs. We study both pure (deterministic) and mixed (probabilistic) strategies and completely characterize the optimal sure and almost-sure (with probability $1$) payoffs that the players can respectively guarantee. We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical properties of their first-price counterparts; namely, an equivalence with {\em random-turn games} in which in each turn, the player who moves is selected according to a (biased) coin toss. The equivalences for all-pay bidding are more intricate and unexpected than for first-price bidding.
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PDF链接:
https://arxiv.org/pdf/2005.06636