投标组合博弈中的构造性比较

Risk-Free Bidding in Complement-Free Combinatorial Auctions

We study risk-free bidding strategies in combinatorial auctions with incomplete information. Specifically, what is the maximum profit that a complement-free (subadditive) bidder can guarantee in a multi-item combinatorial auction? Suppose there are $n$ bidders and $B_i$ is the value that bidder $i$ has for the entire set of items. We study the above problem from the perspective of the first bidder, Bidder~1. In this setting, the worst case profit guarantees arise in a duopsony, that is when $n=2$, so this problem then corresponds to playing an auction against a budgeted adversary with budget $…

Discrete Richman-bidding Scoring Games

We study zero-sum (combinatorial) games, within the framework of so-called Richman auctions (Lazarus et al. 1996) namely, we modify the alternating play scoring ruleset Cumulative Subtraction (CS) (Cohensius et al. 2019), to a discrete bidding scheme (similar to Develin and Payne 2010). Players bid to move and the player with the highest bid wins the move, and hands over the winning bidding amount to the other player. The new game is dubbed Bidding Cumulative Subtraction (BCS). In so-called unitary games, players remove exactly one item out of a single heap of identical items, until the heap i…

组合式多轮递增拍卖

The Combinatorial Multi-Round Ascending Auction

该研究针对新型拍卖形式CMRA，分析其多种事后均衡特征与脆弱性，提出可阻止无风险合谋且保留其他均衡的替代活动规则，并结合丹麦相关拍卖结果验证预测。

带项目投标的组合拍卖的最佳响应动态

Best-Response Dynamics in Combinatorial Auctions with Item Bidding

在一个组合拍卖与项目投标，代理人参与多个单一的第二价格拍卖一次。由于某些物品可能是替代品，代理人需要制定策略，以最大限度地提高其效用。许多结果表明，高福利可以通过这种方式实现，并给出了均衡时福利的界限。然而，最近有人提出批评，认为均衡很难计算，因此不太可能达到。在本文中，我们采取了不同的视角。我们研究简单的最佳反应动力学。也就是说，智能体被一个接一个地激活，并且每个被激活的智能体近视地将其策略更新为针对其他智能体的当前策略的最佳响应。通常，这些动态在收敛之前可能需要指数级的时间，或者它们可能根本不收敛。然而，正如我们所表明的，趋同甚至不是良好福利保障的必要条件。假设代理人的出价更新足够激进但不太激进，则在每个代理人至少更新一次他的出价之后，游戏将保持在良好的福利状态。更详细地说，我们表明，如果代理商有分数次加性估值，自然动态达到并保持在一个状态，提供了一个$1/3$近似的最佳福利后，每个代理人已经更新了他的出价至少一次。对于次加性估值，我们可以保证在$m$项目的情况下的$Ω(1/\log m)$近似值，该项目在每个代理人至少更新一次其出价之后以及之后的任何时间点应用。后一个界限是由一个否定的结果，表明没有一种最佳反应动态可以保证超过一个$o(\log \log m/\log m)$分数的最佳社会福利。

Bidding Games and Efficient Allocations

Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence of pure subgame-perfect equilibria (PSPE). In particular, we show that PSPEs form a semilattice, with a unique and natural \emph{Bottom Equilibrium}. Our main result shows that if only two actions available to the players in each node, then the Bottom Equilibrium has additional properties: (a) utilities are monotone in budget; (b) every outcome is Pareto-ef…

Strategy-Stealing is Non-Constructive

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually find a winning move in a game, when you know by strategy-stealing that one exists? We prove that this problem is PSPACE-hard already for Minimum Poset Games and Symmetric Maker-Maker Games, which are simple classes of games that capture two of the main types of strategy-stealing arguments in the current literature.

次可加组合拍卖的先知不等式

Prophet Inequalities for Subadditive Combinatorial Auctions

本文综述了次可加组合拍卖中的先知不等式，介绍了$O(\log m)$与$O(\log \log m)$界限的构造性明码标价机制，并重点解析了最新解决常数因子先知不等式核心开放问题的非构造性方法。

Online Learning with Simple Predictors and a Combinatorial Characterization of Minimax in 0/1 Games

Which classes can be learned properly in the online model? -- that is, by an algorithm that at each round uses a predictor from the concept class. While there are simple and natural cases where improper learning is necessary, it is natural to ask how complex must the improper predictors be in such cases. Can one always achieve nearly optimal mistake/regret bounds using "simple" predictors? In this work, we give a complete characterization of when this is possible, thus settling an open problem which has been studied since the pioneering works of Angluin (1987) and Littlestone (1988). More prec…