Hindsight and Sequential Rationality of Correlated Play

Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach has been less effective at producing competent players in general-sum games or those with more than two players than in two-player, zero-sum games. An appealing alternative is to consider adaptive algorithms that ensure strong performance in hindsight relative to what could have been achieved with modified behavior. This approach also leads to a game-theoretic analysis, but in the correlated play that arises from joint learning dynamics rather than factored agent behavior at equilibrium. We develop and advocate for this hindsight rationality framing of learning in general sequential decision-making settings. To this end, we re-examine mediated equilibrium and deviation types in extensive-form games, thereby gaining a more complete understanding and resolving past misconceptions. We present a set of examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature, and prove that no tractable concept subsumes all others. This line of inquiry culminates in the definition of the deviation and equilibrium classes that correspond to algorithms in the counterfactual regret minimization (CFR) family, relating them to all others in the literature. Examining CFR in greater detail further leads to a new recursive definition of rationality in correlated play that extends sequential rationality in a way that naturally applies to hindsight evaluation.Comment: Technical report for a paper in the proceedings of the thirty-fifth AAAI Conference on Artificial Intelligence (AAAI-21), February 2-9, 2021, Virtual. 26 pages and 15 figure

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Destroy to save

We study the problem of allocating m identical items among n>m agents with unit demand and private value for consuming the good. We allow payments and focus on dominant-strategy implementation. In the absence of an auctioneer who can absorb payments collected from the agents, the payments must be burnt to support dominant-strategy implementation.Recent work modified the classic VCG mechanism by redistributing as much of the payments as possible back to the agents while still satisfying incentive constraints. This approach guarantees allocative efficiency, but in some cases a large percentage of social welfare is lost. In this paper, we provide a mechanism that is not allocatively efficient but is instead guaranteed to achieve at least 80% of the social welfare as n??. Moreover, in the extreme case of m=n?1 where VCG-based mechanisms provide zero welfare, the percentage of social welfare maintained by our mechanism asymptotically approaches 100

ABSTRACT

��� � �Ò�ÓÖÑ�Ø�ÓÒ �Ò � ÐÓÛ �Ò�ÓÖÑ�Ø�ÓÒ ×�ØØ�Ò� × ÁØ � × ×�ÓÛÒ Ú� � ×�ÑÙÐ�Ø�ÓÒ × Ø��Ø Ø� � ÐÓÒ � ÖÙÒ �ÑÔ�Ö � �Ð �Ö�ÕÙ�Ò �� × Ó� ÔÖ � � × �Ò � Ñ�Ö��Ø Ó � ÒÓ Ö��Ö�Ø ÔÖ � ��ÓØ × �Ò ÓÒÚ�Ö� � ØÓ �ÕÙ�Ð��Ö� � �Ö��ØÖ�Ö�ÐÝ ÐÓ× � ØÓ �Ò �×ÝÑÑ�ØÖ � Æ�× � �ÕÙ�Ð�� Ö�ÙÑ � �ÓÛ�Ú�Ö �Ò×Ø�ÒØ�Ò�ÓÙ × ÔÖ � � ��×ØÖ��ÙØ�ÓÒ × Ò�� � ÒÓØ ÓÒÚ�Ö�