Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead

Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding the model about the opponent. This paper is, to our knowledge, the first to investigate Stackelberg equilibria under uncertainty in extensive-form games, one of the broadest classes of game. We introduce robust Stackelberg equilibria, where the uncertainty is about the opponent's payoffs, as well as ones where the opponent has limited lookahead and the uncertainty is about the opponent's node evaluation function. We develop a new mixed-integer program for the deterministic limited-lookahead setting. We then extend the program to the robust setting for Stackelberg equilibrium under unlimited and under limited lookahead by the opponent. We show that for the specific case of interval uncertainty about the opponent's payoffs (or about the opponent's node evaluations in the case of limited lookahead), robust Stackelberg equilibria can be computed with a mixed-integer program that is of the same asymptotic size as that for the deterministic setting.Comment: Published at AAAI1

Stretchable, Self-Healing, and Remodelable Ionogel via In Situ Phase Separation as a Highly Sensitive Multimode Sensor

An ionogel with high mechanical performance, self-healing ability, adhesion, and remodelability is designed via a simple one-pot process. In situ phase separation occurred and enhanced the ionogel in the process of ultraviolet (UV)-induced polymerization based on the low solubility of poly(acrylic acid) (PAA) in ionic liquids. The degree of in situ phase separation can be regulated by the varying content of AA. By virtue of the admired performance, the resulting ionogel can detect not only mechanical strain or pressure signals to monitor external changes but also joint movements and even subtle changes in a person’s facial expressions with high sensitivity. In addition, it can be applied in a temperature sensor and exhibits a wide temperature detection range (0–120 °C) and a low threshold detection (0.1 °C). Therefore, the ionogels hold broad application prospects in flexible sensors, human–machine interfaces, and other fields

Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins

<i>meso</i>-Tetra­(<i>N</i>-methyl-4-pyridyl)­porphine tetratosylate (TMPyP) templates the synthesis of six new metal–organic materials by the reaction of benzene-1,3,5-tricarboxylate with transition metals, five of which exhibit HKUST-1 or <b>tbo</b> topology (M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in octahemioctahedral cages and can serve as size-selective heterogeneous catalysts for oxidation of olefins

Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins

<i>meso</i>-Tetra­(<i>N</i>-methyl-4-pyridyl)­porphine tetratosylate (TMPyP) templates the synthesis of six new metal–organic materials by the reaction of benzene-1,3,5-tricarboxylate with transition metals, five of which exhibit HKUST-1 or <b>tbo</b> topology (M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in octahemioctahedral cages and can serve as size-selective heterogeneous catalysts for oxidation of olefins

Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins

<i>meso</i>-Tetra­(<i>N</i>-methyl-4-pyridyl)­porphine tetratosylate (TMPyP) templates the synthesis of six new metal–organic materials by the reaction of benzene-1,3,5-tricarboxylate with transition metals, five of which exhibit HKUST-1 or <b>tbo</b> topology (M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in octahemioctahedral cages and can serve as size-selective heterogeneous catalysts for oxidation of olefins

Stretchable, Self-Healing, and Remodelable Ionogel via In Situ Phase Separation as a Highly Sensitive Multimode Sensor

An ionogel with high mechanical performance, self-healing ability, adhesion, and remodelability is designed via a simple one-pot process. In situ phase separation occurred and enhanced the ionogel in the process of ultraviolet (UV)-induced polymerization based on the low solubility of poly(acrylic acid) (PAA) in ionic liquids. The degree of in situ phase separation can be regulated by the varying content of AA. By virtue of the admired performance, the resulting ionogel can detect not only mechanical strain or pressure signals to monitor external changes but also joint movements and even subtle changes in a person’s facial expressions with high sensitivity. In addition, it can be applied in a temperature sensor and exhibits a wide temperature detection range (0–120 °C) and a low threshold detection (0.1 °C). Therefore, the ionogels hold broad application prospects in flexible sensors, human–machine interfaces, and other fields

Stretchable, Self-Healing, and Remodelable Ionogel via In Situ Phase Separation as a Highly Sensitive Multimode Sensor

An ionogel with high mechanical performance, self-healing ability, adhesion, and remodelability is designed via a simple one-pot process. In situ phase separation occurred and enhanced the ionogel in the process of ultraviolet (UV)-induced polymerization based on the low solubility of poly(acrylic acid) (PAA) in ionic liquids. The degree of in situ phase separation can be regulated by the varying content of AA. By virtue of the admired performance, the resulting ionogel can detect not only mechanical strain or pressure signals to monitor external changes but also joint movements and even subtle changes in a person’s facial expressions with high sensitivity. In addition, it can be applied in a temperature sensor and exhibits a wide temperature detection range (0–120 °C) and a low threshold detection (0.1 °C). Therefore, the ionogels hold broad application prospects in flexible sensors, human–machine interfaces, and other fields

Stretchable, Self-Healing, and Remodelable Ionogel via In Situ Phase Separation as a Highly Sensitive Multimode Sensor

An ionogel with high mechanical performance, self-healing ability, adhesion, and remodelability is designed via a simple one-pot process. In situ phase separation occurred and enhanced the ionogel in the process of ultraviolet (UV)-induced polymerization based on the low solubility of poly(acrylic acid) (PAA) in ionic liquids. The degree of in situ phase separation can be regulated by the varying content of AA. By virtue of the admired performance, the resulting ionogel can detect not only mechanical strain or pressure signals to monitor external changes but also joint movements and even subtle changes in a person’s facial expressions with high sensitivity. In addition, it can be applied in a temperature sensor and exhibits a wide temperature detection range (0–120 °C) and a low threshold detection (0.1 °C). Therefore, the ionogels hold broad application prospects in flexible sensors, human–machine interfaces, and other fields

Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins

<i>meso</i>-Tetra­(<i>N</i>-methyl-4-pyridyl)­porphine tetratosylate (TMPyP) templates the synthesis of six new metal–organic materials by the reaction of benzene-1,3,5-tricarboxylate with transition metals, five of which exhibit HKUST-1 or <b>tbo</b> topology (M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in octahemioctahedral cages and can serve as size-selective heterogeneous catalysts for oxidation of olefins

Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins

<i>meso</i>-Tetra­(<i>N</i>-methyl-4-pyridyl)­porphine tetratosylate (TMPyP) templates the synthesis of six new metal–organic materials by the reaction of benzene-1,3,5-tricarboxylate with transition metals, five of which exhibit HKUST-1 or <b>tbo</b> topology (M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in octahemioctahedral cages and can serve as size-selective heterogeneous catalysts for oxidation of olefins