On the Inducibility of Stackelberg Equilibrium for Security Games

Strong Stackelberg equilibrium (SSE) is the standard solution concept of Stackelberg security games. As opposed to the weak Stackelberg equilibrium (WSE), the SSE assumes that the follower breaks ties in favor of the leader and this is widely acknowledged and justified by the assertion that the defender can often induce the attacker to choose a preferred action by making an infinitesimal adjustment to her strategy. Unfortunately, in security games with resource assignment constraints, the assertion might not be valid; it is possible that the defender cannot induce the desired outcome. As a result, many results claimed in the literature may be overly optimistic. To remedy, we first formally define the utility guarantee of a defender strategy and provide examples to show that the utility of SSE can be higher than its utility guarantee. Second, inspired by the analysis of leader's payoff by Von Stengel and Zamir (2004), we provide the solution concept called the inducible Stackelberg equilibrium (ISE), which owns the highest utility guarantee and always exists. Third, we show the conditions when ISE coincides with SSE and the fact that in general case, SSE can be extremely worse with respect to utility guarantee. Moreover, introducing the ISE does not invalidate existing algorithmic results as the problem of computing an ISE polynomially reduces to that of computing an SSE. We also provide an algorithmic implementation for computing ISE, with which our experiments unveil the empirical advantage of the ISE over the SSE.Comment: The Thirty-Third AAAI Conference on Artificial Intelligenc

Effects of cellulose nanofibers on soil water retention and aggregate stability

Innovative solutions that address global challenges such as water scarcity and soil erosion are critical for maintaining sustainable agriculture. Due to their water-absorbing and soil-binding properties, cellulose nanofibers (CNF) can be applied to soil to enhance soil water retention and aggregate stability. In this study, we analyzed the effects of the drying temperature, dosage, irrigation water quality, and soil type on the efficacy of CNFs. Our results revealed that CNF dried at 5 degrees C is more effective at absorbing water than others, and adding 1% CNF enhanced soil water content up to 98%. The CNF samples absorbed water due to their hydrophilic molecular groups and morphological structure, as confirmed by Fourier-transform infrared spectroscopy and scanning electron microscopy. CNF addition increased the soil volumetric water content and prolonged water retention by 22 days in the paddy soil samples, highlighting its potential for drought-prone areas. Furthermore, irrigation water quality, such as pH and cation values, influenced the interactions between CNF and water molecules, suggesting adjustments to the water retention curve. In its hydrated state, CNF promotes colloid flocculation and binds to soil particles, thereby strengthening the bonds crucial for aggregate formation and stability. CNF enhanced macro-aggregate formation by up to 48% and 59% in the masa and paddy soil samples, respectively. Our study emphasizes the potential of CNF for water conservation, soil health, and overall agricultural sustainability