Strategically allocating resources to protect targets against potential threats in an efficient way is a key challenge facing our society. From the classical interdiction game to the recently proposed Stackelberg Security Game, applying computational game models to the security domain has made a real-world impact on numerous fields including military attack and defense, financial system securit...

This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight) about opponents’ strategies and about the initial distribution over players’ characteristics in the game. We model uncertainty by non-additive measures or capacities and prove the Cournot-Nash equilibrium existence theorem for this class of games. Equilibrium distribut...

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and BesselRiesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k ≥ 1 driven by a d-dimensional spatially homogeneous additive Gaussian ...

Abstract: The purpose of this paper is to discuss the properties of regularity and strong regularity of fuzzy measure on metric spaces following the previous results. Some properties are defined with the help of nulladditivity such as inner\outer regularity and the regularity of fuzzy measure. We define the strong regularity of fuzzy measures and show our result that the null-additive fuzzy mea...

We investigate the idea that linear contracts are reliable because they give the same incentives for effort at every point along the contract. We ask whether this reliability leads to a microfoundation for linear contracts, when the principal is profit-maximizing. We consider a principal-agent model with risk neutrality and limited liability, in which the agent observes the realization of a mea...

We shall continue to discuss further properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pr...

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-l...