A theorem on existence of mixed strategy equilibria in discontinuous zero-sum games is proved and is applied to three models of elections. First, the existence theorem yields a mixed strategy equilibrium in the multidimensional spatial model of elections with three voters. A nine-voter example shows that a key condition of the existence theorem is violated for general finite numbers of voters a...

These are two person non-zero(constant)-sum games in which each player has finitely many pure strategies. We call these non-zero(constant)sum games because the interests of the players is not required to be exactly opposed to each other. Of course, these include zero(constant)-sum games and are a true generalization of zero(constant)-sum games. But the methods used to analyze them are different...

We focus on the problem of computing approximate Nash equilibria and well-supported approximate Nash equilibria in random bimatrix games, where each player's payoffs are bounded and independent random variables, not necessarily identically distributed, but with common expectations. We show that the completely mixed uniform strategy profile, i.e. the combination of mixed strategies (one per play...

1. Correlated errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1 Temporal correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Spatial correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Since the seminal paper of Nash [7] game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in 2-player non-zero-sum strategic games, whose Nash equilibria are only mixed.

We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a diffe...

The ground state of dense up and down quark matter under local and global charge neutrality conditions with β-equilibrium has at least four possibilities: normal, regular 2SC, gapless 2SC phases, and mixed phase composed of 2SC phase and normal components. The discussion is focused on the unusual properties of gapless 2SC phase at zero as well as at finite temperature.

Soil is one of our most important natural resources. Regrettably, the expansion human activities has resulted in degradation soil resource due to contamination with a myriad organic and inorganic compounds. The remediation mixed contaminated soils, i.e. soils both compounds metals, challenging as it requires actions simultaneously decrease metal-induced risks contaminant concentrations. Here, w...

Phasor Measurement Units (PMUs) are in growing attention in recent power systems because of their paramount abilities in state estimation. PMUs are placed in existing power systems where there are already installed conventional measurements, which can be helpful if they are considered in PMU optimal placement. In this paper, a method is proposed for optimal placement of PMUs incorporating conve...