This paper introduces the Nash Inequality Ratio (NIR) as a natural characterization of the extent to which inequality is permitted between individual agents in Nash equilibrium outcomes of a given strategic setting. For any particular strategy, the inequality ratio is defined as the ratio between the highest and lowest costs incurred to individual agents in the outcome dictated by that strategy...

We present necessary conditions for linear noncooperativeN -player delta dynamic games on an arbitrary time scale. Necessary conditions for an open-loop Nash-equilibrium and for a memoryless perfect state Nash-equilibrium are proved.

In this paper, we consider a non-cooperative n-person game in the strategic form. As is well known, the game has a mixed-strategy Nash equilibrium. However, it does not always have a pure-strategy Nash equilibrium. Wherein, Topkis (1979), Iimura (2003), and Sato and Kawasaki (2009) provided a sufficient condition for the game to have a pure-strategy Nash equilibrium. However, they did not consi...

This paper generalises the approach taken by Dasgupta & Maskin (1986) and Simon (1989) and provides necessary and su¢ cient conditions for the existence of pure and mixed strategy Nash equilibrium in games with continuous strategy spaces and discontinuous payo¤ functions. The conditions can be applied widely, and examples for existence of pure strategy and monotonic equilibria in First-Price au...

This paper studies equilibrium selection based on a class of perfect foresight dynamics and relates it to the notion of p-dominance. A continuum of rational players are repeatedly and randomly matched to play a symmetric n × n game. There are frictions: opportunities to revise actions follow independent Poisson processes. The dynamics has stationary states, each of which corresponds to a Nash e...

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

In sequential games of traditional game theory, backward induction guarantees existence of Nash equilibrium by yielding a sub-game perfect equilibrium. But if payoffs range over a partially ordered set instead of the reals, then the backward induction predicate does no longer imply the Nash equilibrium predicate. Non-determinism is a solution: a suitable non-deterministic backward induction fun...

We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel links, to control the routing of its own assigned traffic. In a Na...