The problem of finding Nash equilibria is one of the fundamental problems in Algorithmic Game Theory, and has made a nice connection between Game Theory and Computer Science [9]. While Nash [10] introduced the concept of Nash equilibrium and proved every game has a mixed Nash equilibrium, finding a Nash equilibrium in reasonable time seems to be essential. The Nash equilibrium can be used as a ...

The purpose of the course is to study several dynamics generated by strategic interactions in games. Among the topics are adaptive dynamics in evolutionary game theory, robust procedures for on-line algorithms and stochastic approximation. 1. Fictitious play Discrete time Continuous time and best reply dynamics 2. Replicator dynamics n populations One population Evolutionary Stable Strategies 3...

We consider in this paper a class of risk-sensitive stochastic nonzero-sum differential games with parameterized nonlinear dynamics and parameterized cost functions. The parametrization is such that if all or some of the parameters are set equal to some nominal values, then the differential game either becomes equivalent to a risk-sensitive stochastic control (RSSC) problem, or decouples into s...

The objective of the paper is to study how wholesale price and revenue sharing contracts affect operations and marketing decisions in a supply chain under different dynamic informational structures. We suggest a differential game model of a supply chain consisting of a manufacturer and a single retailer that agree on the contract parameters at the outset of the game. The model includes key oper...

We study optimal tolls for network congestion games where players aim to route certain amount of traffic between various source destination pairs. We consider weighted atomic users, unsplittable traffic and arbitrary nondecreasing latency functions. Users are selfish and want to follow routes that minimize their respective latencies. We focus on pure Nash equilibria. A Nash equilibrium profile ...

This paper considers a new class of deterministic finite-time horizon, two-player, zero-sum differential games (DGs) in which the maximizing player is allowed to take continuous and impulse controls whereas minimizing control only. We seek approximate value function, provide verification theorem for this DGs. By means dynamic programming principle (DPP) viscosity solution (VS) framework, we fir...

In this paper, elements of differential game theory are used to analyze a spatially explicit home range model for interacting wolf packs when movement behavior is uncertain. The model consists of a system of partial differential equations whose parameters reflect the movement behavior of individuals within each pack and whose steady-state solutions describe the patterns of space-use associated ...

The strategic pricing decisions of assembly products in assembly products supply chain are studied in this paper. Firstly, a two-stage assembly products supply chain model is developed. By building Nash game model, the Nash equilibrium solution of pricing strategy of supplier and assemblers is obtained. Next, a union decision model is built to analyze the optimal combination pricing strategy of...

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(logm+log n) pure strategies. This result induces an N log logN algorithm for computing an approximate Nash equilibrium in games where the number of actions is polynomial in the number of players (m = poly(n)), where N =...

Epidemiological games combine epidemic modelling with game theory to assess strategic choices in response to risks from infectious diseases. In most epidemiological games studied thus-far, the strategies of an individual are represented with a single choice parameter. There are many natural situations where strategies can not be represented by a single dimension, including situations where indi...