Game Theory and its Application to VLSI Physical Design

VLSI Physical design problems typically involve solving some of the hardest problems of combinatorial optimization. Complex process technologies in the deep submicron regime and rapidly reducing feature sizes have augmented the hardness with increasing number of objectives and constraints. Most of these objectives appear to be conflicting in nature. Game theoretic modeling plays a useful role in solving such multi-objective problems. It relies on features of rationality, coalition formation, competition, and equilibrium. The outcome is typically a solution that is the best for a player with respect to every other player’s objectives and decisions. Each player has an associated payoff function, measuring its expected utility in the game. The goal is to find a solution that is the best (or optimum) for all the players. A game is said to reach equilibrium when the combination of strategies of all the players has the best possible payoff for all the players. Introduced by Von Neumann in early twentieth century, Game Theory was originally a subject of economists, social scientists, and mathematicians. It has recently found applications in Electronic markets, Computer networking and other fields of Computer Science including formulation and solving the hard problems of the VLSI Physical Design.