# Game Theory

DAYSTAR UNIVERSITY

AN ASSIGNMENT IN PARTIAL FULFILLMENT OF THE COURSE ADVANCED MODELLING OF LOGISTICS SYSTEMS (LOG 441A)

PRESENTED BY:

ADAMS MULWA10-0856

CATHERINE MAKAU11-1178

CYNTHIA KANEBA11-0976

MOSES NGONE10-

PRESENTED TO: Mr. MORIASI MARANGA

DUE DATE: 29TH OCTOBER 2013

DEPARTMENT OF COMMERCE

SCHOOL OF BUSINESS AND ECONOMICS

ATHIRIVER CAMPUS

Table of Contents

Game Theory3

History and impact of game theory5

Game theory and information systems6

Definition of key terms6

Dominance8

Nash equilibrium8

Mixed strategies9

Extensive games with perfect information9

Extensive games with imperfect information10

Zero-sum games and computation11

Bidding in auctions12

Game Theory

Game theory is the formal study of conflict and cooperation. Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals, groups, firms, or any combination of these. The concepts of game theory provide a language to formulate structure, analyze, and understand strategic scenarios. The object of study in game theory is the game, which is a formal model of an interactive situation. It typically involves several players; a game with only one player is usually called a decision problem. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these influence the outcome. Games can be described formally at various levels of detail. A coalitional (or cooperative) game is a high-level description, specifying only what payoffs each potential group, or coalition, can obtain by the cooperation of its members. What is not made explicit is the process by which the coalition forms. As an example, the players may be several parties in parliament. Each party has a different strength, based upon the number of seats occupied by party members. The game describes which coalitions of parties can form a majority, but does not delineate, for example, the negotiation process through which an agreement to vote en bloc is achieved. Cooperative game theory investigates such coalitional games with respect to the relative amounts of power held by various players, or how a successful coalition should divide its proceeds. This is most naturally applied to situations arising in political science or international relations, where concepts like power are most important. For example, Nash proposed a solution for the division of gains from agreement in a bargaining problem which depends solely on the relative strengths of the two parties’ bargaining position. The amount of power a side has is determined by the usually inefficient outcome that results when negotiations break down. Nash’s model fits within the cooperative framework in that it does not delineate a specific timeline of offers and counteroffers, but rather focuses solely on the outcome of the bargaining process. In contrast, noncooperative game theory is concerned with the analysis of strategic choices. The paradigm of noncooperative game theory is that the details of the ordering and timing of players’ choices are crucial to determining the outcome of a game. In contrast to Nash’s cooperative model, a noncooperative model of bargaining would post a specific process in which it is prespecified who gets to make an offer at a given time. The term “noncooperative” means this branch of game theory explicitly models the process of players making choices out of their own interest. Cooperation can, and often does, arise in noncooperative models of games, when players find it in their own best interests. Branches of game theory also differ in their assumptions. A central assumption in many variants of game theory is that the players are rational. A rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his opponents to do. The goal of game-theoretic analysis in these...

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