An Overview of Game Theory and Some Applications 113 114 Philosophy and Progress
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112 Philosophy and Progress Philosophy and Progress: Vols. LIX-LX, January-June, July-December, 2016 behavior. The purpose of this paper is to clarify the following ISSN 1607-2278 (Print), DOI : http://dx.doi.org/10.3329/pp.v59i1-2.36683 issues: firstly, to provide very brief overview of game and game theory; secondly, to discuss background and impact of game theory; thirdly, to analyze the prisoner’s dilemma game and finally, to present applications of game theory with special attention to philosophy. Key Words: game, game theory, strategy, prisoner’s dilemma, philosophy. i. Game AN OVERVIEW OF GAME THEORY AND The ‘game’ is the object of studying in game theory. The SOME APPLICATIONS complete set of rules describes a game. A play is an instance of the game. Most games played for fun, entertainment and Bellal Ahmed Bhuiyan* leisure. When someone over reacts, we sometimes say ‘it’s just a game’. Checkers, chess, football, judo, and squash and thousands of other formalized contests are examples of games Introduction in which there are two players or teams. Most of these games Game theory is an autonomous discipline that is used in have only one winner after played (Geckil, 2010). But there are applied mathematics, social sciences, most considerably in many other situations that can be formulated as games. A game economics, as well as in biology, engineering, political science, follows as: international relations, computer science and philosophy. Game A game is an abstract, which is defined as a formal theory is the mathematical study of strategy and conflict, in description of a strategic situation. Any strategic which an agent’s success in making choices depends on the interaction involves two or more decision- makers choice of others. It was initially developed in economics to (players), each with two or more ways of acting understand a large collection of economic behaviors, including (strategies), such that the outcome depends on the behaviors of firms, markets and consumers. Game theory has strategy choices of all the players. Each player has well- been used to attempt to develop theories of ethical or normative defined preferences among all the possible outcomes, behavior as well. In economics and philosophy, scholars have enabling corresponding utilities (payoffs) to be applied game theory to help in the understanding of rational assigned. A game makes explicit the rules governing players’ interactions, the players feasible strategies, and * Lecturer, Department of Philosophy, University of Dhaka their preferences over outcomes (Bicchieri and Sillari, Email: [email protected] 2005, P. 296). An Overview of Game Theory And Some Applications 113 114 Philosophy and Progress All games have three essential elements- players, strategies, d) Normal and extensive form: The strategic form which is payoffs. So, a game in normal form consists of: also called normal form is the basic type of game studied in non-cooperative game theory. A game in strategic form lists a) A (finite) number of players. P= {1,2,3….,n}, each player, and the outcomes that result from each possible {P1,……,Pn} combination of choices. The extensive form, which is also b) A Strategy set Si assigned to each player: {S1 ,…,Sn} known as a game tree, is more detailed than the strategic form c) A utility/payoff function- set players gains: {U1,…,Un} of a game. It is a complete description of how the game is played over time. Different Categories of Game e) Zero-sum and non-zero-sum games: Zero- sum games Games can be distinguished according to various criteria: have the property that the sum of the payoffs to the players a) According to number of players: Usually there should be equals zero. For example, chess, poker, and most sports game more than one player. Maximum number of players is finite. A like basketball are zero-sum game. Real- world games are player may be expounded as a nation, or a team comprising rarely zero-sum game. It is also called constant-sun games. In many people, companies, associates etc. Game categorized as a non-zero-sum games, all players could win or loss together. one- person, two persons, or n-person (n>2) game. Most of the games in our real life and the business world are non-zero-sum game. For example, price wars between firms b) According to rationality of players: A key supposition in are non-zero-sum games. In non-zero-sum game players have many variants of game theory is that the players are rational. A common and conflicting interests (Geckil, 2010). rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his ii) Game Theory competitors to do. There can be distinguished two extreme Game theory is the logical analysis of situations of conflict and ways. The first one is called ‘intelligent’ player who is acting cooperation. Game theory could be formally defined as a rationally. The other extreme is the player who chooses random theory of rational decision in conflict situations. Model of such actions. situations, as they are conceived in game theory, involve c) According to cooperation: Games can be categorized into a) a set of decision makers, called players; cooperative and non- cooperative. A game in which players are allowed to cooperate with each other on a joint strategy is b) a set of strategies available to each player, courses of called a ‘cooperative game’. For example, a cooperative game action which he or she may choose to follow; is a bargaining game between parties in a transaction over the c) a set of outcomes, the strategies chosen by each player value of a target company. For non- cooperative is basic determine the outcome of the game; assumption that individual players can not cooperate. In this d) a set of payoffs accorded to each player in each of the game is associated with the analysis of strategic choices. possible outcomes. (Rapoport, 1974, p.1) An Overview of Game Theory And Some Applications 115 116 Philosophy and Progress So, Game theory is the study of how players should rationally not only mathematical apparatus, but also an important tool in play games. Each player would like to the game to end in an economics, political science, law, psychology, philosophy and outcome which gives him as large a payoff as possible. He has other disciplines. some control over the outcome, since his choice of strategy iii) Background and impact of Game Theory will influence it. Game theory has been widely recognized as an important tool The field known as ‘game theory’ was introduced in the last in different fields. The developments of Game theory is largely century by mathematicians and economists as a tool to analyze broadened. The initial discussion of game theory occurred in a both economic competition and political conflicts. Two letter written by James Waldegrave in 1713. In this letter, distinguished game theorists Robert Aumann and Oliver Hart, Waldegrave provides a mixed strategy solution to a two-person explain the attraction in the following way: version of the card game le Her. James Madison made what we Game Theory may be viewed as a sort of umbrella or now recognize as a game theoretic analysis of the ways states ‘unified field’ theory for the rational side of social can be expected to behave under different system of taxation. science, where ‘social’ is interpreted broadly, to include The earliest example of a formal game-theoretic analysis is the human as well as non- human players (computers, study of a dupopoly by Antoine Cournot in 1838. His animals, plants) … It does not use different, ad hoc publication Researches into the Mathematical Principles of the constructs … It develops methodologies that apply in Theory of Wealth presents a solution that is a restricted version principle to all interactive situations (Aumann and Hart, of the Nash equilibrium (Crider, 2012, p. 4). A formal theory 1992, P. 3) of games was suggested by the mathematician Emile Borel in 1921, which was furthered by the mathematician John Von The subject of Game theory are situations, where the result for Neumann in a “theory of parlor games” in 1928. a player does not only depend on his own decisions, but also on the behavior of the other players. Game theory is the theory of John Von Neumann and Oskar Morgenstern published the independent and interdependent decision making in Theory of Games and Economic Behavior in 1944. It organizations where the outcome depends on the decisions of introduced the economic and mathematical basis for the field two or more autonomous players, one of which may be nature we now call ‘Game theory’. This book contained much of the itself, and where no single decision maker has full control over basic terminology and problem setup that is still in use recent the outcomes (Kelly, 2003). times. Von Neumann and Morgenstern established the field that economic and social questions can often be described as The concepts of game theory provide a common language to mathematical models of suitable games of strategy. This formulate, structure, analyze and eventually understand gigantic work provides the method for finding mutually different strategic scenarios. Game theory is a scientific consistent solutions for two-person zero-sum games (Geckil discipline that investigates conflict situations, the interaction and Anderson, 2010). between the agents and their decisions (Hotz, 2006). To perform the analysis of critical situations, Game theory uses An Overview of Game Theory And Some Applications 117 118 Philosophy and Progress Game theory became closely associated with the Rand having laid the foundations of mechanism design theory” with Corporation after the second world war.