JOURNAL OF CRITICAL REVIEWS ISSN- 2394-5125 VOL 7, ISSUE 3, 2020
A STUDY ON GAME THEORY TECHNIQUES- AN OVER VIEW
P. HEMA1, DR.V. VINOBA2 #Assistant Professor, Department of Mathematics, Rmk College of Engineering And Technology, Puduvoyal 601206 *Head, Department of Mathematics, K. N. Government Arts College for Women, Thanjavur [email protected]
Abstract Game theory is a field of applied mathematics for analysing complex interactions among entities. It is basically a collection of analytic tools that enables distributed decision process. Game theory (GT) provides insights into any economic, political, or social situation that involves individuals with different preferences. GT is used in economics, political science and biology to model competition and cooperation among entities, and the role of threats/penalties in long term relations. Contemporary social science is based on game theory, economics, and psychology in which mathematical logic is applied. Game theory provides a mathematical basis for the analysis of interactive decision-making processes. It provides tools for predicting what might happen and possibly what should happen when agents with conflicting interests interact. It is not a single monolithic technique, but a collection of modeling tools that aid in the understanding of interactive decision problems. Generally game theory breaks naturally into two parts:(i) Non-cooperative theory (ii) Cooperative theory. A cooperative game is a game in which the players have complete freedom of preplay communication to make joint binding agreements. These agreements may be of two kinds to coordinate strategies or to share payoffs. In noncooperative game theory, we focus on the individual player’s strategies and their influence on payoffs and try to predict what strategies players will choose (equilibrium concept). In this paper we completely discuss about the performance analysis of strategic form of cooperative game theory.
Key words; Game theory, Co-operative game theory, Non-cooperative game theory, Nash Equilibrium. Introduction Game theory has been of importance on many fields of the social sciences since its rise to prominence more than fifty years ago (Lim, 1999). The subject first outlined zero-sum games, such that one person's gains are exactly equal net losses of the other Iparticipant. Turocy & von Stengel (2001) define game theory as a formal study of decision-making where several players must make choices that potentially affect the interests of other players. Turocy & van Stengel (2001) highlighted that the game theory was first presented on the study of duopoly by Antoine Cournt in 1838. However Camerer (2003) discovered that the first known discussion of game theory occurred in a letter written by James Waldegrave in 1713. Game theory was further put on the spotlight by John von Nuemann in 1928 in a study of “theory of polar games”. Lim (1999) also argued that game theory was firmly entrenched by von Neumann and Morgenstern in the realm of economics by providing a whole new way of looking at the competitive process, through the eyes of strategic interactions between economic players. More emphases on game theory was observed in 1949 when John Forbes Nash published his thesis titled Non Cooperative games, that’s where the concept of equilibrium point (also known as Nash Equilibrium) was introduced (Hyksova, n.d.). Kerk (n.d.) pointed out that Nash equilibrium is based on the principle that the combination of strategies that players are likely to choose is one in which no player could do better by choosing a different strategy given the strategy the other chooses. Operations Research is a scientific approach to problem solving for executive decision making which requires the formulation of mathematical, economic and statistical models to deal with situations arising out of risk and uncertainty and control them. In fact, decision making and problem control in any organization are more often related to certain daily operations such as inventory control, production scheduling, man power planning and distribution and maintenance.
Decisions on problems involving a finite number of alternatives arise frequently in practice. The tools used to solve these problems depend largely on the type of data available (Deterministic, Probabilistic, or Uncertain). The analytic hierarchy process (AHP) is a prominent tool for dealing with decisions under certainty, where subjective judgment is quantified in a logical manner and then used as a basis for reaching a decision. For probabilistic data, decision trees comparing the expected cost (or profit) for the different alternatives are the basis for reaching a decision. Decisions under uncertainty reflect criteria of the decision maker’s attitude towards risk, ranging from optimism to 1156
JOURNAL OF CRITICAL REVIEWS ISSN- 2394-5125 VOL 7, ISSUE 3, 2020 pessimism. Another tool of decision under uncertainty is Game Theory, where two opponents with conflicting goals aim to achieve the best out of the worst conditions available to each.
II. REVIEW OF LITERATURE: 2.1. According to Turocy & von Stengel (2001) the purpose of study in game theory is game. There players involved in a game are arranged in their preferences, their information, the strategic actions available to them, and how these influence the outcome. A high level description of a game specifies only what payoffs each individual or group can obtain by assistance of its members. Game theory is generally divided into two branches, which are non-cooperative and cooperative game theory (Osborne & Rubinstein, 1994). Lim (1999) further clarified that whether a game is cooperative and non-cooperative would depend on whether the players can communicate with one another 2.2. Turocy & von Stengel (2001) argues that since all players are assumed to be rational in game theory, they make choices which result in the outcome they prefer most, given what their opponents do. Both players are said to have dominant strategies. Kerk (n.d.) explained dominant strategy as the best choice for a player for every possible choice by the other player. A dominant strategy has payoffs such that, regardless of the choices of other players, no other strategy would result in a higher payoff. Dominance is explained by the use of Prisoner’s Dilemma that was first introduced by Tucker in 1950. Kerk (n.d.) further argued that this game captures the key tensions between individual and collective actions and the outcomes which are the consequence of these actions. 2.3. The Nash equilibrium is a game theoretic solution concept that is normally applied in economics. As previously outlined, Nash equilibrium was introduced by John Nash in 1950 and has emerged as one of the fundamental concepts of game theory (Kerk, n.d.). Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy (Osborne, 2002). However, Myerson (1999) viewed the concept of equilibrium as one of the most important and elegant ideas in game theory. Myerson (1999) also pointed out that a game can have many Nash equilibriums, and some of these equilibriums may be unreliable compared to what should be the outcome of a game. Some studies reflect that Nash equilibrium is concern about the actions that will be chosen by players in a strategic game (Osborne, 2002). Players have to know precisely what their opponents will choose (de Bruin, 2009). To do so, players should not base on the assumption that all players are rational. They rather focus on the basis of statistical information about previous game playing situations, if such information is available and reliable.
III. OVERVIEW OF GAME THEORY
Game theory’s roots are extremely old. The idea of game theory has appeared through-out history, apparent in the Bible, the Talmud, the works of Descartes and Sun Tzu, and the writings of Charles Darwin. However, some argue that the first real study of game theory started with the work of Daniel Bernoulli, a mathematician born in 1700. Although his work, the ‘Bernoulli’s Principles’ formed the basis of jet engine production and operations, he is credited for introducing the concepts of expected utility and diminishing returns. Others argue that the first mathematical tool was presented in England in the 18th century, by Thomas Bayes, known as ‘Bayes Theorem’; his work involved using probabilities as the basis for logical conclusion. Nevertheless, the basis of modern game theory can be considered as an outgrowth of a three seminal works; a ‘Research into the Mathematical Principles of the Theory of Wealth’ in 1838 by Augustine Carnot, gives an intuitive explanation of what would eventually be formalized as Nash equilibrium and gives a dynamic idea of players best-response to the actions of others in the game. In 1881, Francis Y Edge worth expressed the idea of competitive equilibrium in a two-person economy. Finally, in 1921, Emile Borel suggested the existence of mixed strategies, or probability distributions over one’s actions that may lead to stable play. It is also widely accepted that modern analysis of Game Theory and its modern methodological framework began with John Von Neumann and Oskar Morgenstern in ‘Theory of Games and Economic Behavior’ published in1944.
Von Neumann and Oskar Morgenstern gave an axiomatic development of utility theory, which now dominates economic thought and introduce the formal notion of a Cooperative game. It is the work of Von Neumann on Zero- Sum games in which he proved the famous minmax theorem for Zero- Sum games. In papers between 1950 and 1953, John Nash contributed to the development of both Non-Cooperative and Cooperative Game Theory. His most important contribution, though, was probably his existence proof of equilibrium in non-cooperative games, the Nash Equilibrium. For this contribution to game theory, Nash shared in the year 1994 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. 1157
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In the fifties and sixties, further development of Game Theory was contributed mainly by domain of mathematicians. Seminal articles in this period were the papers by John F Nash, 1951 on Nash equilibrium and on Bargaining
In the late sixties and seventies game theory became accepted as the most formal language for economics and that was further enhanced by the work of John Harsanyi, 1973 on modeling games with inadequate information [91] and ReinhardSelten, 1986 [112] on game perfect Nash equilibrium. In addition, it is today established throughout the social sciences and a wide range of other sciences like military, etc. Game Theory received a special attention in 1994 with the awarding of the Nobel Prize in economics to John Nash, John Harsanyi and Reinhardselton.
3.1 AN OVERVIEW OF GAME THEORY Game Theory is a collection of mathematical models formulated to study situations of conflict and cooperation. It is concerned about finding the best actions for individual decision makes in these situations and recognizing stable outcomes. Generally a Game is made up of three basic components: a set of players, a set of actions, and a set of preferences. These are collectively known as the rules of the game, and the modeler’s objective is to describe a situation in terms of the rules of a game so as to explain what will happen in that situation. Trying to maximize their payoffs, the player will devise plans, known as strategies that pick actions depending on the information that has arrived at each moment. The strategy can be further classified into Pure Strategy and Mixed Strategy.
Let m be number of strategies of player A, n be the number of strategies of player of B, pi be the probability of selection of the alternative i of player A, i=1,2,….m, probability of selection of the alternative j of Player B , for j 1,2,...... n. The sum of the probabilities of selection of various alternatives of each of the players is equal to1 as shown below mn
pqij1& 1 ij11 If a player selects a particular strategy with a probability of 1, then that strategy is known as a pure strategy. This means that the player is selecting that particular strategy alone ignoring his remaining strategies. If a player follows more than one strategy, then the player is said to follow a mixed strategy. But the probability of selection of the individual strategies will be less than one and their sum will be equal to one. The combination of strategies chosen by each player is known as the equilibrium. Given equilibrium, the modeler can see what actions come out of the conjunction of all players’ plans, and this tells him the outcome of the game.
The number of players will be denoted by n . Let us label the players with the integers 1 to n, and denote the set of players by I = 3,2,1 ...... n . We assume throughout that, there are at least two players, that is, n 2 . There are three main mathematical models or forms used in the study of games, (i) the extensive form, (ii) the strategic or normal form and (iii) the characteristic function form or the coalitional form. These differ in the amount of detail on the play of game built into the model. In the extensive form of a game, we are able to speak of a position in the game, and of a move of the game while moving from one position to another. The set of possible moves from a position may depend on the player whose turn it is to move from the position. In the extensive form of a game, some of the moves may be random moves, such as the dealing of cards on the rolling of dice. The rules of the game specify the probabilities of the outcomes of the random moves. One may also speak of the information players have when they move. When the players know all past moves by all the players and the outcomes of all past random moves, the game is said to be of perfect information. Two-person games of perfect information with win or loss outcome and no chance moves are known as combinatorial games. We find an exposition of it in Costa-Games M, 1976 [88] and in Cooper D and Van Huyck, 1982 [40]. Such a game is said to be impartial if the two players have the same set of legal moves from each position, and it is said to be partizan. Accordingly the taxonomy of Games is shown in Figure 3.1.
In the strategic form, many of the details of the game such as position and move are lost; the main concepts are those of a strategy and a payoff. In the strategic form, each player chooses a strategy from a set of possible strategies. We denote
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JOURNAL OF CRITICAL REVIEWS ISSN- 2394-5125 VOL 7, ISSUE 3, 2020 the strategy set or action space of player i by Ai ,for i 1,2,3,...... n . Each player considers all the other players and their possible strategies, and then chooses a specific strategy from his strategy set. All players make such a choice simultaneously, the choices are revealed and the game ends with each player receiving some payoff. Each player’s choice may influence the final outcome for all players. We model the payoffs as taking on numerical values. The mathematical and Philosophical justification behind the assumption that each player can replace such payoffs with numerical values is said to Utility Theory. This theory is treated in detail in the books of Savage L J, 1954 [119] and of Fishburn, 1970 [90]. We therefore assume that each player receives a numerical payoff that depends on the actions chosen by all the players. Suppose player 1 choose a1 A ,1 player 2 chooses a2 A ,2 etc., and n chooses an An . Then we denote the payoff to player i , for i= 1,2,…..n by fi a1,( a2 .....an ) and call it the payoff function for player i.
Game Theory also classifies games according to other criteria, such that if games are Static or Dynamic. In static games, we assume that there exists only one time step, which means that players move their strategy simultaneously without any knowledge of what other players are going to play. In dynamic games, players move their strategy in predetermined order, meaning that the move of one player is conditioned by the move of the previous players (i.e.) the second mover knows the move of the first mover before making his decision.
Games with Games with static Dynamic complete incomplete Games Games information information
Non - Cooperative Cooperative Bayesian Game Game Theory Game Theory Theory
Nash Equilibrium Coalitional Bargaining Games Games Zero- Sum Games
Bayesian Nash Core Shapley equilibrium
Nash Bargaining
Figure 3.1 Taxonomy of Games
The Strategic form of a game is defined by the three objects:
1. The set,I 1,2,3...... n , of players.
2. The sequence A1, A2 ,...... An of strategy sets of the players, and
the players. f a ,a ,....a ...... f a ,a ,.....a 3. The sequence, to 1 1 2 n n 1 2 n of real-valued payoffs 1159
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A game in strategic form is said to be Zero-Sum if the sum of the payoffs to the players is zero no matter what action are by the players. That is the game is n zero-sum if fi a1,a2,...an 0
In Zero-Sum games each and every participant’s gain or loss of utility is exactly balanced by the losses or gain of the utility of the other participants. So the Type equation here.strategic form is extended to two-person non-zero sum games. In general they have optimal strategies and the theory naturally breaks into two parts:
1. Non-cooperative Game Theory 2. Cooperative Game Theory.
Also according to the knowledge of players on all aspects of game, the non-cooperative / cooperative game further classified into two categories: Complete information and incomplete information. In the complete information game, each player has all the knowledge about other’s characteristics, strategy spaces, payoffs and so forth, but all these information are not necessarily available in an incomplete information game (M.J.Osborne & A.Rubinstein, 1982 [97], V. Srivastavaet al. 2005 [127]). In games with incomplete information, the overhead resulting from information exchange is reduced, because each player predicts the strategies of other players.
In Non-Cooperative Game Theory if the players communicate, binding agreements may not be formed. This is the area of most interest to economists, in Gibbons Robert, 1992 [98] and Bierman H S and Fernandez L, 1998 [39]. In 1994, John Nash, John Harsanyi and ReinhardSelton received the Nobel Prize in Economics for work in this area. The main concept, replacing values and optimal strategy in the notion of a strategic equilibrium, also called Nash equilibrium. This Nash equilibrium is a building block of game theory since it both inspires new solution concepts and corresponds to the solution of many interactive situations.
In Cooperative Game Theory the players are allowed to form binding agreements, and so there is strong incentive to work together to receive the largest total payoff. The problem then is how to split the total payoff between or among the players. This cooperative theory also splits into two parts. If the players measure utility of the payoff in the same units and there is a means of exchange of utility such as side payments, we say the game has transferable utility; otherwise non- transferable utility. When the number of players grows large, even the strategic form of a game, though less detailed than the extensive form, becomes too complex for analysis. In the Coalitional form of a game, the notion of a strategy disappears; the main features are those of a coalition and the value or worth of the coalition. In many player games there is a tendency for the players to form coalitions to favor common interests. It is assumed each coalition can guarantee its members a certain amount, called the value of the coalition. The coalition form of a game is a part of cooperative game theory with transferable utility, so it is natural to assume that the grand coalition, consisting of all the players, will form, and it is a question of how the payoff received by the grand coalition should be shared among the players. There we introduce the important concepts of the Core of an economy. The Core is a set of payoffs to the players where each coalition receives atleast its value. We will also look for principles that lead to a unique way to split the payoff from the grand coalition, such as the Shapley value and the Nucleolus. There is also a substantial body of literature on cooperative games, in which players form coalitions and negotiate via an un specified mechanism to allocate resources. Cooperative Game Theory encompasses concepts such as the Nash Bargaining solution and the Shapley values.
In basic strategic games, it is assumed that each player holds the correct belief about the other player’s actions. To support this assumption, it is often stated that all players have complete information about the game being played. In many modeling situations, however this assumption is not realistic-players are rarely ever perfectly informed about their opponents’ characteristic modeling these situations of imperfect information instead requires the use of Bayesian games, which are generalized strategic games in which players can be uncertain about aspects of their environment that are relevant to their actions.
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3.2 AUCTION GAME THEORY Bidding in auctions Turocy & von Stengel (2001) argued that the design and analysis of auctions is one of the achievements of game theory. Auction theory was established by the economist William Vickrey in 1961. It became more practical applied in the early 90’s, when auctions generated billions of dollars through radio frequency spectrum for mobile telecommunication. Pindyck & Rubinfeld (2009) views bidding in auction through auction markets, which are defined as markets in which products are bought and sold through formal bidding processes. Klemperer (1999) views a game-theoretic auction model as a mathematical game represented by a set of players, a set of strategies available to each player, and a payoff vector corresponding to each combination of strategies. Auctions have been used since olden days for the sale of a variety of objects (Klempere, 1999). In the present days, it is easy to find goods like fish, tobacco, flowers, horses, airplanes, art objects in auctions. Klempere (1999) explained how the auctions work in a practical sense as a situation where there is a valuable object; the bidders take an action that signals how much they are willing to pay for the object. There is a well-defined rule that assigns the object to one of the bidders according to all the bids, and all bidders know the rule. There is also a well-defined rule that dictates how much each bidder should pay, and all bidders know the rule. Studies further presented an example where there is queue for a scarce ticket, a prize will be a ticket, bidders will be the people in the queue, and the bids is the time spent waiting on line (Klempere, 1999). According to Turocy & von Stengel (2001), the most familiar type of auction is the familiar open ascending-bid auction, which is also called an English auction. In this type of auction, an object is put up for sale in the presents of the buyers. An auctioneer raises the price of the object as long as there are at least two interested bidders. The auction only stops when there is only one interested bidder left. The interested bidder gets the object at the price at which the last remaining opponent drops out. More emphasis is also on an open descending price auction as another type of auction; it is also called Dutch auction. On this type of auction, the auctioneer begins by calling out a price high enough, where no bidder is even interested in buying the object at that certain price. When a certain bidder starts showing some interest, the price the price of an object gradually goes down to meet the bidder’s indicates interest. The object is then sold to this bidder at the given price.
3.3 REPEATED GAME THEORY Consider a game G, which will be called the stage game. Let the players/nodes set to be
I = {1, · · · , N }, and refer to a node’s stage game choices a actions. So each node has an action space Ai. If it is a malicious node then sometimes its action is dropping of the incoming packets. t We’ll refer to the action of the stage game G which player i executes in period t as ai . The action profile played in t t t period t is just the n-tuple of individuals’ stage-game actions at a1 ,a2 ,...... an …………. (1) We want to be able to condition the players’ stage-game action choices in later periods upon actions taken earlier by other players. To do this we need the concept of a history: a description of all the actions taken up through the previous t 0 1 t1 period. We define the history at time t to be h a ,a ,...... a …………..(2) In other words, the history at time t specifies which stage-game action profile (i.e., combination of individual stage- game actions) was played in each previous period. Note that the specification of ht includes within it a specification of all previous histories h0 ,h1,...... ht1 . For example, the history h t is just the concatenation of ht1 with the action profile a t1 ; i.e. ht =( ht1 , at1 ) The history of the entire t1 game is hT 1 a0 ,a1,...... aT Note also that the set of all possible histories ht at time t is just At X A t0 …………………….. (3) To condition our strategies on past events, then, is to make them functions of history. So we t t t t write player i’s period-t stage-game strategy as the function si , where ai = si ( h ) is the stage-game action would play t in period t if the previous play had followed the history h . A player’s stage-game action in any period and after any history must be drawn from her action space for that period, but is the stage-game action would play in period t if the t previous play had followed the history h . A player’s stage-game action in any period and after any history must be drawn from her action space for that period, but because the game is stationary her stage-game action space Ai does not change with time. Therefore we write:
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t t tt t t i I t h A si (h ) Ai . Alternatively, we can write iI t si : Ai Ai t t tt t The period-t stage game strategy profile s is s s1 , s2 ...... sn t t t t ttt tt t t t t This profile can be described by si : s ; A A (i.e) h A , s (h ) s1 (h ), s2 (h )...... sn (h )
Let at refer to the action of the stage game G which node i executes in period t. The action profile i t tt t played in period t is just the n- tuple of individuals’ stage game actions a a1 ,a2 ,...... an .We want to be able to condition the nodes’ ’stage game action choices in later periods upon actions taken earlier by other nodes. To do so, we need the concept of history which is a description of all the actions taken up through the previous periods. We define the history at time t as ht a0 ,a1,...... at1 In other words ,the history at time t specifies which stage game action profile was played in each previous period. So we write node i’s period- t t t t t stage game as the function si , where ai = si ( h ) is the stage game action it would play in period t if the previous play had followed the history ht. When the game starts there is no past play, every node executes 0 1 0 its ai stage game. This zero-th period play generates the history h (a )which We now define the players’ payoff functions for the repeated game. When studying will be recorded at the base station, where 0 0 0 0 a a1 ,a2 ,...... an . The history is then revealed to the IDS so that it can condition its period-1 play upon the period-o play. It means that if a node is acting maliciously, by keeping history of game, the IDS is able to notify neighboring nodes of a malicious one. Each node chooses its t=1 stage game, strategy s1(h1). Consequently, in the t =1 stage game the stage game strategy profile a1=s1(ht)=(s1(h1),···,s1(h1)) is played. Each node i has a von Neumann-Morgenstern utility function defined over the outcomes of the stage
game G as ui: A→R, where A is the space of action profiles. Let G be played several times and let us award each node a payoff which is the sum of the payoffs it got in each period from playing G. Then t t t t this sequence of stage games is itself a game, called a repeated game. Here, ui ri ci where ri is the t gain of node i’s reputation c is the cost of forwarding a packet for the node, and α and β are weight i parameters. We assume that measurement data can be included in a single message that we call a packet. Packets all have the same size. The transmission cost for a single packet is a function of the transmission distance. In particular, we assume ct = cr.dµ, where cr is a constant i that includes antenna Characteristics, d is the distance of the transmission and µ is the path loss exponent
By assuming that in each period the same stage game is being played, two statements are implicit:
1. For each node, the set of actions available to it in any period in the game G is the same regardless of which period it is and regardless of what actions have taken place in past.
2. The payoffs to the nodes from the stage game in any period depend only on the action profile for G which was played in that period, and this stage game payoff to a node for a given action profile for G is independent of which period it is played.
We now define the players’ payoff functions for the repeated game. When studying about repeated games, we are concerned about a player who receives a payoff in each of many periods. In order to represent the performance over various payoff streams, we want to meaningfully summarize the desirability of such a sequence of payoffs by a single number. A common assumption is that the player wants to maximize a weighted sum of its per-period pay- offs, where it weights later periods less than earlier periods. For simplicity this assumption often taken the particular form that the sequence of weights forms a geometric series for some fixed δ (0,1), each weighting factor is δ times the previous weight. δ is called discount factor. ∈ t If in each period t, player i receives the payoff ui then we could summarize the desirability of the
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0 1 payoff stream ui ,ui ...... , by the number:
t t t 1(, ) ui t0
Such a preference structure has the desirable property that the sum of the weighted payoffs will be finite. It is often convenient to compute te average discounted value of an infinite payoff stream in terms of a t leading finite sum and the sum of a trailing infinite stream. For example suppose the payoffs vi a player ' receives are some constant payoff vi for the first t periods, and there after it receives a different constant payoff vi in each period. The average discounted value of this payoff stream
is
t1 t t t t t t 1( ) vi 1( ) vi vi 0 0 t
CONCLUSION This paper has viewed that game theory is not simply a matter of mathematics but concerns the real world, in the sense that involves decision-making by several players that also affect the interest of other players. But it does not mean that the purpose of game theory is to predict behaviour in the same sense as in sciences but it is capable of such things. Players are arranged in their preferences, their information, the strategic actions available to them, and how these influence their payoffs (returns). In situations where there are more than two players, a decision by player 1 does also affect the interest of other players (player 2). Game theory covers many aspects such as economics, political science, and psychology, as well as logic and biology
Game theory is also viewed as a broad subject but basically divided into two branches, noncooperative games and cooperative games, which are sets of payoff combinations that satisfy both individual and group rationality. While non- cooperative games looks at a situation where each player maximises his payoff given the other players’ strategies, which means players basically make choices out of their own interest. Game theory also views Nash equilibrium as a basic concept of the subject, but in situations of strategic games players base their random selection of strategies using certain probabilities. The subject looks at different scenarios that involve decision making and Nash equilibrium is said to be the most effective concept that deals with that with the famous application of Prisoner’s Dilemma is also said to be the most common example to illustrate game theory.
The game theory is viewed as analysis of the concepts used in social reasoning when dealing with situations of decision making and conflicts. Much highlight has been given on auction games, where a set of players, a set of strategies available to each player, and a payoff vector corresponding to each combination of strategies. Game theory builds an abstract between theory and real life situation. In real life situation, game theory can be observed in many marketing industries and sale industries, in some through the use of auctions and also in peoples behaviour, the way they make the everyday choices sort of includes the game theory especial when an individual has to make a choice. Big industries also apply game theory in most of the management strategies, when a certain decision or development has to be taken. Some game strategies do come into practise. This theory is of much use in many fields of competitive scenarios and can even be suitable in any economic related field where decision making is of importance.
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