Types game theory pdf

Translate PDF. The interest in this issue is increasing when the provides a beginning for the solution in the process of consistency between the results of the application and complex interactive decision making.

Game theory gives application territory is seen. In this field, the game theory can provide a good score in making economic decisions in the economic Keywords: Game theory, strategy markets where competition takes place.

The game theory is a mathematical approach that analyzes the deciding process 1. Introduction considering the deciding process of the opponents in clash The biggest problem that the business management environments. Thus, the Game Theory is types. Businesses generally aim to reach the prudential a mathematical approach that explains the struggle of the targets they have determined depending on their internal complex wheels OZDIL The businesses, thus, choose to predict the future with the data obtained through To meet the analysis needs of conflict situations, special previous periods and with the quantitative deciding mathematical techniques named as theory of games have techniques such as mathematical programming Operations been developed.

The purpose of this theory is to analyze research , cross section data regression models, time series the most rational movement ways of the both parties which trend analysis in the process of deciding. As there are several factors, real life conflict situations are extremely complex and quiet In these methods, the mutual interactions between hard to be analyzed.

Hence, to make a mathematical the variables are not mostly considered or it is accepted analyzes possible, we need to remove base factors and that this is reflected in the models formed automatically. The purpose of this study is to bring a solution method to the 3-player non-zero-sum games. Accepted date: E-mail: cigdem hotmail. We will call B1 B1 line as B1 which shows the gains for B1 strategy. Kuzu et al. I, Issue I, completely the same.

The geometric method for 2x2 games For the solution of a 2x2 game, a simple geometric interpretation can be given. The 2x2 game whose matrix can be seen on the side is considered and the diagram below is drawn on xy plane.

Our strategy is shown on x axis. I and II perpendiculars are drawn from A1 and A2 points. Table 2. B1 and B2 strategies. We want to find a optimal strategy, that is,drawing in thisforstrategy, Figure 2. To do this, lower bound is drawn for B1 and B2 str 11 maximum12gain maximum gain for for any B11 strategy. To To do do this, this, lower lower bound bound is is drawn drawn for B11 and for B B22 strateg and B strateg a2 a21 a22 2 B strategies.

This lower bound provides minimum gains This This lowerlower bound provides bound minimum for provides our gains all mixed minimum for for our strategies. N point The in whichThe strategies. The N point in wh of all, it is accepted that our opponent uses B1 strategy. This defines a point minimum whosebecomes maximum is the solution of the game. First of all, it is accepted that thisour opponent minimum this minimum uses becomesB becomes maximum this minimum becomes maximum 1 maximum isisthe The reasons is solution theof the solution of thecan of the the these drawing solution of game.

This defines a point whose a11 on I-I andstrategy. Here; 1 whose and a point whose ordinate is a21 on II. The Thereasons of these The reasons reasons of drawing of these these drawingcan drawing canbe can beseen be seen clearly seen fromthe clearly from clearly from thegeneral the general general figure figure figure below. The Figure 2. The geometric geometric drawing drawing for 2x2 gamefor 2x2 game Figure 2.

If we use These s define B1B1 line. The ordinate of the N point is the v value of B1defines defines both the solution and 2. P game. P22 abscissa abscissa is is the the fraction fraction of 2 1 of A 1A22 strategy strategy in in our our optimal optimal mixed mixed strategy.

B strategy is drawn whose abscissa is p2 on B1 B1 line. We will call For B the the line Bsituation 2 1 situation 1 definescan which which both can bethe be seen seensolution below,and below, isthe itit is values. B2 strategy forPB21 abscissa strategy. B is2isstrategy the theisNdrawn fraction point of A is 2 the v value strategy in of our the game.

P optimal abscissa mixed is the strategy. However, fraction However, the the ofsolution We strategy A2want solution is to in our is not not find always always a optimal this mixed in this in optimal point. Wewantwanttoto find find aa optimal strategy, For thethat is,is, in in situation thisthis which For canthe besituation seen below,whichwill canisbe it bedefined seen below,withit the is defined intersection poin We optimal strategy, that strategy, minimum gain strategy, minimum gain will be maximum gain for any maximum with gain for any the intersection B1 of point strategy.

To do this, the solution lower bound is dr strategies. B1 strategy. To do solution is drawn this, for B1bound lower strategies. This lower bound provides minimum gains for our all mixed stra This lower bound provides minimum gains for our all mixed strategies. The N point in which this minimum becomes maximum is the solution of the game. I, Issue I, Figure 3-People non-zero-sum games 2.

Thus, the Figure 2. The geometric drawing for 2x2 game Figure 2. No matter which strategy the In the 2. Figure theThe Thus,2. No matter which strategy the 2. Figure dle point and A2 strategy opponent dominates uses, using A1would A1 strategy strategy.

If they both get into the price war, then both of them would suffer the loss of 3. On the other hand, if organization B cooperates, then both of them would earn equal profits. In this case, the best option would be that organization A enters the market and organization B cooperates.

Simultaneous games are the one in which the move of two players the strategy adopted by two players is simultaneous. In simultaneous move, players do not have knowledge about the move of other players. On the contrary, sequential games are the one in which players are aware about the moves of players who have already adopted a strategy.

However, in sequential games, the players do not have a deep knowledge about the strategies of other players. Simultaneous games are represented in normal form while sequential games are represented in extensive form. Let us understand the application of simultaneous move games with the help of an example. Suppose organizations X and Y want to minimize their cost by outsourcing their marketing activities. However, they have a fear that outsourcing of marketing activities would result in increase of sale of the other competitor.

The strategies that they can adopt are either to outsource or not to outsource the marketing activities. In Table, it can be seen that both the organizations X and Y are unaware about the strategy of each other. Both of them work on the perception that the other one would adopt the best strategy for itself. Therefore, both the organizations would adopt the strategy, which is best for them. The same example can also be used for the explanation of sequential move games.

Suppose organization X is the first one to decide whether it should outsource the marketing activities or not. In Figure-3, the first move is taken by organization X while organization Y would take decision on the basis of the decision taken by X.

However, the final outcome depends on the decision of organization Y. In the present case, the second player is aware of the decision of the first player. Constant sum game is the one in which the sum of outcome of all the players remains constant even if the outcomes are different. Zero sum game is a type of constant sum game in which the sum of outcomes of all players is zero. In zero sum game, the strategies of different players cannot affect the available resources.

Moreover, in zero sum game, the gain of one player is always equal to the loss of the other player. On the other hand, non-zero sum game are the games in which sum of the outcomes of all the players is not zero. A non-zero sum game can be transformed to zero sum game by adding one dummy player. The losses of dummy player are overridden by the net earnings of players. Examples of zero sum games are chess and gambling.

In these games, the gain of one player results in the loss of the other player. However, cooperative games are the example of non-zero games. This is because in cooperative games, either every player wins or loses. In symmetric games, strategies adopted by all players are same. Symmetry can exist in short-term games only because in long-term games the number of options with a player increases. The decisions in a symmetric game depend on the strategies used, not on the players of the game.

Even in case of interchanging players, the decisions remain the same in symmetric games. On the other hand, asymmetric games are the one in which strategies adopted by players are different. In asymmetric games, the strategy that provides benefit to one player may not be equally beneficial for the other player.

However, decision making in asymmetric games depends on the different types of strategies and decision of players. Example of asymmetric game is entry of new organization in a market because different organizations adopt different strategies to enter in the same market.

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