# Ame Theory in Economics: Importance, Limitation and Other Details

(Please this essay will be turin in to check the plagiarism) Write a three page paper (Times New Roman, Font size: 12, line spacing: 1.5) evaluating the following article (The article is provided below and can also be viewed in the website: ).

Assignment: Discuss the concept of Game theory and present your opinion about its importance in Economics through various examples.

Deadline: April 20, 2015 in class. Late submissions will not be accepted. All papers must be printed with name and section number included

Game Theory in Economics: Importance, Limitation and Other Details

The theory of games is one of the most outstanding recent developments in economic theory. It was first presented by Neumann and Morgenstern in their classic work, Theory of Games and Economic Behaviour, published in 1944 which has been regarded as a a?rare eventa? in the history of ideas.

Game theory grew as an attempt to find the solution to the problems of duopoly, oligopoly and bilateral monopoly. In all these market situations, a determinate solution is difficult to arrive at due to the conflicting interests and strategies of the individuals and organisations.

The theory of games attempts to arrive at various equilibrium solutions based on the rational behaviour of the market participants under all conceivable situations. a?The immediate concept of a solution is plausibly a set of rules for each participant which tells him how to behave in every situation which may conceivably arise.a?

The underlying idea behind game theory is that each participant in a game is confronted with a situation whose outcome depends not only his own strategies but also upon the strategies of his opponent. It is always so in chess or poker games, military battles and economic markets.

We shall be concerned mainly with the various solutions of the duopoly problem where the bargaining process is between two parties. But before we start the analysis of the theory of games, it will be useful to digress on certain fundamentals of game theory.

A game has set rules and procedures which two or more participants follow. A participant is called a player. A strategy is a particular application of the rules leading to specific result. A move is made by one player leading to a situation having alternatives. A choice is the actual alternative chosen by a player.

The result or outcome of the strategy followed by each player in relation to the other is called his pay-off. The saddle point in a game is the equilibrium point. There are two types of games: constantsum and non-constant-sum. In a constant-sum game what one player gains the other

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loses. The profits of the participants remain the same, whereas in a non-constant-sum game, profits of each player differ and they may co-operate with each other to increase their profits.

Two-Person Constant-Sum or Zero-Sum Game:

In a constant-sum or zero-sum game between two players, the gain of one player is exactly equal to the loss of the other player. a?There is, for each player, a strategy.... which gives him the mathematical expectation of a gain not less than, or of a loss not greater than, a certain particular value. It also shows that, if the players actually behave in this way, then those expected gains and losses are actually realised and the game has a determinate solution.a?

Assumptions:

The two-person constant-sum game is based on the following assumptions:

(i) A duopolistic market situation exists with firms A and B, each trying to maximize its profits, (ii) Each is engaged in a constant-sum game so that what one firm gains, the other loses,

(iii) One firmas interest is diametrically opposed to the otheras,

(iv) Each firm is in a position to guess the strategy of the other as against its own strategy so as to construct the pay-off matrix for both. Lastly, each firm assumes that its opponent will always make a wise move and it would try to countermove that to protect itself from any possible loss.

Pay-off Matrix and Strategies:

Suppose firm A has three strategies for maximizing its profits. They are to improve the quality of its product, to advertise it and to reduce its price. Its rival firm ? has also the same alternative strategies to profit more. Aas pay-off is shown in Table 1. Since we are concerned with constantsum games, the strategies of both A and ? are depicted in one pay-off matrix, as Aas gain is Bas loss and vice versa.

In order to show how A and ? will choose the various strategies consider the numerical example given in Table I. If A chooses strategy 1 with a pay-off of 5, it estimates that ? will choose strategy 3 with a pay-off 4, thereby reducing Aas profit to its minimum value or security value 4.

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This is recorded at the end of row 1 and beginning of column 5. If A chooses strategy 2 with a value of 3, ? will employ its strategy 1 to counteract Aas move so that A will gain a minimum profit of 2. Finally, when A chooses strategy 3 having a value of 9, Aas pay-off is reduced to 8 by ? as he employs strategy 3.

In employing each strategy, firm A moves cautiously and assumes that whatever strategy it employs, its rival ? will always adopt that counter-strategy which will provide A with the minimum pay-off. Thus each time A adopts a technique, its profit is reduced to the minimum by Bas counterstrategy.

Therefore, A will choose that strategy which gives it the minimum out of the three maximum pay-offs in each row. Thus A is interested in the a?Row Mina? pay-offs 4, 2, 8 shown in the last column of Table 1. It will choose strategy 3 because it provides it with the maximum-minimum or better known as maximin gain of 8 which is the highest among the row minima. This is called maximin or dominant strategy which is defined as a?the worth of the game to the maximizing player because his opponent cannot prevent him from realising it.a?

Firm ? is also cautious about the counter-strategy of its rival A. ? knows that whatever move it will make in adopting a particular strategy, A will counteract it by adopting a counter-strategy, thereby leaving ? with a worse pay-off. Bas worse pay off means that A receives very large profit and ? is left with a very little residual.

This is what ? thinks about the strategy of A. Therefore, ? chooses the maximum pay-off in each strategy because it thinks that by so doing it cannot prevent A from gaining that much in each column of the three strategies. If ? adopts strategy 1, A will choose strategy 3, so that the worst pay-off level for ? is 10. Similarly, by adopting strategy 2, the worst move gives ? the maximum pay-off 9; whereas strategy 3 gives it the pay-off 8.

The maximum pay-off from each strategy is thus 10, 9 and 8 shown in a?Col. Maxa? (column maxima) in Table 1, last row. The best of these pay-offs from Bas point of view is the minimum of the column maxima, 8. It is called the minimax, and the method employed by the minimiser is the minimax strategy. This is Bas dominant strategy.

The Saddle Point:

The saddle point is the equilibrium point. In the pay-off matrix of Table 1, Aas pay-off from its maximin strategy 3 exactly equals Bas pay-off from its minimax strategy 3 (88). When the minimax and the maximin in a pay-off matrix are equal, it is a strictly determined game. Both the players (firms) are guaranteed a common amount of win (profit). They cannot win more because there is a saddle point in the pay-off matrix which occurs both in the a?Row Mina?, and a?Col. Maxa?. It is the equilibrium point 8, common to both A and B.

Thus a constant-sum-two-person game is strictly determined only if it has a saddle point arrived at with pure strategy. The determinate solution of the duopoly situation discussed above is entirely based on pure strategy whereby each firm reasons out which of the several possible courses of action are the most favourable to it.

In a uniquely determined game with pure strategy, there is no need for recognising mutual interdependence on the part of the duopol