Syllabus T. Y. B. A. Paper : IV advanced economic theory with effect from academic year 2010-11 in idol

Two-Person Zero-Sum Game: 
The simplest model is a duopoly market in which each firm 
tries to maximise its market share. Given this aim, it is clear that 
whatever one firm gains, the other losses. In other words, any 
gains of one firm is cancelled by the loss of the other firm so that 
the net gain is zero. Hence the name Zero-sum game. Since only 
two persons or firms are involved, it is called a two person game. 
This model is based on the following assumptions. 
Assumptions: 
1. The firms have only one goal, namely, to maximise their 
market share. 

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2. Each firm knows the strategies available to it and to its rival. 
3. Each firm knows with certainty the pay-offs
— total revenue, 
total costs, and total profits from each combination of 
strategies. 
4. The actions taken by duopolists do not affect the total size of 
the market. 
5. Each firm chooses its strategy expecting the worst from its 
rival. It means that each firm acts in the most conservative 
way, expecting that the rival will choose the best possible 
counter- strategy open to him. This behaviour is called rational. 
6. In the zero sum game, there is no possibility of collusion. Each 
firm wants to maximise its market share. It means that the aims 
of the firm are opposed to each other. 
2.4 GAME THEORY: NASH EQUILIBRIUM: 
 
Simple dominant strategy games 
The simplest case is where there are just two firms with 
identical costs, products and demand. They are both considering 
which of two alternative prices to charge. Figure 2.3 shows typical 
profits they could each make. 
Let us assume that at present both firms (X and Y) are 
charging a price of £2 and that they are each making a profit of 
£10 million, giving a total industry profit of £20 million. This is 
shown in the top left-hand box (A). 
Now assume they are both (independently) considering 
reducing their price to £1.80. In making this decision, they will 
need to take into account what their rival might do, and how this 
will affect them. Let us consider X's position. In our simple 
example there are just two things that its rival, firm Y, might do. 
Either Y could cut its price to £1.80, or it could leave its price at 
£2. What should X do?. One alternative is to go for the cautious 
approach and think of the worst thing that its rival could do. If X 
kept its price at £2, the worst thing for X would be if its rival Y cut 
its price. This is shown by box C: X's profit falls to £5 million.