Question 8 (a)

Zero-sum game

6 marks

Time to write: About 12 minutes
Topic: Games and strategic interaction

Question

Question 8 (a) · 6 marks

Write a brief note on each of the following, along with an example for each:

Zero sum game

Reworded from the university paper; the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.

Before you write

Read off the question and its marks

12 minfor 6 marks

Read from the question

exampleExamples are asked for: one short example with each point.
note onA note opens with the meaning, then two or three key points. No long introduction.

Write it in this order

Read; underline the asks; jot your points 1 min
1 Meaning of a zero-sum game 2 marks 2 min
2 Features pure conflict, payoffs add to zero, no gain from cooperation 1½ marks 3 min
3 Example with a payoff table 1½ marks 3 min
4 Contrast with non-zero-sum games 1 mark 2 min
Check: every ask answered, key terms underlined 1 min

1234

Easy marks

Meaning of a zero-sum game (step 1, 2 marks): a clear definition and a line on what it covers. It opens the answer, so it takes a minute or two.

Short on time? Keep step 1 short. Trim steps 2 and 3 evenly rather than skip one: each is capped at its own marks. End with step 4 in a line or two.

Try it first. About 12 minutes for 6 marks. Write it out, then open the solution.

Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

Meaning. A game is a situation in which each player's payoff, the gain or loss she ends up with, depends on her own choice and on the choices of the others. A zero-sum game is a game of pure conflict: whatever one player gains, the other loses, so the payoffs of the players add up to zero in every outcome and the game creates no net gain or loss in total. If the total is a fixed amount other than zero (as when a fixed prize is divided), it is called a constant-sum game, which works in the same way.

Features.

Pure conflict. The players' interests are exactly opposed: there is a clear winner and a clear loser.
Payoffs sum to zero in every cell of the payoff table; one player's payoff is the negative of the other's.
No room for cooperation. Since the total is fixed, no agreement can make both players better off together; one can gain only at the other's expense.
Players are assumed rational: each picks the strategy that is best for her, expecting the rival to do the same.

Example: a penalty kick. Our own example. In a football match in Kolkata, a striker shoots left or right and the goalkeeper dives left or right, at the same moment. A goal is worth +1 to the striker and −1 to the goalkeeper; a save is worth −1 to the striker and +1 to the goalkeeper. Payoffs are (striker, goalkeeper):

	Keeper dives left	Keeper dives right
Striker shoots left	(−1, +1) save	(+1, −1) goal
Striker shoots right	(+1, −1) goal	(−1, +1) save

In every cell the two payoffs add to zero: the striker's goal is exactly the keeper's loss. Neither player has a strategy that is best whatever the other does, so each tries not to be predictable.

Zero-sum and non-zero-sum games. Many economic interactions are not zero-sum: in voluntary trade both sides can gain, and two rival firms that both spend heavily on advertising can both end up worse off. In such games the total payoff changes with the players' choices, so cooperation or conflict changes the size of the total, not only how it is shared.

Conclusion. A zero-sum game is one in which the players' payoffs always add up to zero, so one player's gain is exactly the other's loss; a penalty kick is an example.

Where the 6 marks sit

#	Component	Marks
1	Meaning of a zero-sum game	2
2	Features (pure conflict, payoffs add to zero, no gain from cooperation)	1.5
3	Example with a payoff table	1.5
4	Contrast with non-zero-sum games	1
	Total	6

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