Question 8 (a)
Strategies and payoffs in strategic games
6 marks
- Time to write
- About 12 minutes
Question
Question 8 (a) · 6 marksWrite a short note on the following, giving examples:
- Strategies and payoff in the setting of strategic games.
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
Read from the question
- examplesExamples are asked for: one short example with each point.
- short noteA note opens with the meaning, then two or three key points. No long introduction.
What the paper leaves open
As printed, the opening sentence of question 8 is followed by three parts (a), (b), (c), each with its own marks (6); the opening sentence is repeated in each part.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Strategy, its meaning and kinds, with an example 2½ marks 4 min
- 2 Payoff, its meaning, with an example 2 marks 3 min
- 3 Worked example linking the two 1½ marks 3 min
- Check: every ask answered, key terms underlined 1 min
Short on time? Trim steps 1–3 evenly rather than skip one: each is capped at its own marks.
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.
A strategic game is an interaction in which what each decision maker receives depends also on the choices of the others. Strategies and payoffs are two of its building blocks, along with the players themselves.
Strategies. A strategy is a player's plan of action for the game. It may be one simple move, or a more complex plan under which the action depends on what has happened earlier.
- A pure strategy means choosing one definite action with certainty, for example a shopkeeper who always opens on Sundays.
- A mixed strategy means choosing among actions according to probabilities, for example a bowler who bowls a yorker on 70 per cent of deliveries and a bouncer on 30 per cent.
In a simultaneous game each player must form a strategy by assuming what the other will choose, while in a sequential game the later mover can make his strategy depend on the action already taken.
Payoffs. A payoff is what a player receives at the end of the game once the strategies have been played: a gain or a loss. It may be in money (profit, wages) or not in money (utility, satisfaction). Each player is assumed to aim at the highest payoff she can get. A player's payoff depends on the whole set of strategies chosen, not only on her own.
Example: two cab companies. Our own example, with imagined figures. Two app-based cab companies in Pune each decide whether to offer a festival discount. In a payoff matrix, the first number in each cell belongs to the player in the rows and the second to the player in the columns. The payoffs are profits in ₹ lakh (Company 1, Company 2).
| Company 2: Discount | Company 2: No discount | |
|---|---|---|
| Company 1: Discount | (5, 5) | (9, 2) |
| Company 1: No discount | (2, 9) | (7, 7) |
Each company has two strategies, Discount and No discount, and each cell shows a pair of payoffs. If Company 1 discounts, its profit is 5 if the rival discounts too, and 9 if the rival does not.
How the two are linked. Strategies are what players choose; payoffs are what they get from the combination chosen. A rational player compares payoffs across her strategies, given what she expects from the others, which is why the same strategy can be good against one rival move and poor against another.
Conclusion. A strategy is a plan of action, pure or mixed; a payoff is the resulting gain or loss to a player. A game's payoff matrix sets out both together.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Strategy, its meaning and kinds, with an example | 2.5 |
| 2 | Payoff, its meaning, with an example | 2 |
| 3 | Worked example linking the two | 1.5 |
| Total | 6 |
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