Question

During the pandemic, stockpiling behavior have been criticized in the newspapers and described as irrational. From a game theory perspective, stockpiling of toilet paper can be modeled as a strategic game. Let’s assume that we have two players who can choose between option 1: running to buy toilet paper (stockpiling behavior); and option 2: waiting to buy toilet paper. They believe that there is a risk that supermarket will run out of stock. The following matrix gives the payoffs of each choice, where in each cell, the first number is the payoff of player A and the second number is the payoff of player B.

		Player B
		Wait to buy	Run to buy
Player A	Wait to buy	3, 3	1,4
	Run to buy	4,1	2,2

1. Explain the strategic interactions behind the stockpiling behavior (answer in 70-130 words).
2. Find the equilibrium by elimination of dominated strategies (answer in 70-130 words).
3. Does individual rationality lead to a socially desirable outcome? Why? (answer in 70-130 words)

Answer 1

From a game theory perspective, stockpiling of toilet paper can be modeled as a strategic game. Let’s assume that we have two players who can choose between option 1: running to buy toilet paper (stockpiling behavior); and option 2: waiting to buy toilet paper. They believe that there is a risk that supermarket will run out of stock.

a. Strategic interaction describes a gamelike event in which an individual's situation is fully dependent on the move of one's opponent and in which both players know this and have the wit to use this awareness for advantage. The stockpiling behaviour of people during some pendmic situations also shows the stretegic interection because during such time people think that there may be a shortage of some necessity goods like toiletpapers, food items, medicines etc. So they try to stock them thinking that others may buy all and hence they will not get any later. Here the behaviour of one person depends on the estimated behaviour of other and almost all people think in the same way and they create shortage of some goods and services though there is no actual shortage.

b. From the above given game we can find the equilibrium by using elimination of dominated stretegies as -

• Firstly we see for player A, whose wait to buy stretegy is strictly dominated by run to buy stretegy because the payoffs in wait to buy is less than the other stretegy(3<4,1<2) and hence the first row is eliminated.
• Secondly we see for player B, for the remaining stretigies, here Player B's wait to buy stretegy is strictly dominated by Run to buy stretegy (1<2). So, first column is eliminated.
• Now we are only left with one set of seretegy any payoff which is the equilibrium.
• Hence the equilibrium is Run to buy, Run to buy (2,2).

C. Yes, individual rationality will lead to a socially desirable outcome.

From the above example we can see that when both the individuals behave irrationally i.e. they show a stockpiling behaviour lime a game than the equilibrium achieved is not socially desirable because in this case both of them gets a lower payoff (2,2).

But if they have behaved rationally i.e. they do not Run to buy but Wait to buy or buy as they do normally there would not have been shortage in the market and hence they would have got a higher payoff (3,3) which is socially desirable outcome as the overall payoff in the society is highest 3+3 =6.