Shoppers in the United States, Europe, Australia, Japan and Hong Kong have caught toilet paper fever on the back of the COVID-19 coronavirus. Store shelves are being emptied as quickly as they can be stocked. This panic buying is the result of the fear of missing out. It's a phenomenon of consumer behavior similar to what happens when there is a run on banks. A bank run occurs when depositors of a bank withdraw cash because they believe it might collapse. What we're seeing now is a toilet paper run. A bank holds only a fraction of its deposits as cash reserves and lends out as much of its deposits as it can. If every customer simultaneously decided to withdraw all of their deposits, the bank would crumble under the liability. Why, then, do we not normally observe bank runs? Or toilet paper runs? And why do we observe them in crises? Both banking and the toilet-paper buying can be thought of as a strategic game.

(a) Assume there are two players - you and everyone else. There are two strategies - "panic buy" or "act normally." If everyone acts normally, then there will be toilet paper on the shop shelves, and you can relax and buy it as needed. But if others panic buy, you should do the same, otherwise you'll be left without toilet paper. Everyone is facing the same strategies and payoffs, so others will be better off to panic buy if you do. Present the game formally using either extensive or strategic form, whichever you think is more appropriate. Assign player payoffs to each strategy combination to match the description above (pay attention to the ranking of the payoffs, not their magnitudes).

(b) Does this game resemble any of the classic games we studied (Prisoners' Dilemma, Chicken, Battle of the Sexes, Coordination)? Explain.

(c) What solution concept is the most appropriate for this game (Dominant Strategy Equilibrium, Iterated Dominance Equilibrium, Nash Equilibrium, Subgame Perfect Equilibrium)? Explain. Solve for the game equilibrium (or equilibria, if there are several); list the equilibrium strategies and payoffs. Is the equilibrium unique? Is the best outcome guaranteed for all players? Explain.

(d) Some people claim that stocking up to prepare for a crisis isn't 'panic buying'. It's actually a pretty rational choice. Does game-theoretic analysis support such a claim? Base your answer on your analysis of the game.