The general strategic game in Thucydides’ history of the Peloponnesian War has been expressed in game-theoretic terms by Professor William Charron of St. Louis University.10 Athens had acquired a...

The general strategic game in Thucydides’ history of the Peloponnesian War has been expressed in game-theoretic terms by Professor William Charron of St. Louis University.10 Athens had acquired a large empire of coastal cities around the Aegean as part of its leadership role in defend‑ ing the Greek world from Persian invasions. Sparta, fearing Athenian power, was contemplating war against Athens. If Sparta decided against war, Athens would have to decide whether to retain or relinquish its em‑ pire. But Athens in turn feared that if it gave independence to the cit‑ ies, they could choose to join Sparta in a greatly strengthened alliance against Athens and receive very favorable terms from Sparta for doing so. Thus there are three players, Sparta, Athens, and Small cities, who move in this order. There are four outcomes, and the payoffs are as follows (4 being best):

(a) Draw the game tree and find the rollback equilibrium. Is there an‑ other outcome that is better for all players?

(b) What strategic move or moves could attain the better outcome? Dis‑ cuss the credibility of such moves.