Reference no: EM133067281

The general strategic game in Thucydides' history of the Peloponnesian War has beenexpressed in game-theoretic terms by Professor William Charron of St. Louis University.10Athens had acquired a large empire of coastal cities around the Aegean as part of itsleadership role in defending the Greek world from Persian invasions. Sparta, fearing Athenianpower, was contemplating war against Athens. If Sparta decided against war, Athens wouldhave to decide whether to retain or relinquish its em- pire. But Athens in turn feared that if itgave independence to the cities, they could choose to join Sparta in a greatly strengthenedalliance against Athens and receive very favorable terms from Sparta for doing so. Thus, thereare three players, Sparta, Athens, and Small cities, who move in this order. There are fouroutcomes, and the payoffs are as follows (4 being best):Outcome Sparta Athens Small citiesWar 2 2 Athens retains empire 1 4 Small cities join Sparta 4 1 Small cities stay independent 3 3 (a) Draw the game tree and find the rollback equilibrium. Is there another outcome that isbetter for all players?(b) What strategic move or moves could attain the better outcome? Discuss the credibility ofsuch moves.