Thucydides on Nash vs. Stackelberg: The Importance of the Sequence of Moves in Games

Abstract

"The paper provides a general characterization of the conditions in two-by-two games under which players will prefer to move first or second, or will be indifferent to the sequence of moves. The general result is that in games without a pure strategy equilibrium either there will be a struggle for the second move, or the players will agree on the sequence of play ; a struggle for the first move is characteristic of games with two pure strategy equilibria; in games with one pure strategy equilibrium, players most of the time will be indifferent about the sequence of moves. Examples from Thucydides' History of the Peloponnesian War and other political and social situations illustrate how players manage to change the sequence of moves."