A Game Theoretic Analysis of the Politics of Taking It in Turns

Abstract

Taking it in turns is an endemic feature of political and social life. For instance, in a democratic system parties take turns in office according to the outcome of elections. Despite its empirical importance, taking it in turns has received virtually no attention from rational choice theorists. First, a general definition of taking it in turns is given. Secondly, the conditions for taking it in turns to be stable and efficient in Prisoners' Dilemma, Chicken, and Co-ordination supergames are discussed. The key result is that, where stable adherence to a taking it in turns pattern demands that players' continued adherence is conditional on the past adherence of others, players will stick with the pattern if they get their turn often enough. The precise conditions are shown to depend on the payoff structure and the discount rate. Potential problems are identified with initiating stable taking it in turns because of the existence of multiple equilibria and players' desire to get a stable taking it in turns pattern that gives them a high expected payoff. The paradigmatic version of this problem is who goes first when two players alternate between getting a high and a low payoff. The applicability of the results is illustrated by considering the questions of democratic stability and transitions to democracy.