Inducible Games: Using Tit-for-Tat to Stabilize Outcomes

Abstract

Assume it is known that one player in a 2 x 2 game can detect the strategy choice of its opponent with some probability before play commences. We formulate conditions under which the detector can, by credibly committing to a strategy of probabilistic tit-for-tat (based on its imperfect detector), induce an outcome favorable to itself. A non-Nash, Pareto-optimal outcome is inducible — that is, it can be stabilized via probabilistic tit-for-tat — in 20 of the 57 distinct 2 x 2 strict ordinal games without a mutually best outcome (35 percent). Sometimes the inducement is “weak,” but more often it is “strong.” As a case study, we consider the current conflict between Israel and Iran over Iran’s possible development of nuclear weapons and show that Israel’s credible commitment to probabilistic tit-for-tat can, with sufficiently accurate intelligence, induce a cooperative choice by Iran in one but not the other of two plausible games that model this conflict.

Keywords: 2 x 2 games, tit-for-tat, inducibility, Israel-Iran Conflict, nuclear weapons

JEL Classification: C72, C78, D74