CHAPTER 11 The Iterated Lift Dilemma How to Establish Meta-Cooperation with your Opponent J.P. Delahaye, P. Mathieu, and B. Beaufils Laboratoire d’Informatique Fondamentale de Lille A very small change in the Iterated Prisoner’s Dilemma (IPD) payoff matrix leads to an iterated game called the Iterated Lift Dilemma 1 the properties of which are very different from those of the classical IPD (CIPD). We show that the following ideas are to be noted: (i) two levels of cooperation are now possible, the best one needs a difficult coordination between considered strategies; (ii) only probabilistic strategies can make a high score when they play against themselves; (iii) complex dynamics can appear (at the edge of chaos) as soon as three strategies are confronted. Our idea, already argumented in the case of the CIPD, is that, in spite of the model simplicity you can obtain many complex phenomena: it is not true that to be good, a strategy must be simple. Building good strategies for the Iterated Lift Dilemma is then much more difficult than for the CIPD. 1. Introduction Conflicting situations are not only a driving force in nature and society, they are also the entry points for many investigations in Artificial Intelligence especially in Distributed Artificial Intelligence, Multi Agents Systems, formal model of rational action, CSCW, concurrent engineering and HCI. The Iterated Prisoner’s Dilemma is a model for studying cooperation and conflicts. It’s an iterated game. An iterated game is a game with two players A and B (also called strategies) who play an unknown finite number of rounds. On each round, each player chooses between two actions C (for Cooperation), and D (for Defection). A round where the player A plays C and the player B plays C is noted [C,C]; a round where the player A plays C and the player B plays D is noted [C,D]; a round where the player A plays D and the player B plays C is noted [D,C]; and finally a round where both players play D is noted [D,D]. When the players play the round number n they play simultaneously taking into account the game history (that is all the preceding choices they both have made at all rounds i with i<n). 1 The term Lift comes from the French expression renvoi d’ascenceur which means I help you this time, you will help me next time