Information and Relational Contracts Preliminary Draft

We investigate the use of information in repeated principal-agent game and report three results. First, consistent with Kandori (1992), garbling signals within each period hurts the e¢ ciency of the game. Second, contrary to Abreu, Milgrom, and Pearce (1991), bundling signals across periods and then fully revealing them never increases the e¢ ciency of the game. Third, and most importantly, we construct an intertemporal garbling of signals that transforms the repeated game into one with private monitoring. The main nding of the paper is that in the transformed game, there exists a belief-based pure-strategy equilibrium that can be more e¢ cient than the optimal equilibrium in the original game with imperfect public monitoring. 1 Introduction This paper studies the use of information in repeated principal agent games, i.e. relational contracts. The prevalence and importance of relational contracts, contracts enforced not by the rule of the court but rather by the self-interests of the participating parties in concern of future contracts, have been emphasized both inside and outside the economics literature. The existing theoretical literature on relational contracts, see for example MacLeod and Malcomson (1988), Levin (2003), and Fuchs (2007), has focused on the e¢ ciency of the relational contract taking the information structure as xed. Little is known about how information structure a¤ects the e¢ ciency of relational contracts. The role of information in repeated-game (without transfers) has received considerable attention from economists. The two most inuential papers in this literature are Abreu, Milgrom, and Pearce (1991) and Kandori (1992). 1 Kandori (1992) shows that in a repeated game with imperfect public monitoring, the e¢ ciency of the game is weakly increased if the commonly observed public signal of the output becomes more informative in the sense of Blackwell. Kandori (1992) also provides conditions under which the e¢ ciency of the game can be strictly increased. Abreu, Milgrom, and Pearce (1991) (AMP hereafter) show that, when the players play strongly-symmetric strategies and their discount factors approach 1, the e¢ ciency of the game can be enhanced through bundling signals across several consecutive periods and then fully revealing them at the end of these periods. In this paper, we investigate the role of information in relational contracts. We show that the logic of Kandori (1992) developed in repeated game without transfers carries through to relational contracts: the e¢ ciency of the relational contracts is weakly enhanced if the signals are more informative in the sense of Blackwell. On the other hand, contrasting AMPs nding, we show that bundling signals across periods and fully revealing them every T periods decreases the e¢ ciency of the relational contract. While these two results would appear to suggest the e¢ ciency of the relational contract increases when the signals become more informative and are revealed more frequently, our main result shows that this is not true. 1Kandori and Obara (2006) show that when the discount factor is close to one, reducing observability allows for asymmetric punishment in repeated games with imperfect public monitoring. This can expand the equilibrium payo¤ set.