Topics: Game theory, Nash equilibrium, Solution concept Pages: 77 (26065 words) Published: August 21, 2013

Implementation, contracts, and renegotiation in environments with complete information*

John Moore

READER'S GUIDE Part one of the chapter is written in an easy style, to try to demystify the subject (it is based on the lecture given at the World Congress). The Biblical story of the Judgement of Solomon is used as a running example for presenting different notions of implementation. Inevitably, perhaps, this part of the chapter contains a number of statements that are rather loose. This is compensated for by the more formal part two, which amplifies certain results and topics - though here, too, some degree of detail has been sacrificed for the sake of readability. The chapter deals with situations in which agents are presumed to have complete information about each other's preferences. Thomas Palfrey's chapter in this volume, "Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design," is a companion to this, and looks at environments with incomplete information. Even though the complete-information environment is a restrictive case, the literature on it is vast and still growing. I have therefore had to be quite selective. The chapter should be seen as an overview of recent research, not as a comprehensive survey; I regret that I have not been able to do justice to the work of a number of authors. PART ONE The text is taken from the Old Testament: the First Book of Kings, chapter 3, verses 16-28. It is the story of the Judgement of Solomon. Two women

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Implementation, contracts, and renegotiation


came before the King, disputing who was the mother of a child. Quoting from the Jerusalem Bible: "If it please you, my lord," one of the women said, "this woman and I live in the same house, and while she was in the house I gave birth to a child. Now it happened on the third day after my delivery that this woman also gave birth to a child. We were alone together; there was no one else in the house with us Now one night this woman's son died And in the middle of the night she got up and took my son from beside me while I was asleep; she put him to her breast and put her own dead son to mine. While I got up to suckle my child, there he was, dead. But in the morning I looked at him carefully, and he was not the child I had borne at all." Then the other woman spoke. "That is not true! My son is the live one, yours is the dead one"; and the first retorted, "That is not true! Your son is the dead one, mine is the live one." And so they wrangled before the king "Bring me a sword" said the king; and a sword was brought into the king's presence. "Cut the living child in two," the king said "and give half to one, half to the other." At this the woman who was the mother of the living child addressed the king, for she burned with pity for her son. "If it please you, my lord," she said "let them give her the child; only do not let them think of killing it!" But the other said, "He shall belong to neither of us. Cut him up." Then the king gave his decision. "Give the child to the first woman," he said "and do not kill him. She is his mother." All Israel came to hear of the judgement the king had pronounced, and held the king in awe, recognising that he possessed divine wisdom for dispensing justice.

That is an early example of implementation theory at work.1 The formal theory has its roots at least as far back as the 1930s and 1940s, with the Hayek-Mises-Lange-Lerner debates concerning the feasibility of market socialism.2 In the 1950s and 1960s, Hurwicz took up these ideas and extended them to other mechanisms. It was he who pointed out that one should think of the mechanism as being the unknown - that is, the economic organization/institution by which economic activity is to be coordinated; and of the economic environment (technology, preferences, and endowments) as being the parameters, or coefficients. It...
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