Truthful Revelation Mechanisms for Simultaneous Common Agency Games

Abstract

Many economic environments can be modelled as common agency games-that is, games where multiple principals contract simultaneously and noncooperatively with the same agent. 1Despite their relevance for applications, the analysis of these games has been made difficult by the fact that one cannot safely assume that the agent selects a contract with each principal by simply reporting his "type" (i.e., his exogenous payoff-relevant information). In other words, the central tool of mechanism design theory-the Revelation Principle-is invalid in these games. 2 The reason is that the agent's preferences over the contracts offered by one principal depend not only on his type, but also on the contracts he has been offered by the other principals. We refer to the players who offer the contracts either as the principals or as the mechanism designers. The two expressions are intended as synonyms. Furthermore, we adopt the convention of using feminine pronouns for the principals and masculine pronouns for the agent. Depending on the application of interest, a contract can be a price-quantity pair, as in the case of competion in nonlinear tariffs; a multidimensional bid, as in menu auctions; or an incentive scheme, as in moral hazard settings. * Pavan: Department of Economics, Northwestern University, 2001 Sheridan Road Arthur Andersen Hall 329 Evanston, IL 60208-2600 (e-mail: alepavan@northwestern.edu). Calzolari: Department of Economics University of Bologna, Piazza Scaravilli 2 40126 Bologna Italy and CEPR (e-mail: giacomo.calzolari@unibo.it). This is a substantial revision of an earlier paper that circulated under the same title. For useful discussions, we thank seminar participants at various conferences and institutions where this paper has been presented. A special thank is to Eddie Dekel, Mike Peters, Marciano Siniscalchi, Jean Tirole, and three anonymous referees for suggestions that helped us improve the paper. We are grateful to Itai Sher for excellent research assistance. For its hospitality, Pavan also thanks Collegio Carlo Alberto (Turin), where this project was completed.† To comment on this article in the online discussion forum, or to view additional materials, visit the articles page at http://www.

Common agency with informed principals: Menus and signals

“…The theory of common agency games has experience a long development since Bernheim and Whinston's (1986b) seminal paper, and has achieved high levels of generality and complexity (see, e.g., Epstein and Peters (1999), Peters (2001), Martimort and Stole (2002), and Pavan and Calzolari (2010)). Until very recently-see Martimort and Moreira (2010)-this theory has always assumed that principals have no private information.…”

“…Following the path suggested by Peters (2001), Martimort and Stole (2002), and Pavan and Calzolari (2010) for games with uninformed principals, my goal is to identify a tractable class of games that allows to replicate all equilibrium outcomes of some underlying general game with informed principals. Similarly to those papers, my analysis identi…es the key strategic roles that mechanisms play in such games.…”

“…This principle says the following: any equilibrium outcome of a game in which principals compete in arbitrary indirect mechanisms is also an equilibrium outcome of a much simpler game in which principals o¤er menus of allocations and delegate the agent to pick one; the converse holds too. The Delegation Principle represents a key step to characterize the outcomes of standard games (see, e.g., Martimort and Stole (2002), and Pavan and Calzolari (2010)). Moreover, it provides important insights to understand the strategic nature of such games.…”

“…First, similarly to the Delegation Principle, it is essential that in the new "signal-menu game" each principal have the same ability to contract as in the underlying game. To ensure this property, I rely on the standard notion of enlargement from the literature on games with uninformed principals (see, e.g., Pavan and Calzolari (2010)). Second, it is crucial that in the new game each principal also has the same ability to signal as in the underlying game.…”

Competition in mechanisms

“…-Infinite Regress: Some authors have followed the route of explicitly solving the infinite regress problem and identifying the full set of feasible mechanisms sellers can offer (e.g. [Peters 2001], [Pavan and Calzolari 2009]). Calculating equilibria when sellers can choose from this full set of mechanisms has proven difficult.…”