Games played in a contracting environment

Abstract

We analyze normal form games where a player has to pay a price to a supplier in order to play a speci…c action. Our focus is on supplier competition, arising from the fact that distinct suppliers supply di¤erent players, and possibly the di¤erent actions of the same player. With private contracts, where a player only observes the prices quoted by his own suppliers, the set of equilibrium distribution over player actions coincides with the set of equilibrium distribution when all actions are supplied competitively, at cost. With public contracts, the two distributions di¤er dramatically even in simple games.

Commitment and observability in a contracting environment

“…Furthermore, a supplier who quotes a price to him must also be indi¤erent between the player's actions, since he can break the player's indi¤erence by a small reduction in price. This implies that such a supplier 2 Not all subgame perfect equilibrium outcomes are accessible, even with generic payo¤s -see the example in Güth et al A similar result is obtained in …nitely repeated games with imperfect private monitoring -Bhaskar and van Damme (2002) show that e¢ cient equilibrium outcomes under perfect monitoring may not be accessible with imperfect private monitoring. 3 Since prices can be chosen from a continuum, the results of Güth et al do not apply in our context.…”

“…This follows the set up in Bhaskar (2005), although the exposition here is self-contained. We will use the term player for someone who plays the game in question, and the term supplier to denote someone with whom a player may need to contract with in order to be able to adopt some action in the game.…”

“…If contracting is public so that the price p is also observed by the entrant, the probability of entry can be conditioned upon p; so as to make the incumbent indi¤erent for any value of p. This removes the supplier's incentive to undercut, and one may construct equilibria that restore accessibility in this example. Public contracting throws up other interesting possibilities when there is competition between rival suppliers in a mixed strategy equilibrium, and we refer the interested reader to Bhaskar (2005) for an analysis of games with public contracting.…”

“…If payo¤s are generic, they show that there always exists a subgame perfect equilibrium outcome of the game with perfect observation that is accessible. 2 Their proof relies on fundamental properties of generic extensive form games -the existence of a strategically stable set and an essential component. This suggests that accessible outcomes are likely to exist in a large class of games.…”

Commitment without reputation: renegotiation-proof contracts under asymmetric information

“…In fact, all (and only) Nash equilibrium outcomes of the original game can be supported as a sequential equilibrium outcome of the game with unobservable and non-renegotiable contracts (Koçkesen and Ok (2004) and Koçkesen (2007)). 3 The strategic role of renegotiable contracts is less understood and the pioneering contribution is provided by Dewatripont (1988 Dewatripont (1988), is that by allowing secret renegotiation, Caillaud et al (1995) enhanced the realism of the model and clarified the role of strategic contracting. 5 The crucial difference between our model and Caillaud et al is that they assume that agents play a simultaneous move game (and principals offer contracts to the agents simultaneously)…”