Voluntary commitments lead to efficiency

Games and Economic Behavior, 1998

In a two-stage game where followers can observe moves by leaders only with noise, pure subgame perfect Nash equilibria of the limiting game without noise may not survive arbitrarily small noise. Still, for almost all games, there exists a subgame perfect equilibrium outcome of the game with no noise that is approximated by equilibrium outcomes of games with small noise. This, however, depends crucially on generic payoffs and does not necessarily hold for all subgame perfect equilibria of the game without noise. Journal of Economic Literature Classification Number: C72.

International Journal of Game Theory, 2003

We study a simple bargaining mechanism in which, given an order of players, the first n−1 players sequentially announce their reservation price. Once these prices are given, the last player may choose a coalition to cooperate with, and pay each member of this coalition his reservation price. The only expected final equilibrium payoff is a new solution concept, the “selective value”, which can be defined by means of marginal contributions vectors of a reduced game. The selective value coincides with the Shapley value for convex games. Moreover, for 3-player games the vectors of marginal contributions determine the core when it is nonempty.

2008

This paper investigates the e¤ects of the ability to jointly rule out actions on the analysis of a strategic form game. If players can voluntarily sign contracts that jointly commit them to rule out some of their actions, mutually bene cial bargains can often be found. It may appear that making sure that such bargains are e¢ cient occasionally requires players to sign random contracts, which commit them to a speci c course of action based on the realization of some extraneous randomization. Indeed, the set of allocations implemented if players have a single opportunity to sign contracts that deterministically rule out some actions, is characterized and often ine¢ cient. The analysis however shows that if players have su¢ ciently many opportunities in which to sign such deterministic contracts, any individually rational allocation is approximately implementable. Therefore, even in games that are not convex, the implementation of any e¢ cient and individually rational allocation does ...

2012

In the reputation literature, players have commitment types which represent the possibility that they do not have standard payos but instead are constrained to follow a particular plan. In this paper, we show that arbitrary commitment types can emerge from incomplete information about the stage payos. In particular, any …nitely repeated game with commitment types is strategically equivalent to a standard …nitely repeated game with incomplete information about the stage payos, such that the types with identical solutions have almost identical prior probability in two games. Then, classic reputation results can be achieved with uncertainty concerning only the stage payos.

Journal of Economic Theory, 2009

We consider non-cooperative environments in which two players have the power to gradually and unilaterally rule out some of their actions. Formally, we embed a strategic-form game into a multi-stage game, in which players can restrict their action spaces in all but the final stage, and select among the remaining actions in the last stage. We say that an action

Journal of the European Economic Association, 2010

In this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies, the traditional coalitional function may not be adequate when utilities are not transferable. (JEL: C70, C71, C78, D70) 1. For a finite set Z, we denote by |Z| the number of elements of Z. 2. We write arg max for the set of maximizers.

2012

In the reputation literature, players have commitment types, which represent the possibility that they do not have standard payoffs, but instead are constrained to follow a particular plan. In this paper, we show that arbitrary commitment types can emerge from incomplete information about the stage payoffs. In particular, any finitely repeated game with commitment types is strategically equivalent to a standard finitely repeated game with incomplete information about the stage payoffs. Then classic reputation results can be achieved with uncertainty concerning only the stage payoffs.

Journal of the European Economic Association

In many matching markets, bargaining determines who matches with whom and on what terms. We experimentally investigate allocative efficiency and how subjects’ payoffs depend on their matching opportunities in such markets. We consider three simple markets. There are no information asymmetries, subjects are patient, and a perfectly equitable outcome is both feasible and efficient. Efficient perfect equilibria of the corresponding bargaining game exist, but are increasingly complicated to sustain across the three markets. Consistent with the predictions of simple (Markov perfect) equilibria, we find considerable mismatch in two of the markets. Mismatch is reduced but remains substantial when we change the nature of bargaining by moving from a structured experimental protocol to permitting free-form negotiations, and when we allow players to renege on their agreements. Our results suggest that mismatch is driven by players correctly anticipating that they might lose their strong bargai...

Proceedings of the AAAI Conference on Artificial Intelligence

Before engaging in a group venture agents may seek commitments from other members in the group and, based on the level of participation (i.e. the number of actually committed participants), decide whether it is worth joining the venture. Alternatively, agents can delegate this costly process to a (beneficent or non-costly) third-party, who helps seek commitments from the agents. Using methods from Evolutionary Game Theory, this paper shows that, in the context of Public Goods Game, much higher levels of cooperation can be achieved through such centralized commitment management. It provides a more efficient mechanism for dealing with commitment free-riders, those who are not willing to bear the cost of arranging commitments whilst enjoying the benefits provided by the paying commitment proposers. We show that the participation level plays a crucial role in the decision of whether an agreement should be formed; namely, it needs to be more strict in terms of the level of participation ...