A Theory of Gradual Coalition Formation

We study noncooperative multilateral bargaining games, based on underlying TU games, in which coalitions can renegotiate their agreements. We distinguish between models in which players continue to bargain after implementing agreements ("reversible actions") and models in which players who implement agreements must leave the game ("irreversible actions"). We show that renegotiation always results in formation of the grand coalition if actions are reversible, but that the process may otherwise end with smaller coalitions. On the other hand, we show that the grand coalition cannot form in one step if the core of the game is empty, irrespective of the reversibility of actions.     

Coordination and bargaining power in contracting with externalities

Building on Genicot and Ray [G. Genicot, D. Ray, Contracts and externalities: How things fall apart, J. Econ. Theory 131 (2006) 71-100] we develop a model of non-cooperative bargaining that combines the two main approaches in the literature of contracting with externalities: the offer game (in which the principal makes simultaneous offers to the agents) and the bidding game (in which the agents make simultaneous offers to the principal). Allowing for agent coordination, we show that the outcome of our bargaining procedure may differ remarkably from those of the offer and the bidding games. In particular, we find that bargaining can break agents' coordination and that the principal's payoff can be decreasing in his own bargaining power.     

Analogy-based expectation equilibrium

In complex situations, agents use simplified representations to learn how their environment may react. I assume that agents bundle nodes at which other agents must move into analogy classes, and agents only try to learn the average behavior in every class. Specifically, I propose a new solution concept for multi-stage games with perfect information: at every node players choose best-responses to their analogy-based expectations, and expectations correctly represent the average behavior in every class. The solution concept is shown to differ from existing concepts, and it is applied to a variety of games, in particular the centipede game, and ultimatum/bargaining games. The approach explains in a new way why players may Pass for a large number of periods in the centipede game, and why the responder need not be stuck to his reservation value in ultimatum games. Some possible avenues for endogenizing the analogy grouping are also suggested.     

On the Least Core and the Mas-Colell Bargaining Set

We show that the least core of a TU coalitional game with a finite set of players is contained in the Mas-Colell bargaining set. This result is extended to games with a measurable space of players in which the worth of the grand coalition is at least that of any other coalition in the game. As a consequence, we obtain an existence theorem for the Mas-Colell bargaining set in TU games with a measurable space of players. Journal of Economic Literature Classification Number: C71.     

The effects of optimism bias in teams

This article imports a behavioural perspective into a team context to study the effort-coordination problem among agents. Specifically, we investigate how the presence of optimism bias impacts the severity of the free-rider problem, the organizational structure of the team and the compensation contracts offered to agents in equilibrium. The results indicate that all agents become more reluctant to exert effort and the team welfare decreases when some of its agents are optimistic, suggesting that optimism aggravates the free-rider problem in teams. Appointing a team leader makes all agents work harder, and the team benefits more by having the optimistic agent as its leader. These findings are in sharp contrast to the effects of overconfidence as identified in the literature. It is advisable to pay the optimistic agents less than the rational agents. Encouragingly, optimistic agents can learn about their own bias in the long run, leaving their team without too much detriment of optimism.     

The averaging mechanism

We consider two-person bargaining games and we assume that the agents want to apply two possibly different bargaining solutions. Problems arise if the allocations chosen by these bargaining solutions do not coincide. We propose a mechanism which mimics a step-by-step bargaining procedure in order to resolve such a conflict and give a characterization of the mechanism.     

Disability and Economy: A Game Theoretic Approach

This paper takes a game theoretic approach to disability‐related issues by constructing a model that studies the case of hereditary deafness on Martha's Vineyard Island, USA from the seventeenth century to the early years of twentieth, where the island community adjusted itself to the hereditary deafness so that it was not treated as a disability. The model of the present paper has two stages. First of all, there are two types of continua of agents, the deaf and the non‐deaf. In the first stage, the non‐deaf agents become either bilinguals or monolinguals. In the second stage, agents are classified into deaf people, bilinguals and monolinguals. They are then randomly matched to form a trio to play a three‐person bargaining game with infinite horizon, random proposers and language constraints. Two bargaining games are considered. The first one is a majority bargaining game where only two out of three can agree to implement a bargaining outcome. The second one is a unanimity bargaining game where all three agents are required to reach an agreement. The majority game exhibits strategic complementarity, while the unanimity game exhibits strategic substitutability. This paper also takes an inductive approach to examine how prejudice against people with disability may emerge.     

The least core, kernel and bargaining sets of large games

Summary. We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countably additive measures. Then we show that in such games the intersection of the prekernel and the least core is non-empty. Finally, we show that the Aumann-Maschler and the Mas-Colell bargaining sets contain the set of all countably additive payoff measures in the prekernel. Received: June 6, 1996; revised version: March 1, 1997     

Gaining power through enlargement: Strategic foundations and experimental evidence

Power indices suggest that adding new members to a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the original members may actually gain even if voters are bargaining over a fixed budget. We show that this phenomenon can occur as an equilibrium of a non-cooperative bargaining game based on the Baron and Ferejohn (1989) model of legislative bargaining. We implement this game in the laboratory and find that power can be gained by adding new members as the theory predicts.     

BARGAINING WITH OPTIMISM: IDENTIFICATION AND ESTIMATION OF A MODEL OF MEDICAL MALPRACTICE LITIGATION

We study a model of bargaining with optimism where players have heterogeneous beliefs about the final resolution. Beliefs and bargaining surplus are identified from the settlement probability and the distribution of accepted transfers. Using data from medical malpractice lawsuits in Florida, we estimate doctor and patient beliefs and the distribution of potential compensation. We find that patients are more optimistic and doctors more pessimistic when the severity of injury is higher, and the joint optimism diminishes as severity increases. We quantify the increase in settlement probability and the reduction in accepted settlement offers under counterfactual caps on the total compensation.     

Learning to alternate

The Individual Evolutionary Learning (IEL) model explains human subjects’ behavior in a wide range of repeated games which have unique Nash equilibria. Using a variation of ‘better response’ strategies, IEL agents quickly learn to play Nash equilibrium strategies and their dynamic behavior is like that of humans subjects. In this paper we study whether IEL can also explain behavior in games with gains from coordination. We focus on the simplest such game: the 2 person repeated Battle of Sexes game. In laboratory experiments, two patterns of behavior often emerge: players either converge rapidly to one of the stage game Nash equilibria and stay there or learn to coordinate their actions and alternate between the two Nash equilibria every other round. We show that IEL explains this behavior if the human subjects are truly in the dark and do not know or believe they know their opponent’s payoffs. To explain the behavior when agents are not in the dark, we need to modify the basic IEL model and allow some agents to begin with a good idea about how to play. We show that if the proportion of inspired agents with good ideas is chosen judiciously, the behavior of IEL agents looks remarkably similar to that of human subjects in laboratory experiments.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

N-PERSON NASH BNARGAINING WITH VARIABEL THREATS*

We consider two models of n-person bargaining problems with the endogenous determination of disagreement points. In the first model, which is a direct extension of Nash's variable threat bargaining model, the disagreement point is determined as an equilibrium threat point. In the second model, the disagreement point is given as a Nash equilibrium of the underlying noncooperative game. These models are formulated as extensive games, and axiomatizations of solutions are given for both models. It is argued that for games with more than two players, the first bargaining model does not preserve some important properties valid for two-person games, e.g., the uniqueness of equilibrium payoff vector. We also show that when the number of players is large, any equilibrium threat point becomes approximately a Nash equilibrium in the underlying noncooperative game, and vice versa. This result suggests that the difference between the two models becomes less significant when the number of players is large.     

Characterising equilibrium selection in global games with strategic complementarities

Global games are widely used to predict behaviour in games with strategic complementarities and multiple equilibria. We establish two results on the global game selection. First, we show that, for any supermodular complete information game, the global game selection is independent of the payoff functions chosen for the game?s global game embedding. Second, we give a simple sufficient criterion to derive the selection and establish noise independence in many-action games by decomposing them into games with smaller action sets, to which we may often apply simple criteria. We also report in which small games noise independence may be established by counting the number of players or actions.     

Uniqueness of stationary equilibrium payoffs in coalitional bargaining

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposer?s identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. The theory of the fixed point index is used to show that stationary equilibrium expected payoffs of this coalitional bargaining game are unique. This generalizes Eraslan [34] insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected.     

A solution to the hold-up problem involving gradual investment

We consider a setting in which the buyer's ability to hold up a seller's investment is so severe that there is no investment in equilibrium of the static game typically analyzed. We show that there exists an equilibrium of a related dynamic game generating positive investment. The seller makes a sequence of gradually smaller investments, each repaid by the buyer under the threat of losing further seller investment. As modeled frictions converge to zero, the equilibrium outcome converges to the first best. We draw connections between our work and the growing literature on gradualism in public good contribution games and bargaining games.     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.     

A weak bargaining set for contract choice problems

In this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of feasible contracts to choose from. We call such problems, contract choice problems. The main result in this paper states that every contract choice problem has a non-empty weak bargaining set. The need for such a solution concept which is considerably weaker than the core arises, since it is well-known that even for very simple contract choice problems, the core may be empty. We also show by means of an example that an analog of the bargaining set due to Mas-Colell [Mas-Colell, A., 1989. An equivalence theorem for a bargaining set. Journal of Mathematical Economics 18, 129–139], as well as the natural analog of the bargaining set due to Aumann and Mashler [Aumann, R., Maschler, M., 1964. The bargaining set for cooperative games. In: Dresher, M., Shapley, L., Tucker, A. (Eds.), Advances in Game Theory. Princeton University Press, Princeton, NJ] may be empty for contract choice problems.     

Moral Hazard and Bargaining Power

Abstract. We introduce bargaining power in a moral hazard framework where parties are risk-neutral and the agent is financially constrained. We show that the same contract emerges if the concept of bargaining power is analyzed in either of the following three frameworks: in a standard principal–agent (P–A) framework by varying the agent's outside opportunity, in an alternating offer game, and in a generalized Nash-bargaining game. However, for sufficiently low levels of the agent's bargaining power, increasing it marginally does affect the equilibrium in the Nash-bargaining game, but not in the P–A model and in the alternating offer game.     

AN ALTERNATIVE APPROACH TO EXPLAINING BARGAINING BEHAVIOUR IN SIMPLE SEQUENTIAL GAMES

Abstract.  For simple sequential games, the payoff structure has certain bargaining power implication. Intuitively, certain actions may have the effect of the carrot and the stick as sanctioning means. Fair outcomes can be alternatively viewed as the consequence of their presence. Experimental data on various games are used to test the hypothesis of carrot and stick behaviour. We show that our stick and carrot heuristic neatly captures puzzling phenomena in a wide class of simple sequential games. The results support the view that punishing subjects are not worse off than myopic pay-off maximizers as long as subjects are involved in a repeated strangers scheme.