Rubinstein bargaining with two-sided outside options

Summary. In this note we show that if in the standard Rubinstein model both players are allowed to leave the negotiation after a rejection, in which case they obtain a payoff of zero, then there exist a continuum of subgame-perfect equilibrium outcomes, including some which involve significant delay. We also fully characterize the case in which, upon quitting, the players can take an outside option of positive value. Received: February 27, 1996; revised version: March 28, 1997     

Bargaining and Search with Incomplete Information about Outside Options

This paper considers a model of bargaining in which the seller makes offers and the buyer can search (at a cost) for an outside option; the outside option cannot be credibly communicated, and the seller's offer is recallable by the buyer for one period. There are essentially two equilibrium regimes. For sufficiently high search cost, the game ends immediately; otherwise the search occurs in equilibrium. Compared to the case where the buyer can communicate his outside option, the seller is worse off, and the game results in search for a smaller set of values of the search cost, i.e., less equilibrium delay.C72.     

Coordination of mobile labor

We study coordination failures in many simultaneously occurring coordination problems. Players encounter one of the problems but have the outside option of migrating to one of the remaining ones. Drawing on the global games approach, we show that such a mobile game has a unique equilibrium that allows us to examine comparative statics. The endogeneity of the outside option value and of the migration activity leads to non-monotonicity of welfare with respect to mobility friction; high mobility may hurt players. We apply these “general equilibrium’’ findings to the problem of the labor market during industrialization as described by Matsuyama [Increasing returns, industrialization and indeterminacy of equilibrium, Quart. J. Econ. 106 (1991) 617-650].     

Social norms and trust among strangers

We study the development of a social norm of trust and reciprocity among a group of strangers via the “contagious strategy” as defined in Kandori (1992). Over an infinite horizon, the players anonymously and randomly meet each other and play a binary trust game. In order to provide the investors with proper incentives to follow the contagious strategy, there is a sufficient condition that requires that there exists an outside option for the investors. Moreover, the investorsʼ payoff from the outside option must converge to the payoff from trust and reciprocity as the group size goes to infinity. We show that this sufficient condition is also a necessary condition to sustain any sequential equilibrium in which the trustees adopt the contagious strategy. Our results imply that a contagious equilibrium only supports trust if trust contributes almost nothing to the investorsʼ payoffs.     

Strategic Delegation By Unobservable Incentive Contracts

Many strategic interactions in the real world take place among delegates empowered to act on behalf of others. Although there may be a multitude of reasons why delegation arises in reality, one intriguing possibility is that it yields a strategic advantage to the delegating party. In the case where only one party has the option to delegate, we analyse the possibility that strategic delegation arises as an equilibrium outcome under completely unobservable incentive contracts within the class of two-person extensive form games. We show that delegation may arise solely due to strategic reasons in quite general economic environments even under unobservable contracts. Furthermore, under some reasonable restrictions on out-of-equilibrium beliefs and actions of the outside party, strategic delegation is shown to be the only equilibrium outcome.     

Gradualism in Bargaining and Contribution Games

This paper identifies a source of gradualism in bargaining and contribution games. In the bargaining games we examine, each party can opt out at any time, and the outside option outcome is assumed to depend on the offers made in the negotiation phase. Specifically, we assume that (1) making a concession in the negotiation phase increases the other party's outside option pay-off and (2) the outside option outcome induces an efficiency loss as compared with a negotiated agreement. The main finding is that the mere presence of such history-dependent outside options forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which the outside option may be interpreted as the option to implement a partial project using the total contributions made so far.     

Endogenous entry and self-selection in private value auctions: An experimental study

This paper presents the results of an experimental study of endogenous entry in first-price independent private value auctions. N potential bidders simultaneously decide whether to participate in an auction or receive a known outside option. In the second stage, entrants submit bids after learning their own private values and the number of entrants. An equilibrium model of heterogeneous risk averse bidders implies a self-selection effect, where bidding in the auction is lower with endogenous entry because only less risk averse bidders enter. This effect is confirmed by the experiment. We also observe excessive entry relative to the theoretical model.     

Bargaining, search, and outside options

This paper studies a two-sided incomplete information bargaining model between a seller and a buyer. The buyer has an outside option, which is modeled as a sequential search process during which he can choose to return to bargaining at any time. Two cases are considered: In Regime I, both agents have symmetric information about the search parameters. We find that, in contrast to bargaining with complete information, the option to return to bargaining is not redundant in equilibrium. However, the no-delay result still holds. In Regime II, where agents have asymmetric information about the outside option, delay is possible. The solution characterizes the parameters for renegotiation and those for search with no return to the bargaining table.     

MARKET‐BASED INCENTIVES

In this article, we study market‐induced, external incentives similar to career concerns jointly with standard, contractual incentives linking compensation to performance. We consider a dynamic principal–agent problem in which the agent's outside option is determined endogenously in a competitive labor market. In equilibrium, strong performance increases the agent's market value. When this value becomes sufficiently high, the threat of the agent quitting forces the principal to increase the agent's compensation. The prospect of obtaining this raise gives the agent an incentive to exert effort, which reduces the need for standard incentives. In fact, whenever the agent's option to quit is sufficiently close to being “in the money,” the market‐induced incentive eliminates the need for standard incentives altogether: Compensation becomes completely insensitive to current performance.     

The Effect of Disagreement on Noncooperative Bargaining

A seemingly mild assumption of the standard alternating offers bargaining model under risk is that the breakdown event is not strictly worse than the worst agreement. When this assumption is relaxed the structure of the equilibrium set of agreements changes in an interesting way. We analyse the effect of disagreement on equilibrium, and relate our result to a class of outside option models. Journal of Economic Literature Classification Number: C78.     

Voting with abstention

Most voting models in the literature neglect abstention, but is such a simplification justified? I investigate this question in a model with outside pressure on voters. For sequential voting (e.g., roll call votes), with and without an abstention option, there is a unique subgame perfect equilibrium, which implies that true majorities always succeed. Abstention can be an equilibrium strategy for some voters, in particular under complex decision rules (e.g., weighted voting, double majorities). Simultaneous voting often has a unique pure strategy equilibrium but also a plethora of mixed and pure/mixed strategy equilibria. Therefore, only with equilibrium selection, can we evaluate the consequences of neglecting abstention. For equal weight voting, equilibria selected by the procedure of Harsanyi and Selten change completely with an abstention option, even if abstention itself is not or rarely used. With small enough outside pressure, however, the selected equilibrium honors true majorities in both cases.     

ON EMPLOYMENT CONTRACTS WITH ENDOGENOUS ON-THE-JOB SEARCH

We consider an equilibrium search model and employment contracts when workers have endogenous on-the-job search. When a firm tries to retain an employee by matching outside offers, variable search intensity leads to a moral hazard problem. We first consider workers with identical productivities. We derive an equilibrium where firms commit not to respond to outside offers and workers search less. Second, we investigate the case with heterogeneous workers and asymmetric information. Assuming that firms can commit to retain all workers irrespective of their ability, we establish conditions under which it is optimal to do so. This policy again reduces the incentive for active on-the-job search. We discuss an equilibrium where all firms use these so-called ‘pooling’ contracts.     

Groups, collective decisions and markets

We consider a general equilibrium model where multi-member households make efficient collective consumption decisions and operate in a competitive market environment. Individuals have the option to leave the household and make it on their own or join another household. We study the effect of these outside options on household formation, household stability and equilibrium existence.     

Merger negotiations and ex-post regret

We consider a setting in which two potential merger partners each possess private information pertaining both to the profitability of the merged entity and to stand-alone profits, and we investigate the extent to which this private information makes ex-post regret an unavoidable phenomenon in merger negotiations. To this end, we consider ex-post incentive compatible mechanisms, which use both players' reports to determine whether or not a merger will take place and what each player will earn in each case. When the outside option of at least one player is known, the efficient merger decision can be implemented by such a mechanism under plausible budget-balance requirements. When neither outside option is known, we show that the potential for regret-free implementation is much more limited, unless the budget balance condition is relaxed to permit money-burning in the case of false reports.     

Choosing What to Protect: Strategic Defensive Allocation against an Unknown Attacker

We study a strategic model in which a defender must allocate defensive resources to a collection of locations and an attacker must choose a location to attack. In equilibrium, the defender sometimes optimally leaves a location undefended and sometimes prefers a higher vulnerability at a particular location even if a lower risk could be achieved at zero cost. The defender prefers to allocate resources in a centralized (rather than decentralized) manner, the optimal allocation of resources can be non‐monotonic in the value of the attacker's outside option, and the defender prefers her defensive allocation to be public rather than secret.     

Specific investments, holdup, and the outside option principle

According to the outside option principle the holdup problem can be solved when the non-investor has a binding outside option. The investor then becomes residual claimant, creating efficient investment incentives. This paper reports about an experiment designed to test this. We find that when the outside option is binding investment levels fall short of the efficient level, but holdup is less of a problem than predicted when the outside option is non-binding.     

SHOULD YOU ALLOW YOUR EMPLOYEE TO BECOME YOUR COMPETITOR? ON NONCOMPETE AGREEMENTS IN EMPLOYMENT CONTRACTS*

We discuss a principal–agent model in which the principal has the opportunity to include a noncompete agreement in the employment contract. We show that not imposing such an agreement can be beneficial for the principal, as the possibility to leave the firm generates implicit incentives for the agent. The principal prefers to impose such a clause if and only if the value created is sufficiently small relative to the agent's outside option. If the principal can use an option contract for retaining the agent, she will never prefer a strict noncompete agreement.     

ON THE EMERGENCE OF TOYBOYS: THE TIMING OF MARRIAGE WITH AGING AND UNCERTAIN CAREERS*

We explore how gender bias in career opportunities affects matching in a marriage market with search frictions and where an individual’s fitness decays with age. We document a “being left on the shelf” effect where young singles, who find the marriage market rapidly thins with age, rush into early partnership. Singles with stronger career opportunities, however, have a greater option value to defer marriage. More equal career opportunities for women (captured by greater schooling and better occupations) potentially explain the recent emergence of toyboy unions, in which the woman is at least 5 years older than her partner.     

A model of boundedly rational “neuro” agents

We consider a model in which each agent in a population chooses one of two options. Each agent does not know what the available options are and can choose an option only after observing another agent who has already chosen that option. In addition, the agents’ preferences over the two options are correlated. An agent can either imitate an observed agent or wait until he meets two agents who made different choices, in which case he can compare their choices and choose accordingly. A novel feature of the model is that agents observe not only the choices made by others, but also some information about the process that led them to those choices. We study two cases: In the first, an agent notes whether the observed agent imitated others or whether he actually compared the available alternatives. In the second, an agent notes whether the observed agent’s decision was hasty or not. It is shown that in equilibrium the probability of making a mistake is higher in the second case and that the existence of these nonstandard “neuro” observations systematically biases the equilibrium distribution of choices.     

The strategy of manipulating joint decision-making

We study a model of strategic persuasion based on the theory of cheap talk, in which a better-informed agent manipulates two decision-makers’ joint decision on alternative proposals. With the heterogeneity of two decision-makers’ value of the outside option, only the decision-maker with the better outside option is critical in determining whether communication is truthful, overselling, or ineffective.