Waiting to settle: Multilateral bargaining with subjective biases

We study multilateral bargaining games where agents disagree over their bargaining power. We show that if agents are extremely optimistic, there may be costly delays in an arbitrarily long finite game but if optimism is moderate, all sufficiently long games end in immediate agreement. We show that the game with extreme optimism is highly unstable in the finite-horizon, and we examine the ramifications of this instability on the infinite-horizon problem. Finally, we consider other voting rules, and show that the majority-rule may be more efficient than the unanimity rule when agents are optimistic.     

Gender differences in optimism

This article examines gender differences in optimism about the economy. We measure optimism using Swedish survey data in which respondents stated their beliefs about the country’s future economic situation. We argue that this measure of optimism is preferable to common measurements in the literature since it avoids confounding individuals’ economic situation with their perception of the future and it can be compared to economic indicators. In line with previous research, we find that men are more optimistic than women; however, men are also more prone to be wrong in their beliefs about the future economic situation. Furthermore, in sharp economic downturns, the gender differences in optimism disappear. This convergence in beliefs can be explained by the amount of available information on the economy.     

Delay and Settlement in Litigation

Delay in litigation is a policy concern in many jurisdictions. Little evidence is available on the causes of such delay, however. We present a version of Spier's (1992) bargaining model of litigation and derive directly a functional form for the conditional probability of case settlement. We then estimate this and test predictions about the effects of legal costs and uncertainty over damages and liability on the conditional probability of settlement, using data from negligence claims against several NHS Trusts. Our results provide a direct test of the model and shed light on the causes of settlement delay in England.     

THE HIDDEN COST OF BARGAINING: EVIDENCE FROM A CHEATING-PRONE MARKETPLACE

It is widely believed that successful bargaining helps consumers increase their surplus. We present evidence from a field experiment showing that bargaining over price reduces buyer surplus in a marketplace where sellers cheat on the weight whose value may more than offset the price discount. Our results show that bargaining entails hidden costs since sellers cheat significantly more when buyers bargain than not and they cheat significantly more when bargaining succeeds than fails. Overall bargaining reduces buyer surplus than not bargaining. Our result is relevant for credence goods markets where bargaining over prices may induce sellers to “undertreat” more.     

Bargaining in the Shadow of Power

Often a bargainer can use some form of power—legal, military, or political—to impose a settlement. How does the “outside” option of being able to impose a settlement, albeit at some cost, affect the bargaining? And, how does the probability that the bargaining will break down vary with the distribution of power between the bargainers? These questions are examined by adding the option of imposing a settlement to Rubinstein's game of dividing a pie. Each actor can accept an offer, make a counteroffer, or try to impose a solution. Imposing a settlement is, however, costly and each bargainer has private information about its cost.Journal of Economic Literatureclassification number: C72.     

Destruction and settlement norms as determinants of conflict: An evolutionary perspective

This paper studies conflict in a simple bargaining framework using an evolutionary game-theoretic approach. Our findings suggest that a player does not always regard the winning probability as an acceptable settlement rule. He accepts a division according to winning probability when the destruction caused to him in conflict is more than a threshold, which in turn depends on cost of conflict to the opponent and the size of the population. Further, our analysis shows that the norms with positive weight to disagreement payoff are effective against conflict, and incentivize peace. Contrary to the findings of extant studies carried out in finite population evolutionary game setting, the settlement possibility set is identical under both ESS and Nash equilibrium in our model with settlement norms.     

Ambiguity on audits and cooperation in a public goods game

We investigate the impact of various audit schemes on the provision of public goods, when contributing less than the average of the other group members is centrally sanctioned and the probability of an audit is unknown. We study how individuals update their beliefs about the probability of being audited, both before and after audits are permanently withdrawn. We find that when individuals have initially experienced systematic audits, they decrease both their beliefs and their contributions almost immediately after audits are withdrawn. In contrast, when audits were initially less frequent and more irregular, they maintain high beliefs and continue cooperating long after audits have been withdrawn. This identifies the compliance effect of irregularity and uncertainty due to learning difficulties. By increasing both the frequency of audits and the severity of sanctions, we also identify an educative effect of frequent and high sanctions on further cooperation.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

MODELING THE EVOLUTION OF EXPECTATIONS AND UNCERTAINTY IN GENERAL EQUILIBRIUM

We develop methods to solve general equilibrium models in which forward‐looking agents are subject to waves of pessimism, optimism, and uncertainty that turn out to critically affect macroeconomic outcomes. Agents in the model are fully rational and conduct Bayesian learning, and they know that they do not know. Therefore, agents take into account that their beliefs will evolve according to what they will observe. This framework accommodates both gradual and abrupt changes in beliefs and allows for an analytical characterization of uncertainty. We use a prototypical Real Business Cycle model to illustrate the methods.     

Bargaining with Voluntary Transmission of Private Information: Does the Use of Final Offer Arbitration Impede Settlement?

We identify two features of final offer arbitration (FOA) whichmay impede settlement in a bargaining game where asymmetricinformation drives the failure to settle. First, under FOA theinformed party has an incentive to conceal private informationabout the expected outcome in arbitration from his bargainingpartner. Revealing this information allows the previously uninformedparty to submit a more advantageous offer to the arbitratorto the detriment of the informed party. Second, in a two-typemodel, the uninformed player may choose to arbitrate all cases,a result which never occurs in a simple litigation game. Eachplayer's offer directly affects the outcome of arbitration underFOA, and it is this feature that generates impediments to settlementthat are not observed in a simple litigation game. Both impedimentsto settlement are removed if bargaining is allowed to take placeafter potentially binding offers have been submitted to thearbitrator.     

Does resorting to online dispute resolution promote agreements? Experimental evidence

This paper presents an experiment performed to test the properties of an innovative bargaining mechanism (called automated negotiation) used to resolve disputes arising from Internet-based transactions. The main result shows that the settlement rule tends to chill bargaining as it creates incentives for individuals to misrepresent their true valuations, which implies that automated negotiation is not able to promote agreements. However, this perverse effect depends strongly on the conflict situation. When the threat that a disagreement occurs is more credible, the strategic effect is reduced since defendants are more interested in maximizing the efficiency of a settlement than their own expected profit. The implications of these results are then used to discuss the potential role of public regulation and reputation mechanisms in Cyberspace.     

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.     

Trade and unions: Does size matter?

Our empirical analysis builds upon the hypothesis that unions are detrimental to a firm's efficiency. Using a rich survey of German manufacturers, we investigate firm-level determinants on the probability of collective wage bargaining with particular focus on the impact of a firm's engagement in foreign markets. An interesting and very robust finding is that exporters are less likely to engage in union wage bargaining. This finding is in line with a pessimistic perception of unions. The negative effect of collective bargaining can be offset by efficiency gains for larger exporters, who can benefit from operation cost saving effects. Size does matter as larger firms export and may find bargaining with a single entity representing the workforce more convenient than bargaining with each worker individually. We are using firm level information on IT investment as instrument for the export dummy and successfully test for the validity of this instrument.     

Managerial Bargaining Power in the Determination of Compensation Contracts and Corporate Investment

This paper considers the design of managerial compensation contracts and their impact on corporate investment decisions and the managerial effort decision. The model relates the compensation scheme to outside share ownership and managerial bargaining position. Using the methods of mechanism design under asymmetric information, a shift in favor of effort is documented in the case where managerial bargaining strength is weak, while a shift toward more use of capital investment results from strong managerial bargaining power. The model distinguishes managerial equity holdings from contingent compensation contracts. Our results are related to the empirical literature on pay-performance sensitivities.     

Contribution to a public good under subjective uncertainty

This paper examines how voluntary contributions to a public good are affected by the contributors' heterogeneity in beliefs about the uncertain impact of their contributions. It assumes that contributors have Savagian preferences that are represented by a two‐state‐dependent expected utility function and different beliefs about the benefit that will result from the sum of their contributions. We establish general comparative statics results regarding the effect of specific changes in the distribution of beliefs on the (unique) Nash equilibrium provision of the public good, under certain conditions imposed on the preferences. We specifically show that the equilibrium public good provision is increasing with respect to both first‐ and second‐order stochastic dominance changes in the distribution of beliefs. Hence, increasing the contributors' optimism about the uncertain benefit of their contributions increases aggregate public good provision, as does any homogenization of these beliefs around their mean.     

Bargaining with Imperfect Commitment

We study the effect of imperfect commitment in noncooperative two-person bargaining games. By establishing the reputation for being stubborn, a player sometimes commits to her initial demand, becoming unable to change her demands or to accept an inferior offer from her opponent. When the probability of being stubborn is small, the set of equilibria is shown to be small and agreement may be reached immediately despite the possibility of stubbornness. A player has greater bargaining power when she is more patient and/or is more likely to be stubborn. Journal of Economic Literature Classification Number: C78.     

Unions and the share economy

This paper contrasts share bargaining and wage bargaining in the context of a “monopoly” model of union bargaining. In the example considered here, employment levels are identical under wage and share systems, but total compensation is higher under share bargaining than under wage bargaining, underscoring the importance of the broader ontext within which a share system is introduced.     

Bargaining Outcomes with Double-Offer Arbitration

Increasingly, arbitration is becoming used to resolve bargaining disputes in a variety of settings. Reducing dispute rates is often listed as a main goal in designing arbitration mechanisms. Conventional arbitration and final-offer arbitration are two commonly used procedures, but theoretical examinations of these arbitration procedures show that disputants’ final bargaining positions do not converge and disagreement is likely. This article contains results from a set of experiments designed to compare bargaining outcomes under the two commonly used arbitration procedures with outcomes under an innovative procedure called “double-offer” arbitration (Zeng et al., 1996). This procedure requires that disputants make two final offers at impasse: a primary and a secondary offer. The arbitrator evaluates the pairs of offers using a linear criterion function, and theory suggests the secondary offers converge to the median of the arbitrator’s preferred settlement distribution. Because the procedure’s rules are that convergence of offers generates a settlement at those offers, this theoretical convergence result implies that arbitration is not needed in the end. Experimental results indicate that dispute rates in double-offer arbitration are, on average, about the same as dispute rates in conventional arbitration. However, other results show reason to favor double-offer arbitration. Specifically, in repeated bargaining, there is concern over whether use of an arbitration procedure becomes addictive and makes bargainers more likely to use the procedure in the future-a “narcotic effect.” The data show that double-offer arbitration is non-addictive, whereas both conventional and final-offer arbitration are.     

Coasean bargaining with symmetric delay costs

Delay costs play a role in Coasean bargaining over environmental conflicts when an injunction restricts actions until a settlement is reached. Results from the lab suggest that efficiency remained relatively robust to discrete and increasing marginal delay costs, but declined significantly with nonincreasing marginal delay costs. Bargainers appear to deal with probability and consequences separately rather than in combination as maintained by expected utility theory, and as such, neglect ends over means. How the distribution of wealth is best organized depends on perspective: constrained self-interest best organizes behavior if expected utility is maintained; pure self-interest dominates if we acknowledge the probability–consequence heuristic.     

RAISING WAGES TO DETER ENTRY INTO UNIONIZED MARKETS*

This paper investigates entry under a unionized oligopoly when entry and wage negotiations are sequential. We find the incumbent has incentives to raise the wage, which strengthens the bargaining position of the union relative to the entrant at subsequent negotiations and thus discourages entry. We show that entry is more likely to be deterred (accommodated) if the union is wage (employment) oriented and that raising unemployment compensation during recession not only reduces the burden of the unemployed but also induces new entry, creating more employment opportunities. However, during a business boom, reducing unemployment compensation is a better policy.