BARGAINING WITH SHARED INFORMATION*

This paper formulates and analyzes models of two-party bargaining behavior where each side possesses private information about its preferences that is unavailable to the other. We examine the strategic behavior that bargainers might exhibit when disclosing information either to an arbitrator or to each other. Our results show that when bargaining is over one issue, it is relatively uncomplicated analytically to calculate the optimal strategy, but, despite this, even sophisticated bargainers tend to make wrong assumptions about the behavior of others and to use strategies that are far from optimal. When the bargaining encompasses several factors, computation of optimal strategies becomes very cumbersome and the use of an optimal strategy does not gain a bargainer much over what he could have achieved with truthful revelation. Thus, in theory, truthful revelation is not the best course of action to adopt for a bargainer interested in maximizing individual gain, but in practice the alternatives may involve mistaken assumptions about the behavior of others and may therefore turn out to be inferior to truthful revelation.     

The impact of biological preferences on parental investments in children and step-children

A remarriage typically involves significant changes in a family’s financial circumstance, and these changes, combined with the relative bargaining relationship between spouses, likely affect the well-being of the children who are part of the family. In this paper, I use the separate-spheres model, a theoretical model that explains the determinants of bargaining power in marriage, to analyze how a remarried couple’s bargaining relationship affects their child investment in stepfamilies. Based on this theoretical model, I build and estimate an empirical model that investigates the determinants of parental investment. As evidence of parental preference for biological children over stepchildren, I find that an increased wage rate of a biological mother significantly improves her child investment when her husband is a stepfather of the child, while there is no such effect for mothers living with the biological father of the child.

Participative Budgeting and Managerial Performance*

Recent analytical and empirical research in budgeting has focused on conditions under which participation may or may not prove beneficial to the firm. The present study seeks to examine (in a budget setting) the impact on firm returns of managerial participation, private state information, and relative skill. Experimental results indicate a significant improvement in firm and managerial welfare across favorable and unfavorable private state information with budgetary participation. A significant interaction between the type of state information and participation is reported for managers but not firm returns. Finally, relative skill signals are shown to lead to improved managerial performance.     

Optimal Offer Strategies in Mergers and Acquisitions*

This paper models the corporate takeover process as a bargaining game under certainty. During the takeover process, an acquirer is generally uncertain about the minimum price the target shareholders will accept. Normally, a takeover is concluded after a sequence of offers have been made. This paper derives optimal offer strategies for the buyer at each stage of this bargaining game under uncertainty. Uncertainty about the target's minimum acceptable price is represented by a probability distribution. Optimal offer strategies depend on the probability distribution of the minimum acceptable price, which can change during the offer process.     

Social security and conflict within the family

A husband and wife, though benefitting from marriage, may yet misappropriate some of the spouse's assets rather than let all be saved. In a Nash equilibrium, family savings may therefore be lower than what each spouse would prefer. Social Security, which is a form of forced, secure saving, can therefore increase welfare.      

Ultimatum decision-making: A test of reciprocal kindness

While fairness is often mentioned as a determinant of ultimatum bargaining behavior, few data sets are available that can test theories that incorporate fairness considerations. This paper tests the reciprocal kindness theory in Rabin (1993 Incorporating fairness into game theory and economics, The American Economic Review 83: 1281-1302) as an application to the one-period ultimatum bargaining game. We report on data from 100 ultimatum games that vary the financial stakes of the game from $1 to $15. Responder behavior is strongly in support of the kindness theory and proposer behavior weakly in support of it. Offer percentages and past offers influence behavior the most, whereas the size of the pie has a marginally significant effect on offer percentages. The data is more in support of reciprocal kindness than alternative theories of equal-split or learning behavior, although the data also weakly support a minimum percentage threshold hypothesis. As a whole, our results together with existing studies suggest that, for smaller stakes games, fairness considerations dominate monetary considerations. This has implications for more complicated naturally occurring bargaining environments in which the financial stakes can vary widely.     

Reference dependent prices in bargaining: An experimental examination of precise first offers

Evidence from psychology and marketing suggests that those who make a “precise” first offer in bargaining get a better deal than those who make a “round” first offer. We report on a series of experiments designed to test for and improve our understanding of the “precise first offer” (PFO) effect in bargaining and whether it likely reflects rational optimizing or equilibrium behavior. Our experiment varies whether decisions are incentivized and whether the PFO effect can emerge as an equilibrium of a cheap-talk signaling game. We find evidence of a PFO effect when subjects read a vignette and make unincentivized individual decisions. When monetary incentives are added to the vignette, we still find the PFO effect, but it is not robust. In a bilateral bargaining situation with a cheap-talk equilibrium, we can not find the PFO effect, which is inconsistent with the equilibrium predictions. Moreover, the PFO effect reemerges in a setting in which initial offers are generated by a random device and thus provides a strong refutation of the signaling model. Our evidence suggests that optimizing and equilibrium accounts of the PFO effect are inadequate. Understanding initial offers as reference points, which subtly change perceptions about the kinds of acceptable counteroffers, provides a plausible account of a new finding on which prior explanations are silent: precise offers induce more precise counteroffers.     

中国国有企业的国际议价能力估算

 通过建立讨价还价理论模型,本文证明了谈判过程中让步成本较小的一方获得的收益较少。由于存在预算软约束和相对严重的委托代理问题,国有企业的让步并不会给代理人造成相应损失,相应地国有企业议价能力较低。运用2006年海关进出口交易数据,使用双边随机前沿分析方法（Two-tier SFA）测度谈判底线,本文估算了中国国有企业的国际议价能力。结果显示：（1）国有企业的讨价还价能力低于民营企业和外资企业;（2）国有企业的讨价还价能力也低于进出口交易伙伴,其进口价格高于公允价格3.69%,出口价格低于公允价格6.17%。因而继续推进市场化改革,中国才能在国际市场上获取公平的贸易收益。     

Fair (and not so fair) division

Drawbacks of existing procedures are illustrated and a method of efficient fair division is proposed that avoids them. Given additive participants’ utilities, each item is priced at the geometric mean (or some other function) of its two highest valuations. The utilities are scaled so that the market clears with the participants’ purchases proportional to their entitlements. The method is generalized to arbitrary bargaining sets and existence is proved. For two or three participants, the expected utilities are unique. For more, under additivity, the geometric mean separates the prices where uniqueness holds and where it fails; it holds for the geometric mean except in one case where refinement is needed.      

Loss Aversion and Bargaining

We consider bargaining situations where two players evaluate outcomes with reference-dependent utility functions, analyzing the effect of differing levels of loss aversion on bargaining outcomes. We find that as with risk aversion, increasing loss aversion for a player leads to worse outcomes for that player in bargaining situations. An extension of Nash's axioms is used to define a solution for bargaining problems with exogenous reference points. Using this solution concept we endogenize the reference points into the model and find a unique solution giving reference points and outcomes that satisfy two reasonable properties, which we predict would be observed in a steady state. The resulting solution also emerges in two other approaches, a strategic (non-cooperative) approach using Rubinstein's (1982) alternating offers model and a dynamic approach in which we find that even under weak assumptions, outcomes and reference points converge to the steady state solution from any non-equilibrium state.