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.     

The tragedy of the commons revisited: The importance of group decision-making

We use a laboratory experiment to compare the way groups and individuals behave in an inter-temporal common pool dilemma. The experimental design distinguishes between a non-strategic problem where players (individuals or groups of three) make decisions without interaction and a strategic part where players harvest from a common pool. This allows us to correct for differences between individuals and groups in the quality of decisions when testing for differences in competitiveness. Group decisions are either made by majority rule or unanimity. The results show that groups are less myopic than individuals (i.e., they make qualitatively better decisions) but that they are more competitive than individuals when placed in a strategic setting. The net result for groups deciding by majority rule is that they make less efficient decisions in the strategic game than individuals do. We are able to show that this is caused by the median voter departing from her original preference in early periods with a shrinking pool. When groups have to make unanimous decisions they start playing the strategic game more efficiently then individuals do, but they rapidly become more competitive with repetition of the game.     

Codetermination,Price Competition and the Network Industry

This research develops a tractable two‐stage non‐cooperative game with complete information describing the behaviour of price‐setting firms that must choose to be profit maximisers or bargainers under codetermination in a network industry with horizontal product differentiation. The existing theoretical literature has already shown that codetermination might arise as the endogenous market outcome in a strategic competitive quantity‐setting duopoly. In sharp contrast with this result, the present article shows that codetermination does never emerge as a Nash equilibrium in a price‐setting non‐network duopoly. Then, it aims at highlighting the role of network externalities in determining changes of paradigm of the game and letting codetermination become a sub‐game perfect Nash equilibrium when prices are strategic substitutes or strategic complements. This equilibrium may be Pareto efficient. Results allow distinguishing between mandatory codetermination and voluntary codetermination. The article also proposes a model of endogenous codetermination according to which every firm may choose to bargain with its own corresponding union bargaining unit only whether the firm's bargaining strength is exactly the profit‐maximising one. The equilibrium outcomes emerging in this case range from a uniform Nash equilibrium, in which both firms are codetermined, to mixed Nash equilibria, in which only one of them chooses to be codetermined. These results are ‘network depending’ and do not hold in a non‐network duopoly.     

Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules

We consider negotiations selecting one-dimensional policies. Individuals have instantaneous preferences represented by continuous, concave and single-peaked utility functions, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. We provide sufficient conditions that guarantee the existence of a unique stationary subgame perfect equilibrium, and we provide its explicit characterization. The uniqueness of the equilibrium permits an analysis of the set of Pareto optimal voting rules. For symmetric distributions of peaks and uniform recognition probabilities unanimity is the unanimously preferred majority rule.     

Gradualism in the GATT: Strategic tariff bargaining and forward manipulation

This paper examines strategic bargaining in a non‐cooperative game of tariff negotiation in the General Agreement on Tariffs and Trade (GATT). In the model, a country bargains sequentially and bilaterally with multiple trading partners under the MFN principle, making take‐it‐or‐leave‐it offers consisting of tariffs and transfers. A dynamic bargaining inefficiency arises in which the country strategically delays the reduction of its tariff until the final stage, and extensions to the model demonstrate gradual trade liberalization over multiple stages. Based on this idea of forward manipulation, the theory provides an explanation for gradualism in tariff reduction during the early GATT rounds.     

STRATEGIC CANDIDACY AND SINGLE‐PEAKEDNESS*

In elections, the voting outcomes are affected by strategic entries of candidates. We study a class of voting rules immune to strategic candidacy. Dutta et al. (2001 ) show that such rules satisfying unanimity are dictatorial if all orderings of candidates are admissible for voters’ preferences. When voters’ preferences are single‐peaked over a political spectrum, there exist non‐dictatorial rules immune to strategic candidacy. An example is the rule selecting the m‐th peak from the left among the peaks of voters’ preferences, where m is any natural number no more than the number of voters. We show that immunity from strategic candidacy with basic axioms fully characterizes the family of the m‐th leftmost peak rules.     

Implementations of the Nash solution based on its Walrasian characterization

Summary. The present paper provides three different support results for the Nash bargaining solution of -person bargaining games. First, for any bargaining game there is defined a non-cooperative game in strategic form, whose unique Nash equilibrium induces a payoff vector that coincides with the Nash solution of the bargaining game. Next this game is modified in such a way that the unique Nash equilibrium that supports the Nash solution is even in dominant strategies. After that an -stage game in extensive form is presented whose unique subgame perfect equilibrium supports the Nash solution of the bargaining game. Finally, the support results are shown to induce implementation results in the sense of mechanism theory. Received: October 3, 1999; revised version: October 26, 1999     

The evaluation of majority rules in a legislative bargaining model

A budget needs to be distributed among jurisdictions through bargaining in the legislature. Using a simple three-player, three-period Baron and Ferejohn [Baron, D.P., Ferejohn, J.A., 1989. Bargaining in legislatures. American Political Science Review 83 (4), 1181–1206] style legislative bargaining model with incomplete information, we evaluate two kinds of majority rules: the simple majority rule and the unanimity rule. Under the simple majority rule, it is less expensive to form a minimum-winning coalition, so that every type of proposer prefers his proposal to be passed immediately. The proposer has fewer incentives to reveal his information by delaying the bargaining, since there is a possibility of being excluded from the majority in future periods. Thus, in contrast to the unanimity rule, there does not exist any fully separating equilibrium. We also show that if the first-period proposer has greater agenda-setting power, it can help to reduce the probability of delay.     

Implementing the Kalai-Smorodinsky bargaining solution

The bargaining game is proposed where the agents bid fractions of dictatorship that are used by all non-winners of the auction to threaten acceptance of the winner's proposal. That procedure non-cooperatively implements the Kalai-Smorodinsky bargaining solution.     

Plea bargaining: on the selection of jury trials

We consider a model of the criminal court process, focusing on plea bargaining. A plea bargain provides unequal incentives to go to trial because innocent defendants are more willing to plead not guilty. We show that the court process implements the preferences of the person or group who is most concerned about wrongful conviction. If a prosecutor is more concerned about wrongful conviction than the jury, the prosecutor can shape the defendant pool at trial so that jurors act according to prosecutor’s preferences against judicial mistakes. Our model also connects insights from strategic jury models that usually omit plea bargaining with the actual criminal court process where most cases are resolved through plea bargaining. As an example, we show that the inferiority of the unanimity rule established in Feddersen and Pesendorfer (Am Polit Sci Rev 92(1):23–35, 1998) persists in spite of the addition of plea bargaining.     

Super‐Majorites,One‐Dimensional Policies,and Social Surplus

In the setting of a one‐dimensional legislative bargaining game, we characterize qualified majority rules maximizing social surplus, that is, the sum of individual benefits. The simple majority rule maximizes social surplus when individual utilities are tent‐shaped. When the utilities are strictly concave, the surplus maximizing rule is a strict supermajority.     

The Second Welfare Theorem in Economies with Non‐Walrasian Markets

The standard version of the second welfare theorem assumes that market operations produce Walrasian outcomes. Therefore, if there are individuals who can manipulate prices, the conclusion of the second welfare theorem is questionable. In this paper, we address the decentralization of a Pareto‐optimal allocation, when markets are non‐Walrasian. Our objective in this paper is to develop a game which can implement Pareto‐optimal allocations as Nash equilibria of strategic exchange in markets. In this way, we develop a version of the second welfare theorem for economies where markets are strategic.     

Wage Bargaining, Inventories, and Union Legislation

This paper analyses a strategic bargaining game where the firm may or maynot be able to sell out of its inventory of finished goods during astrike. Firms and the union are both risk neutral and have the same discountrate. It is shown that the wage equilibrium corresponds to the axiomaticNash bargaining solution where the threatpoints are the agents' payoffsshould bargaining continue indefinitely. We use the 1980 and 1982 EmploymentActs to test this theory, interpreting that legislation change as changingthe firm's threatpoint but not its bargaining power. This allows us toidentify the value of the firm's threatpoint post-1982. Formal testssupport the theory. Also consistent with the theory, it is found that unionwages decrease with inventories after 1982, but not before, and that theunion wage gap is smaller after 1982.     

Proposal power and majority rule in multilateral bargaining with costly recognition

This paper studies a sequential bargaining model in which agents expend efforts to be the proposer. In equilibrium, agents’ effort choices are influenced by the prize and cost effects. The (endogenous) prize is the difference between the residual surplus an agent obtains when he is the proposer and the payment he expects to receive when he is not. Main results include: (1) under the unanimity voting rule, two agents with equal marginal costs propose with equal probabilities, regardless of their time preferences; (2) under a nonunanimity rule, however, the more patient agent proposes with a greater probability; (3) while, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule; and (4) when agents are identical, the unanimity rule is socially optimal.     

Barriers to Global Free Trade through Bilateral Agreements

This paper examines the formation of bilateral free trade agreements (FTAs) in the context of a dynamic noncooperative bargaining game with a random proposer. We show that global free trade (a grand coalition) does not necessarily occur unless transfer payments among countries are allowed. When transfer payments are possible, bilateral FTAs always achieve global free trade, but the ex‐ante and ex‐post inequalities of social welfare among countries are larger than those when all countries are independent because of the strategic bargaining behavior.     

Multilateral institutions for international economic policy coordination: bargaining vs voting

We study a world economy where worldwide policy coordination is essential to optimally stabilize unfavorable common supply shocks. We develop a two-stage game to investigate how to implement the first-best response to these shocks via a multilateral institution, whose board of directors is composed of a representative per each member country. In a first stage, national governments nominate their representatives on the board. In a second stage, the board collectively chooses stabilization policies. We compare the relative merits of two collective choice mechanisms – bargaining and majority voting – in avoiding manipulation of the cooperative agreement through the strategic nomination of national representatives.     

The role of strategic uncertainty in games: An experimental study of cheap talk and contracts in the Nash demand game

We utilise results from a human-subjects experiment to examine the connection between strategic uncertainty and outcomes in games. Our basic game is a Nash demand game where one player has an outside option available. A “chat” treatment allows bargainers to send cheap-talk messages prior to playing the basic game, and in a “contracts” treatment, they can additionally propose and accept binding contracts. We propose that strategic uncertainty comprises at least two facets: “coordination-type”, which is lower in the chat game than in the basic game, and “rationality-type”, which is lower in the contracts game than in the chat game. We find that both types of strategic uncertainty impact bargaining outcomes: moving from the basic game to the chat game, and thence to contracts, improves several aspects of outcomes, such as higher efficiency, less opting out and less under-demanding. Other results include a treatment effect on the types of agreements that are reached.     

A THEORY OF WAGES AND LABOR DEMAND WITH INTRA‐FIRM BARGAINING AND MATCHING FRICTIONS*

This article provides a model of labor market equilibrium with search and within‐firm strategic bargaining. We yield explicit closed form solutions with heterogeneous labor inputs and capital. The solution exhibits overemployment. We show that higher relative bargaining power for some groups of workers may lead to overemployment relative to other groups, with such other groups being underemployed instead if they have a lower relative bargaining power. Similarly, the hold‐up problem between capitalists and employees does not necessarily lead to underinvestment in physical capital.     

Sociological versus strategic factors in bargaining

Most game-theoretic models of strategic interaction, indeed most economic models of any sort, specify potential outcomes entirely in terms of the preferences of the agents, as captured in their (possibly cardinal) utility functions. The underlying assumption is that the outcome of such interactions is determined entirely by these preferences, together with the strategic possibilities available to the agents. The purpose of this paper is to challenge the adequacy of this assumption in general, by investigating it in the specific context of two-person bargaining. In particular, we consider whether certain experimental results reported earlier can be accounted for strictly in terms of players' preferences and strategic possibilities, and we report a new experimental study designed to answer this question. The results strongly support the conclusion that sociological factors, unrelated to what we normally consider to be the ‘economic’ parameters of a game, can decisively influence the outcome of bargaining, in a systematic manner.     

Developing-Country Benefits from MFN Relative to Regional/Bilateral Trade Arrangements

Using a general‐equilibrium model of world trade, this paper evaluates the benefits of most‐favored‐nation (MFN) treatment to developing countries in multilateral relative to bilateral or regional trade agreements, from three sources. First, developing countries may be able to free‐ride on bilateral tariff concessions exchanged between larger countries in MFN‐based GATT/WTO rounds. Second, MFN benefits developing countries by restricting discriminatory retaliatory actions by other countries, evaluated here by a non‐ cooperative Nash tariff game. Finally, MFN changes threat points in bargaining and hence affects the bargaining solution of multilateral MFN‐based trade negotiation compared to a bilateral/regional arrangement. The authors find that the benefits to developing countries are small in the first case as the tariff rates are already low, and the benefits are small in the second case as the optimal tariffs under unconstrained retaliation are not very asymmetric. Benefits from the third case are large as large countries can extract large side‐payments if they bargain bilaterally.