Two concepts of monotonicity in two-person bargaining theory

Monotonicity has been suggested as a principle of fairness and a principle of bargaining. It has been proposed as a substitute to the “independence of irrelevant alternatives” axiom in bargaining solutions and thus applied to the determination of wages and employment. In this paper we will discuss the Kalai-Smorodinsky solution and show that it does not correspond to the monotonicity notion which follows from the “principle of bargaining” idea.     

Efficient equilibria in a differential game of capitalism

One considers a differential game of capitalism ‘à la Lancaster’. Feedback Nash equilibria and Pareto optimal solutions are characterized under the assumption that the planning horizon is infinite. It is then shown that, by combining a Pareto optimal solution with the Nash feedback equilibrium strategy pair, which plays the role of a threat, one can obtain an efficient equilibrium which is also subgame perfect in the sense of Selten. This result modifies sensibly the previous interpretation of the inherent inefficiency of capitalism.     

Bargaining power in stationary parallelogram games

A stationary variant of the repeated prisoners dilemma in which the game frontier is a parallelogram is analyzed. By using the probabilistic cheap talk concept of [3], the discount factor becomes fungible, and for a critical value of the discount factor a unique Pareto-optimal and Pareto-dominant solution can be found. The relative bargaining power of the players can be quantified in terms of the shape of the parallelogram. If the parallelogram is asymmetric, the solution results in an asymmetric allocation of payoffs. Players with more bargaining power receive a greater share of the allocation. The solution satisfies some standard bargaining axioms within the class of parallelogram games. A characterization is provided in terms of these axioms and one new axiom, weak-monotonicity, which is in the spirit of, but different from, the Kalai-Smorodinsky restricted-monotonicity axiom.Received: 15 January 2001, Accepted: 4 December 2003, We thank Wayne Shafer for interlocution and helpful comments.     

Planning for education in the health services: a multicriterion approach.

Administrators are often confronted with problems for which there exist several distinct measures of success. Such problems can be expressed in terms of linear programming models with several linear “criterion” functions instead of a single objective function. Although a variety of techniques are available for the solution of multicriterion problems, there exists a need for one which does not assume technical sophistication on the part of the decision maker and which provides valid solutions with minimum effort. “Efficient Manifold Presentation”, the approach used here, is based on the concept that the ideal solution must be a Pareto optimal solution. A method for finding an expression for the finite set of all Pareto optimal solutions to a linear program with multiple linear criteria is presented. Two processes are involved; first, the discovery of all Pareto optimal vertices of the feasible region, and secondly a grouping of these into sets each of which defines a convex polyhedron of Pareto optimal possibilities. Alternate versions of the second process are suggested for use under varying circumstances. An example of the applicability of the method for modeling enrollment and staffing policy in an educational institution is provided.     

Cost sharing: efficiency and implementation

We study environments where a production process is jointly shared by a finite group of agents. The social decision involves the determination of input contribution and output distribution. We define a competitive solution when there is decreasing-returns-to-scale which leads to a Pareto optimal outcome. Since there is a finite number of agents, the competitive solution is prone to manipulation. We construct a mechanism for which the set of Nash equilibria coincides with the set of competitive solution outcomes. We define a marginal-cost-pricing equilibrium (MCPE) solution for environments with increasing returns to scale. These solutions are Pareto optimal under certain conditions. We construct another mechanism that realizes the MCPE.     

Implementation in generalized matching problems

We search for (Nash) implementable solutions on a class of one-to-one matching problems which includes both the housing market (Shapley and Scarf, Journal of Mathematical Economics, 1974, 1, 23–28) and marriage problems (Gale and Shapley, American Mathematical Monthly, 1962, 69, 9–15). We show that the core correspondence is implementable. We show, furthermore, that any solution that is Pareto efficient, individually rational, and implementable is a supersolution of the core correspondence. That is, the core correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable. A corollary of independent interest in the context of the housing market is that the core correspondence is the only single-valued solution that is Pareto efficient, individually rational, and implementable.     

Existence and computation of the Aumann–Serrano index of riskiness and its extension

Aumann and Serrano (2008) introduce the index of riskiness to quantify the risk of a gamble. We discuss for which gambles this index of riskiness exists by considering the acceptance behavior of CARA-agents. Since for several relevant distributions riskiness is not defined, we suggest an extension of riskiness to all gambles. We prove that this extension is unique and that it satisfies the central duality axiom. Finally, we derive closed-form solutions of extended riskiness and list some applications.     

Pareto efficiency in the jungle

We revisit the jungle economy of Piccione and Rubinstein (Econ J 117(July):883–896, 2007) in which the allocation of resources is driven by coercion. In this economy the unique equilibrium satisfies lexicographic maximization. We show that relaxing the assumptions on consumption sets and preferences slightly, allocations other than lexicographic maximizers can be jungle equilibria. We attribute this result to single unilateral taking where a stronger agent takes goods from only one weaker agent. Once multiple unilateral takings are introduced, we show that jungle equilibria coincide with lexicographic maximization under weak assumptions. However, we also present examples of equilibria that are Pareto inefficient, where voluntary gift giving by stronger agents is needed to achieve Pareto efficiency and even voluntary trade has a role in the jungle.     

Random scheduling with deadlines under dichotomous preferences

A group of individuals share a deterministic server which is capable of serving one job per unit of time. Every individual has a job and a cut off time slot (deadline) where service beyond this slot is as worthless as not getting any service at all. Individuals are indifferent between slots which are not beyond their deadlines (compatible slots). A schedule (possibly random) assigns the set of slots to individuals by respecting their deadlines. We only consider the class of problems where for every set of relevant slots (compatible with at least one individual) there are at least as many individuals who have a compatible slot in that set: we ignore the case of underdemand. For this class, we characterize the random scheduling rule which attaches uniform probability to every efficient deterministic schedule (efficient uniform rule) by Pareto efficiency, equal treatment of equals, and probabilistic consistency (Chambers, 2004). We also show that a weaker version of the probabilistic consistency axiom is enough to achieve our result. Finally we show that efficient uniform rule is strategyproof.     

Quest for appropriate overcapacity in the fisheries industry

The effective management of natural resources is a critical issue that concerns many people with differing interests. This paper examines aspects of overcapacity and optimal capacity within fisheries by accounting for multiple objectives. Overcapacity arises when a fishing fleet is capable of producing more than what is demanded at the industry level, or allowed by a regulatory framework. The presence of multiple objectives within fisheries management is most often an unavoidable reality, where the objectives determine what level of overcapacity is considered optimal. A two-stage model is suggested that can produce information for management in terms of tradeoffs, policy frontiers, objective values and optimal fleet structure. In the first stage, an output-based Data Envelopment Analysis (DEA) model is applied. Efficiency is evaluated and production units transformed such that they use technologically efficient inputs and produce at their full potential. In the second stage, these transformed units are included in an aggregate industry model formulated as a multi-objective optimization program. The model provides information for managers in terms of tradeoffs, policy frontiers, objective values, and optimal fleet structure (by generating Pareto optimal solutions). The proposed model has then been applied to the Danish commercial fishing fleet.     

Nash bargaining in ordinal environments

We analyze the implications of Nash’s (Econometrica 18:155–162, 1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (J Econ Theory 16:247–251, 1977), we introduce a weaker independence of irrelevant alternatives (IIA) axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley–Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker IIA axiom. We also analyze the implications of other independence axioms.     

Bi-objective decision support system for routing and scheduling of hazardous materials

This paper presents a Pareto-based bi-objective optimization of hazardous materials vehicle routing and scheduling problem with time windows and shows its application to a realistic hazardous material logistics instance. A meta-heuristic solution algorithm is also proposed, which returns a set of routing solutions that approximate the frontier of the Pareto optimal solutions based on total scheduled travel time and total risk of whole transportation process. It works in a single-step fashion simultaneously constructing the vehicle route and selecting the optimal paths connecting the routed locations from a set of non-dominated paths obtained in terms of travel time and risk value.     

The topological equivalence of the pareto condition and the existence of a dictator

The paper studies two standard properties of rules for aggregating individual into social preferences: non-dictatorship and the Pareto condition. Together with the condition of independence of irrelevant alternatives, these are the three basic axioms of Arrow's social choice paradox.We prove the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules. The axiom of independence of irrelevant alternatives is not required.The results use a topological framework for aggregation introduced in Chichilnisky (1980), but under different conditions. In Chichilnisky (1980) rules are anonymous and respect unanimity. Since anonymity is strictly stronger than the condition of non-dictatorship, while respect of unanimity is strictly weaker than the Pareto condition, the two sets of conditions are not comparable.     

Iterated Kalai–Smorodinsky–Nash compromise

In this paper, we introduce a new two-person bargaining solution, which we call iterated Kalai–Smorodinsky–Nash compromise (IKSNC). For its characterization, we present an axiom called \(\varGamma \)-Decomposability which is satisfied by any solution that is decomposable with respect to a given reference solution \(\varGamma \). We show that the IKSNC solution is uniquely characterized by \(\varGamma \)-Decomposability whenever \(\varGamma \) satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry.     

Randomization under ambiguity: Efficiency and incentive compatibility

We generalize de Castro and Yannelis (2018) by taking into account the use of randomization. We answer the following questions: Is each efficient allocation of de Castro and Yannelis (2018) still Pareto optimal? Are all efficient allocations still incentive compatible under the Wald’s maxmin preferences? We provide positive answers and give applications.     

The representation problem and the efficiency of the price mechanism

It is shown in this paper that the way in which an allocation is represented (net trades, final allocation, etc.) can affect the design of any realizing mechanism or incentive compatible system. The reason is that a poor choice of representation may be imposing superfluous conditions and demands upon the realizing mechanism. So, in this paper a technique is developed to (1) find the optimal representation of an allocation, and (2) to characterize the associated, realizing mechanisms. Although this approach is designed to be applied to any smooth economic model, it is illustrated and motivated here by applying it to the price mechanism. More specifically, there are assertions in the literature by Mount and Reiter and by Hurwicz that the price mechanism is informationally efficient over the class of Pareto seeking mechanisms. These proofs are incomplete because they consider only one choice of representation for the Pareto allocations. We use this technique to (a) reassert the dimensional efficiency of the price mechanism, (b) compare mechanisms for spaces of economics with and without externalities, (c) characterize for the space of quadratic functions the other dimensionally efficient allocation concepts, and (d) characterize those two agent economics where the price mechanism is dimensionally efficient.     

The <Emphasis Type="Italic">n</Emphasis>-person Kalai-Smorodinsky bargaining solution under pre-donations

This study examines the behavior of simple n-person bargaining problems under pre-donations where the Kalai-Smorodinsky (KS) solution is operant. Pre- donations are a unilateral commitment to transfer a portion of one’s utility to someone else, and are used to distort the bargaining set and thereby influence the bargaining solution. In equilibrium, these pre-donations are Pareto-improving over the undistorted solution; moreover, when the agents’ preferences are sufficiently distinct, the equilibrium solution coincides with the concessionary division rule.     

Strategy-proofness in many-to-one matching problems

We search forstrategy-proof solutions in the context of (many-to-one) matching problems (Gale and Shapley, 1962). In this model, whenever the firms can hire as many workers as they want (the capacities are unlimited) the stable set is a singleton. There exists aPareto efficient, individually rational, andstrategy-proof matching rule if and only if the capacities are unlimited. Furthermore, whenever the capacities unlimited, the matching rule which selects the unique stable matching is the only matching rule that isPareto efficient, individually rational, andstrategy-proof.     

An indifference trap of voting

In this paper strategic situations of voting and abstentions are analysed in a three-candidate voting model where voters are indifferent to various alternatives and candidates are interested in winning the election and seeing their most preferred alternative being realized. A specific decision problem is analysed, described by an Indifference Trap Game, with respect to, e.g., the corresponding Nash equilibria, perfect equilibria, and maximin solution. A second-best outcome is contained in the choice set of all three solutions while the Nash equilibrium concept is compatible with the Pareto efficient outcomes of the game.An alternative scenario where candidates suffer from incumbency but voters still are indifferent to some alternatives also supports the second-best outcome. Again, various solutions concepts are applied. We conclude that indifferent voters imply an eminent coordination problem for the candidates in the given voting game which, in general, ends up in inefficient outcomes. The inherent complexity of the decision situation cannot be sufficiently reduced to single out one and only one outcome.