Iterated egalitarian compromise solution to bargaining problems and midpoint domination

We introduce a new solution for two-person bargaining problems: the iterated egalitarian compromise solution. It is defined by using two prominent bargaining solutions, the egalitarian solution (Kalai, 1977) and the equal-loss solution (Chun, 1988), in an iterative fashion. While neither of these two solutions satisfy midpoint domination – an appealing normative property – we show that the iterated egalitarian compromise solution does so.     

Some remarks on properties for choice functions

In this paper, we present five categories of results by studying the interrelationships between properties for choice functions. The first category is about the localization assumption. The second category is about the relative egalitarian solution. The third category provides an axiomatic characterization of the equal loss solution. The fourth and fifth categories consist of lexicographic extensions of the equal loss and relative egalitarian solutions respectively. This revised version was published online in June 2006 with corrections to the Cover Date.     

An axiomatization of the egalitarian solutions

The egalitarian solutions for general cooperative games which were defined and axiomatized by Kalai and Samet, are compared to the Harsanyi solution. It is shown that axioms used by Hart to characterize the Harsanyi solution can be used to characterize the (symmetric) egalitarian solution. The only changes needed are the omission of the scale covariance axiom and the inclusion, in the domain of the solution, of games which lack a certain smoothness requirement.     

Disagreement point axioms and the egalitarian bargaining solution

We provide new characterizations of the egalitarian bargaining solution on the class of strictly comprehensive n-person bargaining problems. The main axioms used in all of our results are Nash’s IIA and disagreement point monotonicity—an axiom which requires a player’s payoff to strictly increase in his disagreement payoff. For n = 2 these axioms, together with other standard requirements, uniquely characterize the egalitarian solution. For n > 2 we provide two extensions of our 2-person result, each of which is obtained by imposing an additional axiom on the solution. Dropping the axiom of anonymity, strengthening disagreement point monotonicity by requiring player i’s payoff to be a strictly decreasing function of the disagreement payoff of every other player j ≠ i, and adding a “weak convexity” axiom regarding changes of the disagreement point, we obtain a characterization of the class of weighted egalitarian solutions. This “weak convexity” axiom requires that a movement of the disagreement point in the direction of the solution point should not change the solution point. We also discuss the so-called “transfer paradox” and relate it to this axiom.     

Union-wise egalitarian solutions in cooperative games with a coalition structure

4OR - The egalitarian principle has been widely adopted in designing solution concepts for cooperative games. In light of egalitarianism, we introduce two egalitarian values satisfying union...     

Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value

This study provides a unified axiomatic characterization method of one-point solutions for cooperative games with transferable utilities. Any one-point solution that satisfies efficiency, the balanced cycle contributions property (BCC), and the axioms related to invariance under a player deletion is characterized as a corollary of our general result. BCC is a weaker requirement than the well-known balanced contributions property. Any one-point solution that is both symmetric and linear satisfies BCC. The invariance axioms necessitate that the deletion of a specific player from games does not affect the other players’ payoffs, and this deletion is different with respect to solutions. As corollaries of the above characterization result, we are able to characterize the well-known one-point solutions, the Shapley, egalitarian, and solidarity values, in a unified manner. We also studied characterizations of an inefficient one-point solution, the Banzhaf value that is a well-known alternative to the Shapley value.     

Bargaining solutions at work: Qualitative differences in policy implications

Traditional bargaining theory characterizes solutions to bargaining problems by their properties in the utility space. In applications, however, one is usually interested in the implications of the conflict resolution within the economic environment, where the properties of axiomatic bargaining solutions are less well understood. By means of a standard bargaining model for the labor market we demonstrate that economic policy implications may be very sensitive to the choice of the bargaining solution. More specifically, the induced employment effects of a change in the reservation wage under the Nash-solution may differ substantially from those under the Kalai–Smorodinsky, the egalitarian, or the equal-loss solution. Hence, the choice of the bargaining solution is not innocuous, even if one is only interested in qualitative policy conclusions.     

Processor-sharing queues: Some progress in analysis

This paper reviews some recent results based on new techniques used in the analysis of main processor-sharing queueing systems. These results include the solutions of the problems of determining the sojourn time distributions and the distributions of the number of jobs in the M/G/1/t8 queue under egalitarian and feedback (foreground-background) processor-sharing disciplines. A brief discussion of some related results is also given.     

Lorenz comparisons of nine rules for the adjudication of conflicting claims

Consider the following nine rules for adjudicating conflicting claims: the proportional, constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, adjusted proportional, random arrival, and minimal overlap rules. For each pair of rules in this list, we examine whether or not the two rules are Lorenz comparable. We allow the comparison to depend upon whether the amount to divide is larger or smaller than the half-sum of claims. In addition, we provide Lorenz-based characterizations of the constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, and minimal overlap rules.     

Weighted values and the core in NTU games

Monderer et al. (Int J Game Theory 21(1):27–39, 1992) proved that the core is included in the set of the weighted Shapley values in TU games. The purpose of this paper is to extend this result to NTU games. We first show that the core is included in the closure of the positively weighted egalitarian solutions introduced by Kalai and Samet (Econometrica 53(2):307–327, 1985). Next, we show that the weighted version of the Shapley NTU value by Shapley (La Decision, aggregation et dynamique des ordres de preference, Editions du Centre National de la Recherche Scientifique, Paris, pp 251–263, 1969) does not always include the core. These results indicate that, in view of the relationship to the core, the egalitarian solution is a more desirable extension of the weighted Shapley value to NTU games. As a byproduct of our approach, we also clarify the relationship between the core and marginal contributions in NTU games. We show that, if the attainable payoff for the grand coalition is represented as a closed-half space, then any element of the core is attainable as the expected value of marginal contributions.     

The pairwise egalitarian solution for the assignment game

In this note we consider the pairwise egalitarian solution (Sánchez-Soriano, 2003) on the domain of assignment games and study its relation with the core. Strengthening the dominant diagonal condition (Solymosi and Raghavan, 2001), we introduce k-dominant diagonal assignment games (k≥1), analyzing for which values of k the pairwise egalitarian solution fulfills the standards of fairness represented by the Lorenz domination and the kernel. We also characterize the Thompson’s fair division point (Thompson, 1981) for arbitrary assignment games.     

Flow sharing and bankruptcy games

We discuss the relationship between bankruptcy problems and flow sharing problems, respectively, and show that the latter type of problem can be interpreted as a generalization of the former. The corresponding flow sharing game is convex, hence we can use the converse reduced game property to characterize the nucleolus and the constrained egalitarian solution. Our main contribution is thus to introduce the nucleolus as an alternative solution concept for flow sharing problems, and to offer a game-theoretic interpretation of the traditional egalitarian solution.     

Egalitarian allocation and players of certain type

In cooperative game theory the Shapley value is different from the egalitarian value, the latter of which allocates payoffs equally. The null player property and the nullifying player property assign zero payoff to each null player and each nullifying player, respectively. It is known that if the null player property for characterizing the Shapley value is replaced by the nullifying player property, then the egalitarian value is determined uniquely. We propose several properties to replace the nullifying player property to characterize the egalitarian value. Roughly speaking, the results in this note hint that equal division for players of certain types may lead to the egalitarian allocation.     

Pollution,unequal lifetimes and fairness

This paper characterizes the optimal level of pollution in a two-period OLG economy where pollution deteriorates survival conditions. We compare two long-run social optima: on the one hand, the average utilitarian optimum, where the long-run average well-being is maximized, and, on the other hand, the ex post egalitarian optimum, where the realized well-being of the worst-off at the stationary equilibrium is maximized. It is shown that the ex post egalitarian optimum involves, under weak conditions, a higher level of pollution in comparison with the utilitarian optimum. This result is robust to introducing health expenditures in the survival function. Finally, we examine the decentralization of those two social optima, and we compare the associated optimal taxes on capital income aimed at internalizing the pollution externality.     

Non-binding agreements and fairness in commons dilemma games

Usually, common pool games are analyzed without taking into account the cooperative features of the game, even when communication and non-binding agreements are involved. Whereas equilibria are inefficient, negotiations may induce some cooperation and may enhance efficiency. In the paper, we propose to use tools of cooperative game theory to advance the understanding of results in dilemma situations that allow for communication. By doing so, we present a short review of earlier experimental evidence given by Hackett, Schlager, and Walker 1994 (HSW) for the conditional stability of non-binding agreements established in face-to-face multilateral negotiations. For an experimental test, we reanalyze the HSW data set in a game-theoretical analysis of cooperative versions of social dilemma games. The results of cooperative game theory that are most important for the application are explained and interpreted with respect to their meaning for negotiation behavior. Then, theorems are discussed that cooperative social dilemma games are clear (alpha- and beta-values coincide) and that they are convex (it follows that the core is “large”): The main focus is on how arguments of power and fairness can be based on the structure of the game. A second item is how fairness and stability properties of a negotiated (non-binding) agreement can be judged. The use of cheap talk in evaluating experiments reveals that besides the relation of non-cooperative and cooperative solutions, say of equilibria and core, the relation of alpha-, beta- and gamma-values are of importance for the availability of attractive solutions and the stability of the such agreements. In the special case of the HSW scenario, the game shows properties favorable for stable and efficient solutions. Nevertheless, the realized agreements are less efficient than expected. The realized (and stable) agreements can be located between the equilibrium, the egalitarian solution and some fairness solutions. In order to represent the extent to which the subjects obey efficiency and fairness, we present and discuss patterns of the corresponding excess vectors.     

An axiomatic approach to egalitarianism in TU-games

A core concept is a solution concept on the class of balanced games that exclusively selects core allocations. We show that every continuous core concept that satisfies both the equal treatment property and a new property called independence of irrelevant core allocations (IIC) necessarily selects egalitarian allocations. IIC requires that, if the core concept selects a certain core allocation for a given game, and this allocation is still a core allocation for a new game with a core that is contained in the core of the first game, then the core concept also chooses this allocation as the solution to the new game. When we replace the continuity requirement by a weak version of additivity we obtain an axiomatization of the egalitarian solution concept that assigns to each balanced game the core allocation minimizing the Euclidean distance to the equal share allocation.     

The egalitarian solution and reduced game properties in convex games

The main purpose of this paper is to axiomatise the egalitarian solution of Dutta and Ray over the class of convex games. The main axioms used are the two reduced game properties due to Davis-Maschler and Hart-Mas Colell. The egalitarian solution is the only solution satisfying either of the two reduced game properties and agreeing with the egalitarian solution on two person games. Moreover, it is also shown that there is no solution satisfying symmetry, individual rationality and a monotonicity condition on two-person games and which simultaneously satisfies both the reduced game properties.     

Groupstrategyproofness of the egalitarian mechanism for constrained rationing problems

Motivated by applications in many economic environments, Bochet et al. (2010) generalize the classic rationing model (Sprumont 1991) as follows: there is a moneyless market, in which a non-storable, homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. Transfers between a supplier and a demander are feasible only if they are linked, and the links form an arbitrary bipartite graph. Information about individual preferences is private, and so is information about feasible links: an agent may unilaterally close one of her links if it is in her interest to do so. For this problem they propose the egalitarian transfer solution, which equalizes the net transfers of rationed agents as much as permitted by the bilateral constraints. Furthermore, they show that the egalitarian mechanism elicits a truthful report of both preferences and links. In the variant where demanders are not strategic but demands need to be exactly met Bochet et al. (2013), they propose a similar mechanism for which truthfully reporting the peaks is a dominant strategy, but truthful reporting of links is not.The key contribution of the paper is a comprehensive study of the egalitarian mechanism with respect to manipulation by a coalition of agents. Our main result is that the egalitarian mechanism is group strategyproof : no coalition of agents can (weakly) benefit from jointly misreporting their peaks. Furthermore, we show that the egalitarian mechanism cannot be manipulated – by misreporting links or by misreporting peaks – by any coalition of suppliers (or any coalition of demanders) in the model where both the suppliers and demanders are agents. Our proofs shed light on the structure of the two models and simplify some of the earlier proofs of strategyproofness. An implication of our results is that the well known algorithm of Megiddo (1977) to compute a lexicographically optimal flow in a network is group strategyproof with respect to the source capacities and sink capacities.     

A proportional approach to claims problems with a guaranteed minimum

In distribution problems, and specifically in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. Nonetheless, when using the egalitarian division, agents may receive more than her claim. We propose a compromise between the proportional and the egalitarian approaches by considering the restriction that no one receives more than her claim. We show that the most egalitarian compromise fulfilling this restriction ensures a minimum amount to each agent. We also show that this compromise can be interpreted as a process that works in two steps as follows: first, all agents receive an equal share up to the smallest claim if possible (egalitarian distribution), and then, the remaining estate (if any) is allocated proportionally to the remaining claims (proportional distribution). Finally, we obtain that the recursive application of this process finishes at the Constrained Equal Awards solution (CEA).     

Two characterizations of the consistent egalitarian solution and of the core on NTU games

In this paper, we provide two characterizations in the context of NTU games: of the consistent egalitarian solution and of the core. The first characterization is based on reduced games and contraction and expansion independence. The second one is based on reduced games and sub-reduced games.