On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. We first show that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games by providing alternative solutions that satisfy these axioms. However, when considering an assignment game as a communication graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph buyers are connected with sellers only, we show that Myerson's component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount

How well do buffer circles capture the ranging behaviours of territorial raptors?

As the world's human population increases, so does the competition for natural resources between humans and wildlife. This competition may be intense for apex predators, such as raptors, which generally require large natural areas in order to maintain their populations. Anthropogenic development within territories can cause individuals to either abandon these sites, reduce their breeding productivity, or cause direct mortality to the territory holding birds. To mitigate such impacts, one method, employed as part of Environmental Impact Assessments (EIA), is the use buffer circles centred on nest sites. Within these buffers the most damaging forms of development are prohibited. This approach assumes that raptors use the space around their nest in a uniform way, but this assumption may not always be correct and few have evaluated the effectiveness of buffer circles at protecting a species' home range. This study uses tracking data to evaluate the effectiveness of buffer circles to cover the ranging movements of six southern African raptor species, throughout the year, as well as during their breeding and non-breeding season. My study revealed that buffer circles whose dimensions were based on the species' 95% Kernel Density Estimate (KDE) did relatively well at capturing the proportion of individual GPS fixes, but did less well at capturing the KDE area from tracked birds. For buffer circles to capture 95% of the home range polygons (95% KDE) they would generally need to be at least twice as large as those that were derived from the 95% KDE home range area, and for some species with very large home ranges (e.g. Lappet-faced Vultures) even buffer circles that were 3 times the size failed to cover 95% of the KDE polygons

Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties

A well known and established model in communication policy in sociology and marketing is that of opinion leadership. Opinion leaders are actors in a society who are able to affect the behavior of other members of the society called followers. Hence, opinion leaders might have a considerable impact on the behavior of markets and other social agglomerations being made up of individual actors choosing among a number of alternatives. For marketing or policy purposes it appears to be interesting to investigate the effect of different opinion leader-follower structures in markets or any other collective decision-making situations in a society. We study a two-action model in which the members of a society are to choose one action, for instance, to buy or not to buy a certain joint product, or to vote yes or no on a specific proposal. Each of the actors has an inclination to choose one of the actions. By definition opinion leaders have some power over their followers, and they exercise this power by influencing the behavior of their followers, i.e. their choice of action. After all actors have chosen their actions, a decision-making mechanism determines the collective choice resulting out of the individual choices. Making use of bipartite digraphs we introduce novel satisfaction and power scores which allow us to analyze the actors' satisfaction and power with respect to the collective choice for societies with different opinion leader-follower structures. Moreover, we study common dictator and opinion leader properties of the above scores and illustrate our findings for a society with five members.Bipartite digraph ; influence ; inclination ; collective choice ; opinion leader ; follower ; satisfaction ; power ; dictator properties ; opinion leader properties

An Owen-type value for games with two-level communication structures

We introduce an Owen-type value for games with two-level communication structures, being structures where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of communication restrictions are modeled by an undirected communication graph, so there is a communication graph between the unions of the coalition structure as well as a communication graph on the players in every union. We also show that, for particular two-level communication structures, the Owen value and the Aumann-Drèze value for games with coalition structures, the Myerson value for communication graph games and the equal surplus division solution appear as special cases of this new value

The balanced solution for cooperative transferable utility games

The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this contribution we de¯ne the balanced solution which assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. We prove its existence for all monotone transferable utility games, discuss other properties of this solution, and deal with its characterization through a reduced game consistency

The Shapley value, the Proper Shapley value, and sharing rules for cooperative ventures

In this note, we discuss two solutions for cooperative transferable utility games, namely the Shapley value and the Proper Shapley value. We characterize positive Proper Shapley values by affine invariance and by an axiom that requires proportional allocation of the surplus according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games characterize the Shapley value

Equal loss under separatorization and egalitarian values

We characterize the equal division value, the equal surplus division value, and the class of their affine combinations for TU-games involving equal loss under separatorization. This axiom requires that, if a player becomes a dummifying player (Casajus and Huettner, 2014), then any two other players are equally affected

An efficient and fair solution for communication graph games\ud

We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness. This latter axiom compares for every component in the communication graph the total payo to the players of this component in the game itself to the total payoff of these players when applying the solution to the subgame induced by this component

Explicit and Latent Authority in Hierarchical Organizations

In this paper we consider the problem of the control of access to a firm's productive asset, embedding the relevant decisionmakers into a general structure of formal authority relations. Within such an authority structure, each decision maker acts as a principal to some decision makers, while she acts as an agent in relation to certain other decision makers. We study under which conditions decision makers decide to exercise their own authority and to accept their superiors' authority.We distinguish two types of behavior within such an authority situation. First, we investigate a non-cooperative equilibrium concept describing the explicit, myopic exercise of authority. We find that if monitoring costs are sufficiently small, such explicit authority is exercised fully.Second, we consider the possibility of subordinates to submit themselves to authority even though such authority is not enforced explicitly. Again for sufficiently small monitoring costs such latent authority can be supported as an equilibrium