Division Of Surplus Research Articles

On egalitarian values for cooperative games with level structures

In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with level structures. In the case of the equal surplus division value we propose three possible extensions, one of which has already been described in the literature. We provide axiomatic characterizations of the values considered, apply them to a particular cost sharing problem and compare them in the framework of such an application.

Incentivizing cooperative electricity-heat operation: A distributed asymmetric Nash bargaining mechanism

Synergies in an integrated electricity and heat system (IEHS) are acknowledged to improve the overall economic efficiency. Due to heterogeneity in the IEHS, however, such cooperation can hardly be realized unless the resultant surplus is shared in an incentive-compatible and privacy-concerned way, which is seldom discussed by conventional holistic studies. To this end, a distributed asymmetric Nash bargaining (D-ANB) mechanism is designed. First, to cope with the uncertainties in the IEHS, a two-stage stochastic dispatch model is formulated. Then, the individual contribution rate is quantified in a subjective manner, while the favorable properties of the D-ANB mechanism are proved. Finally, to maintain the autonomy and privacy, both distributed formulation and distributed solution in D-ANB are introduced. Specifically, by exploiting the specific features of D-ANB, the efficiency of the alternating direction method of multipliers (ADMM) is significantly improved by introducing a warm-start strategy and deriving the closed-form solution of the bargaining subproblems. Case studies verify that D-ANB achieves both high computation efficiency with privacy preservation and Pareto optimality with fair surplus division. Both the electricity and heat sectors enjoy cost savings of around 10.5%–19.5%, while the coordination efficiency is enhanced by 3–4 orders of magnitude.

Robust Predictions in Coasian Bargaining

This paper studies robust predictions when players may have additional information in an otherwise standard seller-offer bargaining with private values. Players’ extra information gives rise to higher-order uncertainties about the underlying surplus. We show that the equilibrium outcomes in the frequent-offer limit depend critically on the nature of second-order uncertainty: (i) when the seller’s beliefs about the buyer’s values are public, the limiting equilibrium outcomes are efficient and any surplus division is possible; (ii) when the seller’s beliefs are private, any feasible and individually rational payoffs can be the limiting equilibrium payoffs.(JEL C78, D82, D83)

Escaping search when buying

This paper studies a duopoly with horizontally differentiated products and costly sequential consumer search. Prices are posted and search costs must be paid to observe the match values of goods. Consumers choose both in what order to inspect the products and whether to inspect the goods before purchasing. When the expected match value is relatively high, consumers always consider the cheaper product first. However if the expected match value is low, then consumers may check the more expensive product first. The fact that a consumer may buy a product without inspection softens price competition. As a result, the comparative statics of prices and surplus division with respect to search costs is different from that of a sequential search model with observable prices.

Founder social capital and value appropriation in R&D alliance agreements

This paper investigates the micro-foundations of value appropriation involving startups and examines the relationship between founder social capital and value obtained by startups in R&D alliance agreements. We build on the bargaining framework for surplus division and propose that founder social capital facilitates a more expansive pool of partnering opportunities and thereby bestows bargaining advantages to a startup, leading it to obtain more value in an R&D alliance deal. More importantly, we develop a novel hypothesis about the complementarity between founder social capital and a startup's technological capabilities to suggest that the bargaining impact of founders’ social capital becomes more pronounced when a startup is also endowed with superior technological capabilities. Furthermore, we suggest that founder social capital can be particularly valuable for startups to secure outside opportunities when there is weak institutional financial support available. Empirical analyses of R&D alliance agreements in the biotechnology industry furnish evidence for our theory.

The Equal Surplus Division Based the Bargaining Power of Priori Coalition in the Coalition Structure Game

The Equal Surplus Division Based the Bargaining Power of Priori Coalition in the Coalition Structure Game

New results on egalitarian values for games with a priori unions

Several extensions of the equal division value and the equal surplus division value to the family of games with a priori unions have been proposed by Alonso-Meijide et al. [On egalitarian values for cooperative games with a priori unions. TOP. 2020;28:672–688]. In this study, we provide new axiomatic characterizations of these values. Furthermore, using the equal surplus division value in two steps, we propose a new coalitional value. The balanced contributions and quotient game properties generate a different modification of the equal surplus division value.

Surplus Division between Labor and Capital: A Review and Research Agenda

The division of firm surplus between labor and shareholders, and its impact on firms’ value creation, are central topics in strategy theory and practice. Early studies of value appropriation within...

Sharing the surplus and proportional values

We introduce a family of proportional surplus division values for TU-games. Each value first assigns to each player a compromise between her stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value in this family.

Bargaining power and U.S. military aid in the post-cold war era

This study examines the effect of bargaining power on the allocation of U.S. military assistance. Conceptualising U.S. military assistance as an aid-for-policy deal, it applies a two-tiered stochastic frontier model to a data sample of the post-Cold War era. It shows that the bargaining effect accounts for a huge variation in U.S. military aid distribution. The volume of U.S. military assistance in equilibrium is lower than the baseline volume by 4% at the mean and by 6% at the median. The donor U.S. extracts a slightly larger portion of the transaction surplus at these central points. However, the game of surplus division is not always about equally strong hagglers as it may first appear. In fact, the quartile values show substantial variance in bargaining performance and, hence, an outcome of surplus division across transactions. The bargaining effect is highly significant in the allocation of U.S. military assistance in the post-Cold War era. The donor U.S enjoys a bargaining advantage at the mean and median, but rich variations are noticeable.

The Herfindahl‐Hirschman Index and the Distribution of Social Surplus*

I show that in a broad range of oligopoly models, the Herfindahl‐Hirschman index (HHI) reflects the ratio of producer surplus to consumer surplus and therefore the division of surplus between firms’ owners and consumers.

Compromising between the proportional and equal division values

We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an α-mollified value, is obtained in two steps. First, linear functions are defined that associate a real number to every TU-game. Second, the weight assigned by this function is used to weigh proportionality and equality principles in allocating the worth of the grand coalition. We provide an axiomatic characterization of this family, and show that this family contains the affine combinations of the equal division value and the equal surplus division value as the only linear values. Further, we identify the proportional division value and the affine combinations of the equal division value and the equal surplus division value as those members of this family, that satisfy projection consistency.

Selling “Money” on eBay: A field study of surplus division

Abstract We study the division of trade surplus in a natural field experiment on German eBay. Acting as a seller, we offer Amazon gift cards with face values between 5 and 500 Euro. eBay users, the subjects of our experiment, make price offers according to the Buy-it-Now or Best Offer trading protocol. Using a novel decomposition method, we infer the trade surplus from the data and find that on average the buyers offer one quarter of the surplus to the seller. Additionally, we document: (i) insignificant effects of stake size; (ii) poor use of strategically relevant public information; and (iii) differences between East and West German subjects.

Selling Money on Ebay: A Field Study of Surplus Division

We study the division of trade surplus in a competitive market environment by conducting a natural field experiment on German eBay. Acting as a seller, we offer Amazon gift cards with face values of up to 500 Euro. Randomly arriving buyers, the subjects of our experiment, make price offers according to eBay rules. Using a novel decomposition method, we infer offered shares of trade surplus and find that the average share proposed to the seller amounts to 29%. Additionally, we document: (i) insignificant effects of stake size; (ii) poor use of strategically relevant public information; and (iii) behavioural differences between East and West German subjects.

Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency

A solution on a set of transferable utility (TU) games satisfies strong aggregate monotonicity (SAM) if every player can improve when the grand coalition becomes richer. It satisfies equal surplus division (ESD) if the solution allows the players to improve equally. We show that the set of weight systems generating weighted prenucleoli that satisfy SAM is open, which implies that for weight systems close enough to any regular system, the weighted prenucleolus satisfies SAM. We also provide a necessary condition for SAM for symmetrically weighted nucleoli. Moreover, we show that the per capita nucleolus on balanced games is characterized by single-valuedness (SIVA), translation covariance (TCOV) and scale covariance (SCOV), and equal adjusted surplus division (EASD), a property that is comparable to but stronger than ESD. These properties together with ESD characterize the per capita prenucleolus on larger sets of TU games. EASD and ESD can be transformed to independence of (adjusted) proportional shifting, and these properties may be generalized for arbitrary weight systems p to I(A)Sp. We show that the p-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, TCOV, SCOV, and IASp and on larger sets by additionally requiring ISp.

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.

The Equal Surplus Division Value for Cooperative Games with a Level Structure

In this paper, we investigate the equal surplus division value for cooperative games with a level structure, which is a sequence of coalition structures becoming coarser and coarser. We propose three axiomatizations of the value. Among them, the first two use different variations of the recent population solidarity axiom, and the third one invokes a special reduced game consistency axiom. Due to the existence of a level structure, our axioms impose special restrictions on the players we focus. We show that our value can be characterized with these axioms and other variations of well-known axioms, such as efficiency, standardness, and quotient game property. Besides characterizing the value, we also connect it to the recent field of ordered tree cooperative games, wherein we find that the iterative value can be viewed as a special case of our value.

Similarities in axiomatizations: equal surplus division value and first-price auctions

We compare axiomatizations between a value for cooperative games with transferable utilities (TU games), and a rule for auctions. The equal surplus division value on the set of zero-monotonic TU games is characterized by the following: individual rationality, Pareto efficiency, and equal effect of players’ nullification on others. Meanwhile, first-price auctions, on the general preference domain, are characterized by individual rationality, envy-freeness, and weak equal effect of buyers’ nullification on others. Here, envy-freeness implies Pareto efficiency in the model of auctions. Given the agents’ general preferences in the auction model, the characteristic of a weak equal effect of buyers’ nullification on others weakens the requirement of equal effect of players’ nullification on others. Although the two models are different, the corresponding axioms in both models require conditions corresponding to each other. In particular, individual rationality requires voluntary participation of agents, Pareto efficiency (or its stronger axiom of envy-freeness in the model of auctions) requires outcomes with no waste, and (weak) equal effect of players’ (buyers’) nullification on others requires equal treatment of agents when an agent is nullified. Therefore, in terms of axiomatizations, we can similarly interpret the equal surplus division value and first-price auctions.

On egalitarian values for cooperative games with a priori unions

In this paper, we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal surplus division value we propose three possible extensions. We provide axiomatic characterizations of the new values. Furthermore, we apply the proposed modifications to a particular motivating example and compare the numerical results with those obtained with the original values.

Compromising between the Proportional and Equal Division Values: Axiomatization, Consistency and Implementation

We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an alpha-mollified value, is obtained in two steps. First, a linear function with respect to the worths of all coalitions is defined which associates a real number to every TU-game. Second, the weight assigned by this function is used to weigh proportionality and equality principles in allocating the worth of the grand coalition. We provide an axiomatic characterization of this family, and show that this family contains the affine combinations of the equal division value and the equal surplus division value as the only linear values. Further, we identify the proportional division value and the affine combinations of the equal division value and the equal surplus division value as those members of this family, that satisfy projection consistency. Besides, we provide a procedural implementation of each single value in this family.