Prices in Mixed Cost Allocation Problems

We consider mixed cost allocation problems, i.e., joint cost problems that involve two types of heterogeneous outputs, divisible and indivisible. The Aumann–Shapley price mechanism is extended to this setting. We also present a set of properties which characterize this cost sharing rule. Journal of Economic Literature Classification numbers: D63, C79.     

Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games

This paper axiomatizes the Shapley value on minimum cost spanning tree games by using axioms which are different from those used in network games. Journal of Economic Literature Classification Numbers: C71, A14.     

Characterization of additive cost sharing methods

The set of additive cost sharing methods when individual demands are integer valued and cost shares are non negative is characterized by its extreme points and by a network flow representation. The extreme methods allocate costs incrementally along a chain of demand vectors independent of the cost function. The result generalizes Wang’s characterization in that we do not assume the Dummy axiom.     

On demand responsiveness in additive cost sharing

Under partial responsibility, the ranking of cost shares should never contradict that of demands.The Solidarity axiom says that if agent i demands more, j should not pay more if k pays less. It characterizes the quasi-proportional methods, sharing cost in proportion to `rescaled' demands.Full responsibility rules out cross-subsidization for additively separable costs. Restricting solidarity to submodular cost characterizes the fixed-flow methods, containing the Shapley-Shubik and serial methods.The quasi-proportional methods meet—but most fixed-flow methods fail—Group Monotonicity: if a group of agents increase their demands, not all of them pay less. Serial cost sharing is an exception.     

Strategyproof Cost Sharing of Multiple Excludable Public Goods

In a model of cost sharing of multiple excludable public goods, we examine the properties of mechanisms satisfying strategyproofness, no subsidy, outcome non‐bossiness, budget balance, individual rationality and consumer sovereignty. We show that such mechanisms in general will not satisfy the equity property of equal treatment of equals. This contrasts with the single excludable public good case.     

Envy,wealth, and class hierarchies

A persion i is said to not envy another person j if he likes his own bundle of goods as well as he would like j's bundle. This paper explores the social structure defined by the non-envy relation, and relates it to the social structure defined by market values of bundles, or wealth.     

Cost Sharing under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley–Shubik cost sharing, and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.Journal of Economic LiteratureClassification Numbers: C72, D63.     

The political business cycle: An extension of Nordhaus's model

Summary Nordhaus's (1975) model of the political business cycle is extended in this paper by explicitly formulating the link between the economic sphere (represented by the Phillips curve) and fiscal policy. This extended model yields the hypothesis that during an electoral period the budgetary policy is contractionary in the first half and expansionary in the second half with the consequences of a reduction in unemployment (increase in inflation) before elections and a rise in unemployment (decrease in inflation) after elections. This hypothesis is tested against the data of the Austrian economy by a non-parametric test (which leads to a rejection of our hypothesis for Austria). The extent of the political business cycle bias is demonstrated by policy simulations within a macroeconomic model.

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Zusammenfassung Das Modell vonNordhaus (1975) über den Politischen Konjunkturzyklus wird in diesem Artikel erweitert, indem explizit die Beziehung zwischen dem ökonomischen Bereich (repräsentiert durch die Phillips-Kurve) und der Fiskalpolitik hergestellt wird. Dieses erweiterte Modell führt zu der Hypothese, daß während einer Legislaturperiode die Budgetpolitik in der ersten Hälfte restriktiv und in der zweiten Hälfte expansiv ist. Als Konsequenz dieser Politik kommt es zu einer Verringerung der Arbeitslosigkeit (einem Anstieg der Inflation) vor Wahlen und einem Anstieg der Arbeitslosigkeit (einer Verringerung der Inflation) nach den Wahlen. Diese Hypothese wird an Hand österreichischer Daten mit Hilfe eines nichtparametrischen Tests geprüft (was zu einer Ablehnung unserer Hypothese für Österreich führt). Das quantitative Ausmaß des durch den Politischen Konjunkturzyklus entstehenden bias wird dann mit Hilfe von politischen Simulationen im Rahmen eines makroökonomischen Modells demonstriert.

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Definitions AK Public purchases of goods and services + public investment (A.S.) - AT Unemployed persons, in total (in 1.000) - AZA Worked hours per worker (in hours) - BAU Central government's expenditures (outlays) in total (A.S.) - BEI Central government's revenues (receipts) in total (A.S.) - BS Budget deficit of the Central government (A.S.) - CB Labour supply (in 1.000) - CH Unemployment rate (%) - CON Public consumption (A.S.) - COR Public consumption (A.S. 1964) - CPN Private consumption (A.S.) - CPR Private consumption (A.S. 1964) - CUB Current balance (A.S.) - DS Direct taxes + public income from property-transfers to households + transfers from households (A.S.) - DX DS-public income from property (A.S.) - D7273 Dummy for monetary policy and Dummy for change from gross turnover tax to VAT (1972+1; 1973–1; other 0) - D7278 Dummy for investment tax (1972+1; 1973–1; 1977+1; 1978–1; other 0) - D73US Dummy for shift of employers to employees (1973+1; other 0) - D7375 Dummy for incomes tax reform (1973–1; 1975–1; other 0) - D7778 Dummy for extra VAT (1977+1; 1978–1; other 0) - EBE Population in total (in 1.000) - EET Employment in total + unemployed (total labour supply; in 1.000) - ESE Employers (in 1.000) - EUS Employees (in 1.000) - FBN Monetary base (A.S.) - FGN Money M1 (A.S.) - FG Money M1 (A.S. 1964) - GDN Gross domestic product (A.S.) - GDR Gross domestic product (A.S. 1964) - GER Energy (1.000 t/TCE) - GIR Industry output (A.S. 1964) - GE Profits in total (A.S.) - GV Profits in total (A.S. 1964) - IS Indirect taxes—transfers to firms (A.S.) - ITN Gross fixed investment (A.S.) - ITR Gross fixed investment (A.S. 1964) - JR Final domestic demand (A.S. 1964) - LA Stocks and statistical discrepancies; National account basis (A.S.) - LEAD Difference of one major party over the other in parliament in percentage points - LB Foreign balance (A.S.) - LKV Long term capital transactions (A.S.) - MA Money M1 + profits (A.S. 1964) - MMN Imports of goods and services (A.S.) - MMR Imports of goods and services (A.S. 1964) - OIN Public investment (A.S.) - OKG Public purchases of goods and services (A.S.) - PC Private consumption deflator (1964=100) - PEN Energy prices (1964=100) - PI Gross fixed investment deflator (1964=100) - PK Imports of goods and services deflator (1964=100) - PL Exports of goods and services deflator (1964=100) - PT Gross domestic product deflator (1964=100) - RES Value change in balance of payments reserves (A.S.) - RIR Interest rate for long term bonds (%) - SD Stocks and statistical discrepancies; National account basis (A.S. 1964) - ST Overall indirect taxes—subsidies; National account basis (A.S.) - STD Direct taxes (A.S.) - STI Indirect taxes (A.S.) - TAH Transfers to households (A.S.) - TBB Trade balance (A.S.) - TTT Time (1960, 1961,..., 1979) - TUN Transfers to firms (A.S.) - TVH Transfers from households (A.S.) - VW Gross fixed investment plus exports of goods and services (A.S. 1964) - WON Changes in foreign currency reserves of the National Bank (A.S.) - WKU Changes in foreign currency reserves of all commercial banks (A.S.) - WW Changes in balance of payments' official reserves (A.S.) - XB Relative energy prices (1964=100) - XXN Exports of goods and services (A.S.) - XXR Exports of goods and services (A.S. 1964) - YLN Wages and salaries (compensation of employees; A.S.) - YOB Public income from property (A.S.) - YVN Net disposable income (A.S.) - YY Net disposable income (A.S.) - YYN National income (A.S.) - ZST Statistical discrepancies in balance of payments (A.S.) - A.S billion Austrian Schilling at current prices - A.S. 1964 billion Austrian Schilling at constant prices (basis 1964)     

Allocation problems among sharing groups

We deal with allocation problems among sharing groups. There are n agents. The agents are divided into several sharing groups. A homogeneous good is allocated among sharing groups rather than among the agents. The good is a private good for sharing groups, and a public good for the members of each sharing group. That is, all of them in the same sharing group can consume it without rivalry. We introduce some allocation rules and axioms. The utilitarian allocation rule and the egalitarian allocation rule are characterized by some axioms.     

The separability axiom and equal-sharing methods

A quasi-linear social choice problem is defined as selecting one (among finitely many) indivisible public decision and a vector of monetary transfers among agents to cover the cost of this decision. This decision is based upon individual preferences, which are assumed to be additively separable and linear in money. The Separability axiom is a consistency property for choice methods on societies with variable size: the decision is not affected if we remove an arbitrary agent under the condition that he be guaranteed his original utility level and the cost to the remaining agents is modified accordingly. Thus the utility level assigned by the social choice function to agent i is the price at which the other agents are unanimously willing to buy agent is share of the decision power. A general characterization of choice methods satisfying this axiom is provided. Three subclasses of particular interest are characterized by additional milder axioms. Those are: (i) equal sharing of the surplus left over some reference utility (e.g., the utility at a status quo decision), (ii) utilitarian methods that merely select the efficient public decision and perform no monetary transfers, and (iii) equal allocation of nonseparable costs, which divides equally the surplus left over from the utility derived from the pivotal mechanism (also known as the Vickrey-Clarke-Groves mechanism).     

A Comment on Dehez and Tellone, “Data games: sharing public goods with exclusion”

This comment shows that the data cost game introduced in Dehez and Tellone (Journal of Public Economic Theory, 2013) coincides with the nonadditive component of the library cost game studied in Driessen, Khmelnitskaya, and Sales (TOP, 2012) where the core, nucleolus, and Shapley value were also investigated.     

Cost-axiomatic regulatory pricing

The axioms of the Shapley value and semi-values of non-atomic games can be taken as the starting point for axioms on the relation between costs and prices of a regulated multiproduct monopoly. The price mechanisms that result from this system of axioms are called cost- axiomatic prices. This paper shows the applicability of such pricing to all cases of regulatory constraints that require revenue to be a given percentage of costs (including cost-plus regulation, break-even pricing or Amtrak's 50% clause). Moreover, we show that all such price mechanisms, including a fairly general system of taxation or subsidization of consumers, are demand compatible if cost-axiomatic pricing leads to deficits or profits.     

Problems of fair division and the Egalitarian solution

The problem of fair division is considered in situations where the number of agents among whom the division is to take place may vary. The approach is axiomatic. Along with four familiar axioms, Weak Pareto-optimality, Symmetry, Independence of Irrelevant Alternatives, and Continuity, a new axiom, named Monotonicity with Respect to Changes in the Number of Agents, is imposed, expressing a certain form of solidarity among the agents as their number varies but the resources at their disposal remain fixed. The only solution to satisfy these axioms is the Egalitarian solution, which selects the only feasible alternative that yields equal utilities to all agents and is undominated by any other feasible alternative.     

Subjective evaluations of n-person games

Using an axiomatization of subjective expected utility due to Fishburn, we characterize a class of utility functions over a set of n-person games in characteristic-function form. A probabilistic value is defined as the expectation of some player's marginal contribution with respect to some probability measure on the set of coalitions of other players. We decribe conditions under which a utility function on the set of n-person games is a probabilistic value; we prove as well an analogous result for simple games. We present additional axioms that characterize the semivalues and, in turn, the Shapley and Banzhaf values.     

Sharing a Polluted River Network

A polluted river network is populated with agents (e.g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network. Based on the two theories in international disputes, namely the Absolute Territorial Sovereignty (ATS) and the Unlimited Territorial Integrity (UTI), we propose three different cost sharing methods for the problem. They are the Local Responsibility Sharing (LRS), the Upstream Equal Sharing (UES), and the Downstream Equal Sharing (DES), respectively. The LRS and the UES generalize Ni and Wang (Games Econ Behav 60:176–186, 2007) but the DES is new. The DES is based on a new interpretation of the UTI. We provide axiomatic characterizations for the three methods. We also show that they coincide with the Shapley values of the three different games that can be defined for the problem. Moreover, we show that they are in the cores of the three games, respectively. Our methods can shed light on pollution abatement of a river network with multiple sovereignties.     

Strategyproof sharing of submodular costs:budget balance versus efficiency

Summary. A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms and find that the mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance – the more common route in the literature – we find that there is a single Clarke-Groves mechanism that satisfies certain reasonable conditions: we call this the marginal cost pricing mechanism. We compare the size of the marginal cost pricing mechanism's worst budget surplus with the worst welfare loss of the Shapley value mechanism. Received: October 26, 1998; revised version: December 3, 1999     

Public-good valuation and intra-family allocation

I derive values of marginal changes in a public good for two-person households, measured alternatively by household member i’s willingness to pay (WTP) for the good on behalf of the household, WTP _i (H), or by the sum of individual WTP values across family members, WTP(C). Households are assumed to allocate their resources in efficient Nash bargains over private and common household goods. WTP _i (H) is then defined by trade-offs between the public good and the household good, and WTP(C) by trade-offs of between the public good and private goods. WTP _i (H) is found to be higher (lower) than WTP(C) when member i has a relatively high (low) marginal valuation of the public good, but tends on average to equal WTP(C). As a consequence, individuals tend to represent households correctly on average when questioned about the household’s WTP for a public good, even when they are purely selfish and answer truthfully. Adding all members’ WTP answers on behalf of the household then leads to double counting. Pure and paternalistic altruism (the latter attached to consumption of the public good) move each member’s WTP on behalf of the household closer to the true sum of individual WTP, but only paternalistic altruism raises this sum.      

Strategies as states

We define rationality and equilibrium when states specify agents’ actions and agents have arbitrary partitions over these states. Although some suggest that this natural modeling step leads to paradox, we show that Bayesian equilibrium is well defined and puzzles can be circumvented. The main problem arises when player j's partition informs j of i's move and i knows j's strategy. Then i's inference about j's move will vary with i's own move, and i may consequently play a dominated action. Plausible conditions on partitions rule out these scenarios. Equilibria exist under the same conditions, and more generally ε equilibria usually exist.     

On weighted Kalai–Samet solutions for non-transferable utility coalitional form games

We investigate the implications of the axiom of coalitional concavity for non-transferable utility coalitional form games. This axiom says that if the feasible set of some coalition is uncertain whereas the feasible sets of other coalitions are known, then all players in the coalition with the uncertain feasible set should (weakly) benefit from reaching a compromise before the uncertainty is resolved. By imposing this axiom, in addition to other minor axioms, we characterize the weighted Kalai–Samet [Econometrica 53 (1985) 307] solutions: these solutions coincide with the weighted egalitarian solutions on the domain of bargaining problems, and with the weighted Shapley values on the domain of transferable utility coalitional form games.     

Unit versus Ad Valorem Taxes in Multiproduct Cournot Oligopoly

The welfare dominance of ad valorem taxes over unit taxes in a single‐market Cournot oligopoly is well known. This article extends the analysis to multimarket oligopoly. Provided all ad valorem taxes are equal and positive, unit costs are constant, firms are active in all considered markets, and a representative consumer has convex preferences, ad valorem taxes are shown to dominate in multiproduct equilibrium. Conditions exist, however, under which economic efficiency declines upon replacing specific taxes with ad valorem taxes that preserve output levels. We discuss the roles of unit cost covariances across multiproduct firms, and also of complementarity in demand, in determining the extent of cost efficiencies arising under ad valorem taxation. For goods that are complementary or independent in demand, conditions are found such that industry profits decline upon use of ad valorem taxes.