Sharing a Polluted River
|
|
- Sibyl Rich
- 5 years ago
- Views:
Transcription
1 Sharing a Polluted River Debing Ni School of Management University of Electronic Science and Technology of China Chengdu, Sichuan, P.R. China, Yuntong Wang Department of Economics University of Windsor Windsor,Ontario,Canada, N9B 3P4 January 12, 2006 Debing Ni is a visiting scholar at the Department of Economics, University of Windsor, Windsor, Ontario, Canada. Wang thanks the Social Sciences and Humanities Research Council of Canada. Corresponding author. Tel: (519) ext.2382; Fax: (519) ; yuntong@uwindsor.ca 1
2 ABSTRACT: A river carries pollutants to people living along it if it is polluted. To make the water in the river clean, some costs are incurred. This poses a question of how to split the costs of cleaning the whole river among the agents located along it. To answer this question, we resort to the two main advocated doctrines in international disputes: the theory of Absolute Territorial Sovereignty (ATS) and the theory of Unlimited Territorial Integrity (UTI). Applying these two doctrines, we accordingly propose two methods: the Local Responsibility Sharing (LRS) method and the Upstream Equal Sharing (UES) method. For each method, we provide an axiomatic characterization. Interestingly, both the LRS method and the UES method coincide with the Shapley value solutions to the corresponding (cost) games that are naturally induced according to the ATS and the UTI doctrines respectively. Moreover, both the LRS solution and the UES solution are the core allocations of the corresponding games. Thus, both the LRS method and the UES method can be considered as fair or reasonable solutions to the pollution cost allocation problem. JEL classification: D61; D62; C71 Keywords: Externality; Fair allocation of pollution costs; Shapley value. 2
3 1 Introduction There are 148 rivers in the world flowing through two countries, 30 through three, 9 through four and 13 through five or more (See, Ambec and Sprumont 2002, and Barret 1994). Transborder rivers provide people in different countries with water resources, but they also bring pollutants to those people if they are polluted. The same problem also occurs to the people who live within a national border but in different regions through which a river flows. A polluted river, which is polluted to some degree but not so seriously that people cannot make any use of it, has both a beneficial aspect and a harmful aspect to people who live along it. On the beneficial side, Ambec and Sprumont (2002) develop a model to study how agents (e.g. countries, regions, or cities) living along a river share the water resources. Since the property rights over flowing water are not welldefined, the Coase (1960) theorem cannot be applied. Instead, they base on two main doctrines advocated in international disputes, namely the theory of Absolute Territorial Sovereignty and the theory of Unlimited Territorial Integrity (for short, ATS and UTI, respectively) to define rights owned by the agents. The ATS theory says that a country has absolute sovereignty over the area of any river basin on its territory, while the UTI theory says that a country shouldn t alter the natural conditions on its own territory to the disadvantage of a neighboring country. 1 With their welfare interpretation of rights, ATS implies a core-like constraint (the core lower bounds) while UTI implies the constraint of the aspiration upper bounds on welfare allocation. Interestingly, Ambec and Sprumont (2002) show that these two bounds uniquely determine a method, called the downstream incremental distribution, to allocate the optimal total welfare among the agents. This paper focuses on the harmful side, namely the pollution. Consider a river which is divided into n segments. Within each segment there are some agents who dump certain amount of pollutants of some kind into the river. The pollutants usually do harm to people so that some costs are incurred for people to prevent them from the harmfulness. 2 This raises two questions: who are responsible for the costs? How should the costs be shared? It 1 For more detailed discussion on ATS and UTI, see Godana (1985) and Kilgour and Dinar (1996). 2 In practice, the costs, for example, may be incurred by firm s installing a filter or household s installing a swimming bath. 3
4 is relatively easy to answer the first question. It is generally accepted that those, who discharge pollutants in the river, should take the responsibility for the costs. However, it is not straightforward to answer the second question, i.e., how to divide fairly the total river-polluting responsibility among the polluters? This research on the pollutant cost sharing problem is inspired by Ambec and Sprumont (2002). However, our problem is different and we look at the theories of ATS and UTI from a different perspective. We argue that there is a dual relationship between rights and responsibilities (or duties). We regard responsibilities as the counterpart of rights. We therefore interpret the ATS and the UTI doctrines in terms of responsibilities in our pollution cost allocation problem. Specifically, the ATS doctrine can be read as a statement that people living the jth segment have an absolute sovereignty to ask any polluter located within the segment j to pay the costs of cleaning pollutants. Under the ATS, the responsibility for the costs of cleaning river pollutants in the jth segment should be assigned to the polluters located in that segment. We call this translation of the ATS the principle of local responsibility (or LR for short). On the other hand, the responsibility version of the UTI extends the scope of a polluter s responsibilities for pollutant-cleaning. It says that people in segment j have the rights to ask polluters in the jth segment as well as all upstream polluters to pay the pollutant-cleaning costs. This means that an upstream polluter bears some responsibilities for all downstream pollutant-cleaning costs. We call this interpretation of the UTI the principle of downstream responsibility (or DR for short). To make the problem well defined, we shall first make clear what is the relevant amount of the pollutant-cleaning costs to be divided among the polluters? We assume that each segment uses the most efficient way to cleaning pollutants in order that the water falls in line with the environmental standard specified by the environmental supervision authority in that segment. 3 Thus the pollutant-cleaning costs of all the segments are at their lowest levels 3 Here, efficient way means both technologically and economically. That is, the most advanced technology is adopted and arranged efficiently to do the job of cleaning. Moreover, the authorities in different segments may set different environmental-supervision standards. For example, the U.S. Water Quality Act of 1965 permits states to set their own standards of water quality (Boyd 2003). 4
5 determined by the corresponding environmental requirements. 4 Now our problem can be specified as follows. For the n pollutant-cleaning costs, how do we split them among the polluters according to the LR and/or the DR principles? The LR tells us a clear-cut structure of cost-sharing which implies that if the costs in segment j are zero, all agents in segment j should have zero cost shares. Accordingly, we propose an axiom, called No Blind Cost, to capture this implication of the LR principle. As for the DR principle, it is less straightforward. First of all, it is clear that for the costs incurred in segment j, all downstream polluters should not take any responsibility for that costs. This can be captured by an axiom, called Irrelevance of Upstream Costs. On the other hand, the DR principle says that all upstream polluters are responsible for downstream costs. But it does not specify how to allocate them among all upstream polluters. Because of the fact that upstream pollutants go downstream with the water and that the cross-pollutant interactions (such as chemical reactions) often happen in a polluted river, it is difficult to distinguish each upstream polluter s contribution to the downstream costs. We take a viewpoint of equality and assume that for any given downstream costs, all upstream polluters share them equally. This assumption is captured by an axiom called Upstream Symmetry. Accordingly, we propose two methods to share the total pollutant-cleaning costs. The first is called Local Responsibility Sharing (or LRS for short) method which corresponds to the LR principle. It simply charges the agent in a given segment his own local costs (see Section 2 or 3). The second is called Upstream Equal Sharing (or UES for short) method which corresponds to the DR principle. The UES method charges an agent the sum of the equal divisions of all downstream costs including his own local costs (see Section 2 or 4). We provide axiomatic characterizations for both the LRS method and the UES method, respectively. We show that the LRS method is characterized by No Blind Cost, Additivity and Efficiency (Theorem 1), and the UES method by Irrelevance of Upstream Costs, Upstream Symmetry, Additivity and Efficiency (Theorem 2). Interestingly, both the LRS method and the UES method coincide with the Shapley value of the associated cost games generated from the problem (Propositions 1 and 3). Moreover, these two 4 We assume that the pollutant-cleaning costs in segment j are zero if the water quality meets the environmental standard. 5
6 solutions are in the cores of the corresponding games since both games are convex (to be exact, concave cost games) (Propositions 2 and 4). The rest of this paper is organized as follows. Section 2 develops a model for the problem of sharing the total pollutant-cleaning costs. Section 3 provides a characterization of the LRS method and shows that the LRS coincides with the Shapley value and is in the core of the corresponding game generated from the problem. Section 4 provides a characterization of the LRS method and shows that the UES coincides with the Shapley value and is in the core of a different game generated from the problem. 2 A Model Consider a river which is divided into n segments indexed in a given order i = 1, 2,..., n from upstream to downstream. There are n household-firm pairs (agents) located along a river, each of which is located in one of segments according to the above order. We assume that each firm generates a certain amount of pollutants of some kind which all households try to avoid and that in each segment, firm i is located immediately before the household i. In every segment i (i = 1, 2,..., n), an environmental authority sets a standard of the degree of pollution which requires agent i (i.e. a household-firm pair) spending c i to clean the pollutants in segment i so that the quality of the waterbody satisfies the environmental standard. We want to find meaningful methods to allocate the total pollutant-cleaning costs (c c n ) among all the household-firm pairs. From the viewpoint of responsibility, this cost allocation problem can be viewed as how to split the total costs among the n firms because they are responsible for the pollution of the river. 5 Formally, a pollution cost sharing problem is a pair (N, C) where N = {1,..., n} and C = (c 1,..., c n ) R+. n A solution to a problem (N, C) is a vector x = (x 1,..., x n ) R+ n such that i x i = i c i. A method is a mapping x that assigns to each problem (N, C) a solution x(n, C). When N is fixed, 5 In this paper, we are not concerned with the allocation within a household-firm pair. There exist various approaches in the literature to solve this problem. For example, theoretically it may be solved by the Coase theorem if the property rights of any given segment of the river is well-defined and other conditions, such as no transaction cost, perfect competition, complete information, etc., are satisfied (Canterbury and Marvasti 1992). 6
7 we simply call vector C a problem. Under the LR and the DR principles mentioned in the introduction, we propose the following two methods. The Local Responsibility Sharing (LRS) method corresponds to the LR principle while the Upstream Equal Sharing (UES) method corresponds to the DR principle. Definition 1 For any C R+, n The Local Responsibility Sharing method is given by x LRS i (C) = c i, i = 1,..., n (1) Definition 2 For any C R+, n the Upstream Equal Sharing method is given by x UES i (C) = 1 i c i + 1 i + 1 c i n c n, i = 1,..., n (2) In order to provide a game theoretic analysis on these two methods (e.g., their connections with the Shapley value and core), we define the following two games that are related to the LR and the DR principles, respectively. Let N = {1, 2,..., n} be the set of firms (or household-firm pairs, hereafter we refer to firms only). Suppose that all the n households keep their locations unchanged no matter how the firms form their coalitions. Let S N be any coalition of the n firms. Denote by min S the smallest element in S, i.e. the most upstream firm in the coalition S. Under the LR principle, each member of S is responsible only for the pollutant-cleaning costs in its own segment, and the total responsibility of the coalition S is simply the sum of its members local responsibilities. Thus, for any given C R+, n the total costs of the coalition S can be written as v C (S) = c i (3) i S While under the DR principle, each member of S takes the responsibility not only for the pollutant-cleaning costs in its own segment but also for all the costs in its downstream segments. Thus the total costs of the coalition S should be w C (S) = i=min S c i (4) 7
8 Assume that v C ( ) = w C ( ) = 0. Now, for any given C R+, n we have generated two games, (N, v C ) and (N, w C ), respectively. In the next two sections, we will show that the cost allocations according to the LRS method and the UES method are consistent with the Shapley value of the game (N, v C ) and (N, w C ), respectively, and that they are in the core of the corresponding games. 3 A Characterization of the LRS Method In this section, we first provide an axiomatic characterization of the LRS method. Then we investigate its relationship with the Shapley value as well as the core of the game (N, v C ). We now introduce the following axioms. Additivity: For any C 1 = (c 1 1,..., c 1 n) R n + and C 2 = (c 2 1,..., c 2 n) R n +, we have x j (C 1 + C 2 ) = x j (C 1 ) + x j (C 2 ) for all j N. No Blind Cost: For any i N and any C R n +, if c i = 0, then x i (C) = 0. Efficiency: n j=1 x j = n j=1 c j. Theorem 1 The LRS method is the only method satisfying Additivity, No Blind Cost, and Efficiency. Proof: It is clear that the LRS method satisfies the above three axioms. In the following we show that the LRS is the only method satisfying these axioms. Consider C k = (0,..., 0, 1, 0,..., 0) where 1 is the k-th component of the n-dimensional vector C k, k = 1, 2,..., n. By No Blind Cost, x j (C k ) = α if j = k and x j (C k ) = 0 otherwise. By Efficiency, we have x j (C k ) = α = c k j = 1 j=1 j=1 Thus, x j (C k ) = 1 if j = k and x j (C k ) = 0 if j k. 8
9 Note that the cost vectors, C k (k = 1, 2,..., n), form a basis of R n. Thus, for any C R+, n we can write C = n k=1 c k C k = (c 1, c 2,..., c n ). Then Additivity implies x j (C) = x j ( c k C k ) k=1 = c k x j (C k ) k=1 = c j for all j N. The theorem is proved. = c j = x LRS j (C) (5) Remark 1: The LRS method clearly indicates that all firms are treated fairly in the sense that no cost is imposed on a firm which bears no local responsibility at all, and that the cost distribution is anonymous: even if a firm changes its location, its cost share does not change. These two features together with Additivity and Efficiency remind us that there would be some connections between the LRS method and the Shapley value of certain game induced from the problem. Indeed, the following proposition shows that the LRS solution exactly coincides with the Shapley value ϕ of the game (N, v C ) for all C R n +. Recall that the Shapley value of a game (N, v) is defined by ϕ i (v) = 0 s n 1 s!(n s 1)! n! We have the following proposition. ( S N\i, S =s v(s {i}) v(s)). Proposition 1 For all C R n + and v C defined by (3), we have x LRS i (C) = ϕ i (v C ), i N. Proof: For any C R n + and any i N, it is obvious that firm i s marginal contribution is v C (S {i}) v C (S) = c i for all S N \ {i} (including ). 9
10 Let s = S be the size of S, then the Shapley value of the game (N, v C ) for firm i is ϕ i (v C ) = = 0 s n 1 0 s n 1 = c i ( = c i ( 0 s n 1 0 s n 1 = c i = x LRS i (C) s!(n s 1)! n! s!(n s 1)! n! ( ( s!(n s 1)! n! 1 n ) for all i N. The proposition is proved. S N\i, S =s S N\i, S =s v C (S {i}) v C (S)) c i ) (n 1)! s!(n s 1)! ) Furthermore, the following proposition shows that the Shapley value, and therefore the LRS solution, is in the core of the game (N, v C ). It is well known that a convex game always has a nonempty core and, in particular the Shapley value is in the core (see Moulin 1988). For cost sharing games, the corresponding convexity is instead defined by the concavity of the game. A game v is called concave if, for all i N, all S, T N \ i, S T, we have v(s {i}) v(s) v(t {i}) v(t ) (6) Proposition 2 For all C R+, n the Shapley value of the game (N, v C ) is in the core, i.e. for any S N, i S ϕ i (v C ) = i S x LRS i (C) v C (S). Proof: It suffices to show that the game (N, v C ) is concave, i.e. for all i N and all S, T N \ i, if S T, then v C (S {i}) v C (S) v C (T {i}) v C (T ) (7) By (3), both the left hand and the right hand of (7) are equal to c i. Thus the game (N, v C ) is concave. The proposition is proved. 10
11 Remark 2: Propositions 1 and 2 show that the LRS method satisfies the stand-alone or subsidy-free principle. 6 That is, the costs charged to any firm or any coalition of the n firms do not exceed the costs incurred by the firm or the coalition. Thus, the LRS method ensures that no firm or coalition has any incentive to change locations. In this sense, the LRS method ensures the stability of the cooperation on sharing a polluted river. 4 A Characterization of the UES Method In this section, we first provide an axiomatic characterization of the UES method. Then we examine its relationship with the Shapley value and core. First, we introduce the following two axioms. Independence of Upstream Costs: For any i N, any C, C R n + such that c l = c l, l > i, for all j > i, we have x j (C) = x j (C ). Upstream Symmetry: For any i N, for all j, k i, we have x j (0,..., 0, c i, 0,..., 0) = x k (0,..., 0, c i, 0,..., 0). Now we have the following theorem. Theorem 2 The UES method is the only method satisfying Additivity, Independence of Upstream Costs, Upstream Symmetry, and Efficiency. Proof: It is easy to check that the UES satisfies the above four axioms. Below, we show that it is the only method satisfying these four axioms. For any k = 1, 2,..., n, consider C k = (0,..., 0, 1, 0,..., 0) where 1 is the k-th component of the n-dimensional vector C k. By Independence of Upstream Costs, x j (C k ) = x j (0,..., 0) = 0 for all j > k. By Upstream Symmetry, x j (C k ) = α for all j k. By Efficiency, we have x j (C k ) = kα = 1. j=1 Thus, x j (C k ) = 1 k if j k, x j(c k ) = 0 if j > k. 6 For detailed exposition of the principle, see Faulhaber (1975). 11
12 Since the cost vectors, C k (k = 1, 2,..., n), form a basis of R n, for any C R n +, it can be written as C = n k=1 c k C k = (c 1, c 2,..., c n ). Then Additivity implies that, for all j N, The theorem is proved. x j (C) = x j ( c k C k ) k=1 = c k x j (C k ) k=1 = 1 j c j + 1 j + 1 c j n c n = x UES j (C) Remark 3: The UES solution requires that, for a cost component c i (1 < i n), all upstream firms should bear equal responsibility for that cost. For example, all firms have the same share (1/n) of c n. If there is a firm j which does not need to pay any cost to clean the waterbody in segment j according to the standard of its local environmental supervision authority (i.e. c j = 0), it would argue that it should not share any cost for cleaning the river. This seemingly challenges the fairness of the cost allocation according to the UES method. However, Firm j s discharge of pollutants has a social impact on its downstream households even if it passes the test of its local authority. If the DR principle is accepted as a guideline to divide the total pollution costs, it should take some responsibilities for its downstream pollutant-cleaning costs. Indeed, the following proposition shows that, under the DR principle, the UES method splits the total costs of cleaning the pollutants in the river in the same way as suggested by the Shapley value. Proposition 3 For all C R n + and w C defined by (4), we have x UES i (C) = ϕ i (w C ), i N. Proof: Consider C k = (0,..., 0, 1, 0,..., 0) where 1 is the k-th component of the n-dimensional vector C k, k = 1, 2,..., n. The games corresponding to C k (k = 1, 2,..., n) is given by w Ck (S) = 0 if min S > k; and w Ck (S) = 1 otherwise. 12
13 Clearly, for the game (N, w Ck ), all agents i > k are dummies and all agents i k are symmetric. The axiomatization of the Shapley value (Shapley 1953) implies that the Shapley value of the game (N, w Ck ) is ϕ i (w Ck ) = 0 if i > k ; and ϕ i (w Ck ) = 1 k otherwise. (8) Note again that for any C R n +, write C = n k=1 c k C k. By the definition of the game (N, w C ), we have, for all S N, w C (S) = = = = c j j=min S ( [c k C k ] j ) j=min S k=1 c k ( [C k ] j ) k=1 j=min S c k w Ck (S) k=1 where [C] j is the jth component of the vector C. By Additivity and equation (8), we have ϕ i (w C ) = c k ϕ i (w Ck ) k=1 = 1 i c i + 1 i + 1 c i n c n = x UES i (C) for all i N. The proposition is proved. The following proposition shows that the Shapley value of the game (N, w C ) or the UES solution is a core allocation. Proposition 4 For all C R+, n the Shapley value of the game (N, w C ) is in the core, i.e. for any S N, i S ϕ i (w C ) = i S x UES i (C) w C (S). 13
14 Proof: It suffices to show that the game (N, w C ) is concave. For any S, T N, S T, any i / T, denote 1 = w C (S {i}) w C (S) 2 = w C (T {i}) w C (T ) 3 = w C (S {i}) w C (T {i}) 4 = w C (S) w C (T ). Clearly, the concavity of the game (N, w C ) is equivalent to or Since S T N \ i, we have min S min T. Then for any given i N, i / T, there are three possibilities: i min T min S, min T < i min S and min T < min S i. Now we check the concavity of (N, w C ) in each of these three cases. Case 1. Suppose that i min T min S. In this case, min T {i} = min S {i} = i. By the definition of w C, we have 3 = 0 and 4 0. Thus, Case 2. Suppose that min T < i min S. In this case, min T {i} = min T and i = min S {i} min S. The definition of w C implies that 1 0 and 2 = 0. Thus, Case 3. Suppose that min T < min S i. In this case, min T {i} = min T and min S {i} = min S. Again by the definition of w C, we have 1 = 0 and 2 = 0. Thus, 1 2 = 0. To summarize, we show that for any S, T N, S T, any i / T, w C (S {i}) w C (S) w C (T {i}) w C (T ), thus the game (N, w C ) is concave. The proposition is proved. Remark 4: As in Remark 2, Propositions 3 and 4 show that the UES method, as the Shapley value of certain game, embodies certain equity properties and, as core allocation, meets the stand-alone tests, in the problem of sharing a polluted river if the DR principle is accepted. On the other hand, 14
15 the UES method seems treating upstream firms unfairly. For instance, firm 1 s cost share is generally very much greater than its local costs c 1. We argue that the UES allocation method can be justified by Tiebout s (1956) equilibrium theory of locations, which says that people voluntarily choose locations to best satisfy their preferences even if the (living) costs may be higher. The same is true for firms. For example, the technologies (production functions) of upstream firms must be operated with more clean water and they are willing to pay a greater share of pollutant-cleaning costs. References [1] Ambec, S. and Sprumont, Y. Sharing a River. Journal of Economic Theory 107 (2002), [2] Barret, S. Conflict and cooperation in managing international water resources, Working Paper 1303, World Bank, Washington [3] Boyd, J. Water pollution taxes: A good ideal doomed to failure. Discussion paper 03-20, Research for the Future, Washington [4] Canterbury, E.R. and Marvasti, A. The Coase theorem as a negative externality. Journal of Economic Issues 26 (1992), [5] Coase, R. The problem of social cost. Journal of Law and Economics 1 (1960), [6] Faulhaber, G. Cross-subsidization: Pricing in public enterprises. American Economic Review 65 (1975), [7] Godana, B. Africa s shared water resources. France Printer, London, [8] Kilgour, M. and Dinar A. Are stable agreements for sharing international river waters now possible? Working Paper 1474, World Bank, Washington [9] Moulin, H. Axioms of Cooperative Desion Making, Cambridge University Press,
16 [10] Shapley, L. S. A Value for n-person Games. In Contributions to the Theory of Games II. edited by H. W. Kuhn and A. W. Tucker. Annals of Mathematics Studies 28 (1953), [11] Tiebout, C. A Pure Theory of Local Expenditures. Journal of Political Economy 64 (1956),
Polluted River Problems and Games with a Permission Structure
TI 2015-108/II Tinbergen Institute Discussion Paper Polluted River Problems and Games with a Permission Structure René van den Brink 1 Simin He 2 Jia-Ping Huang 1 1 Faculty of Economics and Business Administration,
More informationTransboundary Externalities and Property Rights: An International River Pollution Model
TI 2012-006/1 Tinbergen Institute Discussion Paper Transboundary Externalities and Property Rights: An International River Pollution Model Gerard van der Laan Nigel Moes Faculty of Economics and Business
More informationNo-envy in Queueing Problems
No-envy in Queueing Problems Youngsub Chun School of Economics Seoul National University Seoul 151-742, Korea and Department of Economics University of Rochester Rochester, NY 14627, USA E-mail: ychun@plaza.snu.ac.kr
More information5. Externalities and Public Goods. Externalities. Public Goods types. Public Goods
5. Externalities and Public Goods 5. Externalities and Public Goods Externalities Welfare properties of Walrasian Equilibria rely on the hidden assumption of private goods: the consumption of the good
More information5. Externalities and Public Goods
5. Externalities and Public Goods Welfare properties of Walrasian Equilibria rely on the hidden assumption of private goods: the consumption of the good by one person has no effect on other people s utility,
More informationBIPARTITE GRAPHS AND THE SHAPLEY VALUE
BIPARTITE GRAPHS AND THE SHAPLEY VALUE DIPJYOTI MAJUMDAR AND MANIPUSHPAK MITRA ABSTRACT. We provide a cooperative game-theoretic structure to analyze bipartite graphs where we have a set of employers and
More informationThe Shapley value for airport and irrigation games
The Shapley value for airport and irrigation games Judit Márkus, Miklós Pintér and Anna Radványi Corvinus University of Budapest April 2, 2011 Abstract In this paper cost sharing problems are considered.
More information3 rd Christmas Conference of German Expatriate Economists
3 rd Christmas Conference of German Expatriate Economists 20 22 December 2006 CESifo Conference Centre, Munich Sharing a River among Satiable Agents Stefan Ambec & Lars Ehlers CESifo Poschingerstr. 5,
More informationGame Theory: Spring 2017
Game Theory: Spring 2017 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 Plan for Today Today we are going to review solution concepts for coalitional
More informationCORVINUS ECONOMICS WORKING PAPERS. Young's axiomatization of the Shapley value - a new proof. by Miklós Pintér CEWP 7/2015
CORVINUS ECONOMICS WORKING PAPERS CEWP 7/2015 Young's axiomatization of the Shapley value - a new proof by Miklós Pintér http://unipub.lib.uni-corvinus.hu/1659 Young s axiomatization of the Shapley value
More informationInducing stability in hedonic games
School of Economics Working Paper 2016-09 SCHOOL OF ECONOMICS Inducing stability in hedonic games by Dinko Dimitrov* Emiliya A. Lazarova** Shao-Chin Sung*** *Chair of Economic Theory, Saarland University
More informationDividends and Weighted Values in Games with Externalities
Dividends and Weighted Values in Games with Externalities Inés Macho-Stadler David Pérez-Castrillo David Wettstein August 28, 2009 Abstract In this paper, we provide further support for the family of average
More informationCoincidence of Cooperative Game Theoretic Solutions in the Appointment Problem. Youngsub Chun Nari Parky Duygu Yengin
School of Economics Working Papers ISSN 2203-6024 Coincidence of Cooperative Game Theoretic Solutions in the Appointment Problem Youngsub Chun Nari Parky Duygu Yengin Working Paper No. 2015-09 March 2015
More informationEconomics 201B Second Half. Lecture 12-4/22/10. Core is the most commonly used. The core is the set of all allocations such that no coalition (set of
Economics 201B Second Half Lecture 12-4/22/10 Justifying (or Undermining) the Price-Taking Assumption Many formulations: Core, Ostroy s No Surplus Condition, Bargaining Set, Shapley-Shubik Market Games
More informationEC487 Advanced Microeconomics, Part I: Lecture 5
EC487 Advanced Microeconomics, Part I: Lecture 5 Leonardo Felli 32L.LG.04 27 October, 207 Pareto Efficient Allocation Recall the following result: Result An allocation x is Pareto-efficient if and only
More informationThe Shapley Value for games with a finite number of effort levels. by Joël Adam ( )
The Shapley Value for games with a finite number of effort levels by Joël Adam (5653606) Department of Economics of the University of Ottawa in partial fulfillment of the requirements of the M.A. Degree
More informationConverse consistency and the constrained equal benefits rule in airport problems
Converse consistency and the constrained equal benefits rule in airport problems Cheng-Cheng Hu Min-Hung Tsay Chun-Hsien Yeh June 3, 009 Abstract We propose a converse consistency property and study its
More informationCan everyone benefit from innovation?
Can everyone benefit from innovation? Christopher P. Chambers and Takashi Hayashi June 16, 2017 Abstract We study a resource allocation problem with variable technologies, and ask if there is an allocation
More informationUtilitarian resource allocation
Utilitarian resource allocation Albin Erlanson and Karol Szwagrzak March 19, 2014 Extended Abstract Keywords: Claims; Indivisible objects; Consistency; Resource-monotonicity JEL classification: D70, D63,
More informationMechanism Design for Resource Bounded Agents
Mechanism Design for Resource Bounded Agents International Conference on Multi-Agent Systems, ICMAS 2000 Noa E. Kfir-Dahav Dov Monderer Moshe Tennenholtz Faculty of Industrial Engineering and Management
More informationSolutions without dummy axiom for TU cooperative games
Solutions without dummy axiom for TU cooperative games L. Hernandez Lamoneda, R. Juarez, and F. Sanchez Sanchez October, 2007 Abstract In this paper we study an expression for all additive, symmetric and
More informationThe core of voting games: a partition approach
The core of voting games: a partition approach Aymeric Lardon To cite this version: Aymeric Lardon. The core of voting games: a partition approach. International Game Theory Review, World Scientific Publishing,
More informationDepartment of Applied Mathematics Faculty of EEMCS. University of Twente. Memorandum No Owen coalitional value without additivity axiom
Department of Applied Mathematics Faculty of EEMCS t University of Twente The Netherlands P.O. Box 217 7500 AE Enschede The Netherlands Phone: +31-53-4893400 Fax: +31-53-4893114 Email: memo@math.utwente.nl
More informationUNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics CONSISTENT FIRM CHOICE AND THE THEORY OF SUPPLY
UNIVERSITY OF NOTTINGHAM Discussion Papers in Economics Discussion Paper No. 0/06 CONSISTENT FIRM CHOICE AND THE THEORY OF SUPPLY by Indraneel Dasgupta July 00 DP 0/06 ISSN 1360-438 UNIVERSITY OF NOTTINGHAM
More information2.1 Definition and graphical representation for games with up to three players
Lecture 2 The Core Let us assume that we have a TU game (N, v) and that we want to form the grand coalition. We model cooperation between all the agents in N and we focus on the sharing problem: how to
More informationOn properties of division rules lifted by bilateral consistency. Hokari, Toru and Thomson, William. Working Paper No. 536 December 2007 UNIVERSITY OF
On properties of division rules lifted by bilateral consistency Hokari, Toru and Thomson, William Working Paper No. 536 December 007 UNIVERSITY OF ROCHESTER On properties of division rules lifted by bilateral
More informationFirms and returns to scale -1- John Riley
Firms and returns to scale -1- John Riley Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Natural monopoly 1 C. Constant returns to scale 21 D. The CRS economy 26 E. pplication
More informationCORVINUS ECONOMICS WORKING PAPERS. On the impossibility of fair risk allocation. by Péter Csóka Miklós Pintér CEWP 12/2014
CORVINUS ECONOMICS WORKING PAPERS CEWP 12/2014 On the impossibility of fair risk allocation by Péter Csóka Miklós Pintér http://unipub.lib.uni-corvinus.hu/1658 On the impossibility of fair risk allocation
More informationEquilibria in Games with Weak Payoff Externalities
NUPRI Working Paper 2016-03 Equilibria in Games with Weak Payoff Externalities Takuya Iimura, Toshimasa Maruta, and Takahiro Watanabe October, 2016 Nihon University Population Research Institute http://www.nihon-u.ac.jp/research/institute/population/nupri/en/publications.html
More informationSharing a River among Satiable Countries
2006-10 Sharing a River among Satiable Countries AMBEC, Steve EHLERS, Lars Département de sciences économiques Université de Montréal Faculté des arts et des sciences C.P. 6128, succursale Centre-Ville
More informationIntroduction to Game Theory
COMP323 Introduction to Computational Game Theory Introduction to Game Theory Paul G. Spirakis Department of Computer Science University of Liverpool Paul G. Spirakis (U. Liverpool) Introduction to Game
More informationNash Bargaining in Ordinal Environments
Nash Bargaining in Ordinal Environments By Özgür Kıbrıs April 19, 2012 Abstract We analyze the implications of Nash s (1950) axioms in ordinal bargaining environments; there, the scale invariance axiom
More informationOn Bankruptcy Game Theoretic Interval Rules
On Bankruptcy Game Theoretic Interval Rules arxiv:1301.3096v1 [q-fin.gn] 7 Jan 2013 Rodica Branzei University Alexandru Ioan Cuza, Iaşi, Romania branzeir@info.uaic.ro Marco Dall Aglio Luiss University,
More informationSURPLUS SHARING WITH A TWO-STAGE MECHANISM. By Todd R. Kaplan and David Wettstein 1. Ben-Gurion University of the Negev, Israel. 1.
INTERNATIONAL ECONOMIC REVIEW Vol. 41, No. 2, May 2000 SURPLUS SHARING WITH A TWO-STAGE MECHANISM By Todd R. Kaplan and David Wettstein 1 Ben-Gurion University of the Negev, Israel In this article we consider
More informationInterval values for strategic games in which players cooperate
Interval values for strategic games in which players cooperate Luisa Carpente 1 Balbina Casas-Méndez 2 Ignacio García-Jurado 2 Anne van den Nouweland 3 September 22, 2005 Abstract In this paper we propose
More informationIMPOSSIBILITY OF A WALRASIAN BARGAINING SOLUTION 1
IMPOSSIBILITY OF A WALRASIAN BARGAINING SOLUTION 1 Murat R. Sertel 2 Turkish Academy of Sciences Muhamet Yıldız 3 MIT Forthcoming in Koray and Sertel (eds.) Advances in Economic Design, Springer, Heidelberg.
More informationCournot and Bertrand Competition in a Differentiated Duopoly with Endogenous Technology Adoption *
ANNALS OF ECONOMICS AND FINANCE 16-1, 231 253 (2015) Cournot and Bertrand Competition in a Differentiated Duopoly with Endogenous Technology Adoption * Hongkun Ma School of Economics, Shandong University,
More informationAlmost Transferable Utility, Changes in Production Possibilities, and the Nash Bargaining and the Kalai-Smorodinsky Solutions
Department Discussion Paper DDP0702 ISSN 1914-2838 Department of Economics Almost Transferable Utility, Changes in Production Possibilities, and the Nash Bargaining and the Kalai-Smorodinsky Solutions
More informationStability and fairness in the job scheduling problem
Department of Economics Working Paper Series 401 Sunset Avenue Windsor, Ontario, Canada N9B 3P4 Administrator of Working Paper Series: Christian Trudeau Contact: trudeauc@uwindsor.ca Stability and fairness
More informationAlgorithmic Game Theory and Applications
Algorithmic Game Theory and Applications Lecture 18: Auctions and Mechanism Design II: a little social choice theory, the VCG Mechanism, and Market Equilibria Kousha Etessami Reminder: Food for Thought:
More informationWorst-Case Efficiency Analysis of Queueing Disciplines
Worst-Case Efficiency Analysis of Queueing Disciplines Damon Mosk-Aoyama and Tim Roughgarden Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, CA 94305 Introduction Consider
More informationBargaining, Contracts, and Theories of the Firm. Dr. Margaret Meyer Nuffield College
Bargaining, Contracts, and Theories of the Firm Dr. Margaret Meyer Nuffield College 2015 Course Overview 1. Bargaining 2. Hidden information and self-selection Optimal contracting with hidden information
More informationDual Bargaining and the Talmud Bankruptcy Problem
Dual Bargaining and the Talmud Bankruptcy Problem By Jingang Zhao * Revised January 2000 Department of Economics Ohio State University 1945 North High Street Columbus, OH 43210 1172 USA Zhao.18@Osu.Edu
More informationExternalities, Potential, Value and Consistency
Externalities, Potential, Value and Consistency Bhaskar Dutta, Lars Ehlers, Anirban Kar August 18, 2010 Abstract We provide new characterization results for the value of games in partition function form.
More informationINTUITIVE SOLUTIONS IN GAME REPRESENTATIONS: THE SHAPLEY VALUE REVISITED. Pradeep Dubey. March 2018 COWLES FOUNDATION DISCUSSION PAPER NO.
INTUITIVE SOLUTIONS IN GAME REPRESENTATIONS: THE SHAPLEY VALUE REVISITED By Pradeep Dubey March 2018 COWLES FOUNDATION DISCUSSION PAPER NO. 2123 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY
More informationMarket Equilibrium and the Core
Market Equilibrium and the Core Ram Singh Lecture 3-4 September 22/25, 2017 Ram Singh (DSE) Market Equilibrium September 22/25, 2017 1 / 19 Market Exchange: Basics Let us introduce price in our pure exchange
More informationConsistency, anonymity, and the core on the domain of convex games
Consistency, anonymity, and the core on the domain of convex games Toru Hokari Yukihiko Funaki April 25, 2014 Abstract Peleg (1986) and Tadenuma (1992) provide two well-known axiomatic characterizations
More informationAVERAGE TREE SOLUTION AND SUBCORE FOR ACYCLIC GRAPH GAMES
Journal of the Operations Research Society of Japan 2008, Vol. 51, No. 3, 203-212 AVERAGE TREE SOLUTION AND SUBCORE FOR ACYCLIC GRAPH GAMES Dolf Talman Tilburg University Yoshitsugu Yamamoto University
More informationFirms and returns to scale -1- Firms and returns to scale
Firms and returns to scale -1- Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Constant returns to scale 19 C. The CRS economy 25 D. pplication to trade 47 E. Decreasing
More informationUniversity of Hawai`i at Mānoa Department of Economics Working Paper Series
University of Hawai`i at Mānoa Department of Economics Working Paper Series Saunders Hall 542, 2424 Maile Way, Honolulu, HI 96822 Phone: (808) 956-8496 www.economics.hawaii.edu Working Paper No. 17-2 Profit-Sharing
More informationCOALITIONALLY STRATEGY-PROOF RULES IN ALLOTMENT ECONOMIES WITH HOMOGENEOUS INDIVISIBLE GOODS
Discussion Paper No. 686 COALITIONALLY STRATEGY-PROOF RULES IN ALLOTMENT ECONOMIES WITH HOMOGENEOUS INDIVISIBLE GOODS Kentaro Hatsumi and Shigehiro Serizawa March 2007 Revised July 2008 Revised February
More informationMartin Gregor IES, Charles University. Abstract
On the strategic non-complementarity of complements Martin Gregor IES, Charles University Abstract This paper examines the equilibrium provision of a public good if the private monetary contributions of
More informationAxiomatic bargaining. theory
Axiomatic bargaining theory Objective: To formulate and analyse reasonable criteria for dividing the gains or losses from a cooperative endeavour among several agents. We begin with a non-empty set of
More informationCol.lecció d Economia E13/301. Cooperative games with size-truncated information. F. Javier Martínez-de-Albéniz
Col.lecció d Economia E13/301 Cooperative games with size-truncated information F. Javier Martínez-de-Albéniz UB Economics Working Papers 2013/301 Cooperative games with size-truncated information Abstract:
More informationEconomics th April 2011
Economics 401 8th April 2011 Instructions: Answer 7 of the following 9 questions. All questions are of equal weight. Indicate clearly on the first page which questions you want marked. 1. Answer both parts.
More informationNoncooperative Games, Couplings Constraints, and Partial Effi ciency
Noncooperative Games, Couplings Constraints, and Partial Effi ciency Sjur Didrik Flåm University of Bergen, Norway Background Customary Nash equilibrium has no coupling constraints. Here: coupling constraints
More informationStrategic Regional Competition among Local Government Firms
Strategic Regional Competition among Local Government Firms Kazuharu Kiyono Takao Ohkawa Makoto Okamura Yang Yu December, 2005 Abstract China, like other transition economies, holds various firms differing
More information1 Surplus Division. 2 Fair Distribution (Moulin 03) 2.1 Four Principles of Distributive Justice. Output (surplus) to be divided among several agents.
1 Surplus Division 2 Fair Distribution (Moulin 03) Output (surplus) to be divided among several agents. Issues: How to divide? How to produce? How to organize? Plus: adverse selection, moral hazard,...
More informationRANDOM ASSIGNMENT OF MULTIPLE INDIVISIBLE OBJECTS
RANDOM ASSIGNMENT OF MULTIPLE INDIVISIBLE OBJECTS FUHITO KOJIMA Department of Economics, Harvard University Littauer Center, Harvard University, 1875 Cambridge St, Cambridge, MA 02138 kojima@fas.harvard.edu,
More informationRepresentation of TU games by coalition production economies
Working Papers Institute of Mathematical Economics 430 April 2010 Representation of TU games by coalition production economies Tomoki Inoue IMW Bielefeld University Postfach 100131 33501 Bielefeld Germany
More informationCoalitional Structure of the Muller-Satterthwaite Theorem
Coalitional Structure of the Muller-Satterthwaite Theorem Pingzhong Tang and Tuomas Sandholm Computer Science Department Carnegie Mellon University {kenshin,sandholm}@cscmuedu Abstract The Muller-Satterthwaite
More informationAXIOMATIC CHARACTERIZATIONS OF THE SYMMETRIC COALITIONAL BINOMIAL SEMIVALUES. January 17, 2005
AXIOMATIC CHARACTERIZATIONS OF THE SYMMETRIC COALITIONAL BINOMIAL SEMIVALUES José María Alonso Meijide, Francesc Carreras and María Albina Puente January 17, 2005 Abstract The symmetric coalitional binomial
More informationGame Theory: Spring 2017
Game Theory: Spring 2017 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 Plan for Today In this second lecture on mechanism design we are going to generalise
More informationA partial characterization of the core in Bertrand oligopoly TU-games with transferable technologies
A partial characterization of the core in Bertrand oligopoly TU-games with transferable technologies Aymeric Lardon To cite this version: Aymeric Lardon. A partial characterization of the core in Bertrand
More informationDepartment of Applied Mathematics Faculty of EEMCS. University of Twente. Memorandum No. 1796
Department of Applied Mathematics Faculty of EEMCS t University of Twente The Netherlands P.O. Box 217 7500 AE Enschede The Netherlands Phone: +31-53-4893400 Fax: +31-53-4893114 Email: memo@math.utwente.nl
More informationCadet-Branch Matching
Cadet-Branch Matching TAYFUN SÖNMEZ Boston College Prior to 2006, the United States Military Academy (USMA) matched cadets to military specialties (branches) using a single category ranking system to determine
More information4 Lecture Applications
4 Lecture 4 4.1 Applications We now will look at some of the applications of the convex analysis we have learned. First, we shall us a separation theorem to prove the second fundamental theorem of welfare
More informationCoalitional solutions in differential games
2012c12 $ Ê Æ Æ 116ò 14Ï Dec., 2012 Operations Research Transactions Vol.16 No.4 Coalitional solutions in differential games Leon A. Petrosyan 1 Abstract The two-stage level coalitional solution for n-person
More informationENCOURAGING THE GRAND COALITION IN CONVEX COOPERATIVE GAMES
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LIV, Number 1, March 2009 ENCOURAGING THE GRAND COALITION IN CONVEX COOPERATIVE GAMES TITU ANDREESCU AND ZORAN ŠUNIĆ Abstract. A solution function for convex
More informationWeek 6: Consumer Theory Part 1 (Jehle and Reny, Chapter 1)
Week 6: Consumer Theory Part 1 (Jehle and Reny, Chapter 1) Tsun-Feng Chiang* *School of Economics, Henan University, Kaifeng, China November 2, 2014 1 / 28 Primitive Notions 1.1 Primitive Notions Consumer
More informationFinal Examination with Answers: Economics 210A
Final Examination with Answers: Economics 210A December, 2016, Ted Bergstrom, UCSB I asked students to try to answer any 7 of the 8 questions. I intended the exam to have some relatively easy parts and
More informationTHE DISPUTED GARMENT PROBLEM: THE MATHEMATICS OF BARGAINING & ARBITRATION. Richard Weber
THE DISPUTED GARMENT PROBLEM: THE MATHEMATICS OF BARGAINING & ARBITRATION Richard Weber Nicky Shaw Public Understanding of Mathematics Lecture 7 February, 2008 The Disputed Garment Problem The Babylonian
More informationContractually Stable Networks
Contractually Stable Networks (very preliminary version) Jean-François Caulier CEREC, FUSL Jose Sempere-Monerris University of Valencia Ana Mauleon FNRS and CEREC, FUSL and CORE, UCL Vincent Vannetelbosch
More informationEconomic Growth: Lecture 8, Overlapping Generations
14.452 Economic Growth: Lecture 8, Overlapping Generations Daron Acemoglu MIT November 20, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 8 November 20, 2018 1 / 46 Growth with Overlapping Generations
More informationAAEC 6524: Environmental Theory and Policy Analysis. Outline. Theory of Externalities and Public Goods. Klaus Moeltner Spring 2019.
AAEC 6524: Theory and Policy Analysis Theory of Externalities and Public Goods Klaus Moeltner Spring 2019 January 21, 2019 Outline Overarching and Related Fields and Microeconomics (consumer, firm, s)
More informationIntro Prefs & Voting Electoral comp. Political Economics. Ludwig-Maximilians University Munich. Summer term / 37
1 / 37 Political Economics Ludwig-Maximilians University Munich Summer term 2010 4 / 37 Table of contents 1 Introduction(MG) 2 Preferences and voting (MG) 3 Voter turnout (MG) 4 Electoral competition (SÜ)
More informationUNIVERSIDADE DE SANTIAGO DE COMPOSTELA DEPARTAMENTO DE ESTATÍSTICA E INVESTIGACIÓN OPERATIVA
UNIVERSIDADE DE SANTIAGO DE COMPOSTELA DEPARTAMENTO DE ESTATÍSTICA E INVESTIGACIÓN OPERATIVA On the core of an airport game and the properties of its center J. González-Díaz, M. A. Mirás Calvo, C. Quinteiro
More informationComputation of Efficient Nash Equilibria for experimental economic games
International Journal of Mathematics and Soft Computing Vol.5, No.2 (2015), 197-212. ISSN Print : 2249-3328 ISSN Online: 2319-5215 Computation of Efficient Nash Equilibria for experimental economic games
More informationTHE MINIMAL OVERLAP COST SHARING RULE
THE MINIMAL OVERLAP COST SHARING RULE M. J. ALBIZURI*, J. C. SANTOS Abstract. In this paper we introduce a new cost sharing rule-the minimal overlap cost sharing rule-which is associated with the minimal
More information2008/73. On the Golden Rule of Capital Accumulation Under Endogenous Longevity. David DE LA CROIX Grégory PONTHIERE
2008/73 On the Golden Rule of Capital Accumulation Under Endogenous Longevity David DE LA CROIX Grégory PONTHIERE On the Golden Rule of Capital Accumulation under Endogenous Longevity David de la Croix
More informationLecture 2 The Core. 2.1 Definition and graphical representation for games with up to three players
Lecture 2 The Core Let us assume that we have a TU game (N, v) and that we want to form the grand coalition. The Core, which was first introduced by Gillies [1], is the most attractive and natural way
More informationTrade policy III: Export subsidies
The Vienna Institute for International Economic Studies - wiiw June 25, 2015 Overview Overview 1 1 Under perfect competition lead to welfare loss 2 Effects depending on market structures 1 Subsidies to
More informationEconomics 2450A: Public Economics Section 8: Optimal Minimum Wage and Introduction to Capital Taxation
Economics 2450A: Public Economics Section 8: Optimal Minimum Wage and Introduction to Capital Taxation Matteo Paradisi November 1, 2016 In this Section we develop a theoretical analysis of optimal minimum
More informationAGRICULTURAL ECONOMICS STAFF PAPER SERIES
University of Wisconsin-Madison March 1996 No. 393 On Market Equilibrium Analysis By Jean-Paul Chavas and Thomas L. Cox AGRICULTURAL ECONOMICS STAFF PAPER SERIES Copyright 1996 by Jean-Paul Chavas and
More informationAre innocuous Minimum Quality Standards really innocuous?
Are innocuous Minimum Quality Standards really innocuous? Paolo G. Garella University of Bologna 14 July 004 Abstract The present note shows that innocuous Minimum Quality Standards, namely standards that
More informationProblem 1 (30 points)
Problem (30 points) Prof. Robert King Consider an economy in which there is one period and there are many, identical households. Each household derives utility from consumption (c), leisure (l) and a public
More informationMechanism Design: Basic Concepts
Advanced Microeconomic Theory: Economics 521b Spring 2011 Juuso Välimäki Mechanism Design: Basic Concepts The setup is similar to that of a Bayesian game. The ingredients are: 1. Set of players, i {1,
More informationBilateral consistency and converse consistency in axiomatizations and implementation of the nucleolus
Bilateral consistency and converse consistency in axiomatizations and implementation of the nucleolus Cheng-Cheng Hu Min-Hung Tsay Chun-Hsien Yeh April 10, 2013 Abstract We address whether bilateral consistency
More informationLecture 10: Mechanism Design
Computational Game Theory Spring Semester, 2009/10 Lecture 10: Mechanism Design Lecturer: Yishay Mansour Scribe: Vera Vsevolozhsky, Nadav Wexler 10.1 Mechanisms with money 10.1.1 Introduction As we have
More informationCooperative Games. M2 ISI Systèmes MultiAgents. Stéphane Airiau LAMSADE
Cooperative Games M2 ISI 2015 2016 Systèmes MultiAgents Stéphane Airiau LAMSADE M2 ISI 2015 2016 Systèmes MultiAgents (Stéphane Airiau) Cooperative Games 1 Why study coalitional games? Cooperative games
More informationTaxes, compensations and renewable natural resources
Taxes, compensations and renewable natural resources June 9, 2015 Abstract We start from a dynamic model of exploitation of renewable natural resources in which extinction is the expected outcome in the
More informationHandout 4: Some Applications of Linear Programming
ENGG 5501: Foundations of Optimization 2018 19 First Term Handout 4: Some Applications of Linear Programming Instructor: Anthony Man Cho So October 15, 2018 1 Introduction The theory of LP has found many
More informationThe Max-Convolution Approach to Equilibrium Models with Indivisibilities 1
The Max-Convolution Approach to Equilibrium Models with Indivisibilities 1 Ning Sun 2 and Zaifu Yang 3 Abstract: This paper studies a competitive market model for trading indivisible commodities. Commodities
More informationTrade Rules for Uncleared Markets with a Variable Population
Trade Rules for Uncleared Markets with a Variable Population İpek Gürsel Tapkı Sabancı University November 6, 2009 Preliminary and Incomplete Please Do Not Quote Abstract We analyze markets in which the
More informationGREThA, Université de Bordeaux, Avenue Léon Duguit, Pessac Cedex, France;
Games 014, 5, 17-139; doi:10.3390/g50017 OPEN ACCESS games ISSN 073-4336 www.mdpi.com/journal/games Article The Seawall Bargaining Game Rémy Delille and Jean-Christophe Pereau * GREThA, Université de Bordeaux,
More informationAdvanced Microeconomics
Advanced Microeconomics Cooperative game theory Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics 1 / 45 Part D. Bargaining theory and Pareto optimality 1
More informationStrategic Properties of Heterogeneous Serial Cost Sharing
Strategic Properties of Heterogeneous Serial Cost Sharing Eric J. Friedman Department of Economics, Rutgers University New Brunswick, NJ 08903. January 27, 2000 Abstract We show that serial cost sharing
More informationProfit-Sharing and Efficient Time Allocation
Profit-Sharing and Efficient Time Allocation Ruben Juarez a, Kohei Nitta b, and Miguel Vargas c a Department of Economics, University of Hawaii b Department of Economics, Toyo University c CIMAT, A.C.,
More informationDiscussion Paper Series
INSTITUTO TECNOLÓGICO AUTÓNOMO DE MÉXICO CENTRO DE INVESTIGACIÓN ECONÓMICA Discussion Paper Series Lower bounds and recursive methods for the problem of adjudicating conflicting claims Diego Domínguez
More informationFixed Water Sharing Agreements Sustainable to Drought
Fixed Water Sharing Agreements Sustainable to Drought Stefan Ambec Ariel Dinar and Daene McKinney October 2011 Abstract By signing a fixed water sharing agreement (FWSA), countries voluntarily commit to
More information