Natural Resource Management: A Network Perspective

Transcription

1 s -Use A Natural A Efthymia Kyriakopoulou 1 Anastasios 2 Advanced Policy Workshop: Sustainability Valuation, SDSN-G, A Université du Luxembourg 1, Athens University of Economics Business 2 28 June 2017 (UL,AUEB) Natural s 28 June / 57

2 s Social -Use A Social networks influence behavior criminal activities, voting environmentally-friendly behaviors, recycling smoking training studying Social economic interactions are shaped by the local structure of network sharing of information, risk etc. transmission of opinions, viruses... information about jobs political alliances, environmental alliances choices of education. (UL,AUEB) Natural s 28 June / 57

3 s Friendship (Colors: grade) -Use A Source: Crnovrsanin et al. "Visualization of friendship aggression networks". Nodes: Students, Line: indicates a friendship. By color-coding the nodes by grade, we see that these clusters are primarily organized by grade. (UL,AUEB) Natural s 28 June / 57

4 s Friendship (Colors: gender) -Use A Source: Crnovrsanin et al. "Visualization of friendship aggression networks". Nodes: Students, Line: indicates a friendship. Some grades are segregated by gender others are not. (UL,AUEB) Natural s 28 June / 57

5 s Transportation (Athens Metro Map) -Use A (UL,AUEB) Natural s 28 June / 57

6 s Transportation (Athens International Airport as a hub) -Use A (UL,AUEB) Natural s 28 June / 57

7 s Powerful Families Florentine Marriages, 1430 s -Use A Source: Jackson, (UL,AUEB) Natural s 28 June / 57

8 s Better-rated employees -Use A Source: Cross, 2011, The Most Valuable People in Your, Harvard Business Review Better-rated employees look more like Susan than Richard. Innovative employees don t have bigger networks, but bridging ties, that connect them to other employees who are themselves less connected. People with ties to the less-connected are more likely to hear about ideas that haven t gotten exposure elsewhere (UL,AUEB) Natural s 28 June / 57

9 Natural s Questions -Use A What do we know about network structure? do networks form? close are the observed networks to the optimal network structure? do networks influence behavior? do behaviors influence network structure? (UL,AUEB) Natural s 28 June / 57

10 Natural s Non-Market Interactions & Externalities -Use A Model explain non-market interactions. Interactions involve externalities, both positive negative. Example 1: a person gets a job in a growing company this may benefit her friends who will learn quickly about new opportunities. Example 2: Second-h smoking, imposed by a smoker to surrounding people. Understing externalities is important for policy. (UL,AUEB) Natural s 28 June / 57

11 Behaviors Natural s -Use A are important because they drive behavior in cases that involve systematic externalities. Two basic themes emerge from this observation: 1 Rom Models. Relationships are governed purely by some stochastic process Strategic Models. The payoff or net benefit of a relationship depends potentially on the larger network 2 Behaviors Diffusion Learning Games on (UL,AUEB) Natural s 28 June / 57

12 Behaviors Natural s -Use A 1 people do not consider the full societal impact of their decisions to form or maintain links / relationships. Suboptimal. 2 Behaviors behaviors that involve peer interactions, such as choices to undertake criminal activities, or to adopt a new technology. Positive externalities lead decisions to be taken at a low level. Negative externalities lead decisions to be taken at too high a level, relative to social optimum. (UL,AUEB) Natural s 28 June / 57

13 Behaviors Natural s : Routes -Use A Which networks form? Rom graph models - "" Economic / Game theoretic models - "Why" (UL,AUEB) Natural s 28 June / 57

14 Natural s Game Theoretic Models -Use A Costs benefits for agents who are associated with each network Agents choose to connect or not with other agents Private incentives vs. social effi ciency. (UL,AUEB) Natural s 28 June / 57

15 s Modeling Choices -Use A should we model agents incentives to form or sever links: can these incentives cause changes in the network structure? is consensus needed? are agents rational? is the process dynamic or static? can they compensate each other for creating a relationship? (UL,AUEB) Natural s 28 June / 57

16 Natural s Relevant Questions -Use A Are networks stable? Which networks are likely to form? Are observed networks effi cient? What is the gap between market effi cient Can policy interventions improve effi ciency? Which policy instruments could be used? (UL,AUEB) Natural s 28 June / 57

17 Natural s -Use A does network structure affect behavior? Diffusion: Infection, contagion. Learning: Information, opinions Games on networks: decisions, choices. (UL,AUEB) Natural s 28 June / 57

18 s Diffusion -Use A Spread of Tuberculosis (McKenzie et al., 2006). Black nodes: persons with clinical disease, pink nodes: exposed persons with dormant infection, green nodes: exposed persons with no infection. (UL,AUEB) Natural s 28 June / 57

19 s Learning -Use A Modelling: DeGroot model: Repeated communication Naive updating of beliefs: information comes only once (weighted average of neighbors beliefs) structure plays an important role Bayesian learning: Observe each other Repeated actions over time (optimal information extraction) Homogeneity of actions payoffs Computationaly deming (UL,AUEB) Natural s 28 June / 57

20 s Games on Modelling -Use A Agents make real decisions not just diffusion or updating of beliefs Complementarities or Substitutabilities Strategic interplay Inter-dependencies Equilibrium existence structure Equilibrium response to network structure (UL,AUEB) Natural s 28 June / 57

21 s Games on Complements / Substitutes -Use A Strategic Complements: For all i, a a : u i (1, a) u i (0, a) u i (1, a ) u i (0, a ) My friend s choice to take an action increases my relative payoff to take that action. Strategic Substitutes: For all i, a a : u i (1, a) u i (0, a) u i (1, a ) u i (0, a ) My friend s choice to take an action decreases my relative payoff to take that action. (UL,AUEB) Natural s 28 June / 57

22 Games on Natural s Other s behaviors affect my utility / welfare. Externalities Others behaviors affect my decisions, actions, opinions. -Use A Others actions affect individual payoffs. Traditional game theory: each agent interacts with everyone else. Games on networks: each agent interacts with their neighbors. Agents interact with a different number of neighbors. New links may be formed / severed in case of dynamic networks. (UL,AUEB) Natural s 28 June / 57

23 s Games on Examples -Use A Strategic Complements: conformism imitation. Recycling, energy-saving decisions (peer effects) Education decisions Smoking Learn a language Strategic Substitutes: incentives to free ride. Local public goods (share products) Information gathering (UL,AUEB) Natural s 28 June / 57

24 & Pairwise Stability Natural s -Use A Agents may be able or not to form links without the consent of their neighbors. Modelling depends on specific economic problem. Unilateral link formation is allowed in cases of literature citations or Internet site referrals. Mutual link formation is required in international environmental agreements, information / technology sharing, friendships, in the majority of socioeconomic problems. This leads to the notion of pairwise stability (Jackson Wolinsky, 1996): agents coordinate to form profitable links a stable network is obtained when no agent wishes to form a new link or no agent want to (unilaterally) sever existing links. (UL,AUEB) Natural s 28 June / 57

25 Applications of Social Natural s -Use A The main areas where social networks have been studied (overview Jackshon Zenou, 2015, Jackson, Rogers & Zenou, 2016) Financial networks (Kelly & Ó Gráda (2000), Elliott et al. (2014), Acemoglu et al. (2015)). Labour markets (Ioannides & Loury (2004), Wahba & Zenou (2005), Calvó-Armengol & Jackson (2004,2007)). Education (Zimmerman (2003), Calvó-Armengol et al. (2009), Sacerdote (2011)). Crime (Patacchini & Zenou (2008), Calvó-Armengol et al. (2005)) Development economics (Banerjee et al. (2013), Beaman et al. (2016)). Exchange theory, bargaining trade (Cook & Cheshire (2013), Condorelli & Galeotti (2016), Manea (2016)). (UL,AUEB) Natural s 28 June / 57

26 s -Use -Use A Analysis of environmental resource economics Externalities Policies to correct the detrimental externalities Use of social networks where nodes could be: polluting firms, firms adopting clean technologies agents harvesting an exhaustible or a renewable resource, countries emitting greenhouse gases adopting mitigation or adaptation policies consumers engaging in polluting or pollution reducing activities. (UL,AUEB) Natural s 28 June / 57

27 -Use Natural s -Use A Despite the straightforward association of environmental issues with social networks very little research has been undertaken. A broad discussion on how networks can be used in the context of environmental issues can be found in Currarini, Marchiori Tavoni (2016). Adoption of innovative, environmentally-friendly technologies by firms (Conley Udry, 2001) Common-pool resource use with multiple sources cities, (İlkiliç, 2011). (UL,AUEB) Natural s 28 June / 57

28 -Use Complementarities Substitutabilities Natural s -Use A Particular characteristic of environmental networks: they can be characterized by strategic heterogeneity. Strategic heterogeneity: the network includes both strategic complementarities substitutabilities. Strategic complementarities: Links indicating cost reducing technology agreements /or cooperation among agents. Strategic substitutabilities.: congestion effects or increasing search or extraction costs when the stock of a resources is depleted. The study of strategic heterogeneity will provide new insights in terms of market outcomes policy to attain the social optimum. (UL,AUEB) Natural s 28 June / 57

29 A Natural s -Use A In Kyriakopoulou (2017), we study a network associated with the exploitation of a depletable resource which is characterized by strategic heterogeneity. Purpose: Study market outcomes associated with specific network structures. Social optimum when regulator focuses on development. Social optimum when regulator focuses on resource conservation. Characterize the most effi cient market structures. Policies that will control: the level of externalities the desired link structure among agents Show that ineffi cient policies emerge when ignoring the network structure. (UL,AUEB) Natural s 28 June / 57

30 A Natural s -Use A A network consisting of three agents located at distinct spatial points exploiting a depletable resource (located at a different site). The exploited quantity depends on (following Smith, 1968, 1969): resource stock externalities, crowding externalities positive technological spillovers Market outcome: agents maximize their private profits. Social Optimum 1: maximization of the private value of the network (sum of agents payoffs) Social Optimum 2: Social Optimum 1 + conservation value (which captures the exhaustible nature of the resource). We show that the special nature of natural resources calls for different treatments than producible goods, if ignored, we end up in overexploitation of the resource. (UL,AUEB) Natural s 28 June / 57

31 A Natural s -Use A 1 Model 2 Market outcome 3 Theory of 4 Application of Dynamic Theory in the current framework 5 Extension: Introducing Heterogeneity 6 Outcome 7 of Effi cient Structures (UL,AUEB) Natural s 28 June / 57

32 s A 1 resource, 3 agents Decentralized Competitive Equilibrium Congestion Externalities -Use A Figure: A 3-agent resource network with congestion externalities. (UL,AUEB) Natural s 28 June / 57

33 A Decentralized Competitive Equilibrium Natural s 1 resource, 3 agents Harvest function: Congestion Externalities H(E, S) = qes -Use A E : amount of effort during harvesting S : resource stock q : "catchability-coeffi cient". The pay-off of agent i will be: u i = ph i β 2 (E i ) 2 γh i 3 j = 1 j = i H j (UL,AUEB) Natural s 28 June / 57

34 s A Maximization problem: Decentralized Competitive Equilibrium Congestion Externalities -Use A the solution: ( ) 2 Hi max ph i β γh i H i 2 qs }{{} private cost H i = pq2 S 2 β + 2γq 2 S 2 3 j = 1 j = i H j }{{} congestion cost Notice that dh i ds > 0, larger stock higher harvested amount. No congestion: price equals private marginal cost, p = β ( Hi q 2 S 2 ), which leads to H o i = pq2 S 2 β Congestion reduces the use of the resource, i.e. H i < H o i (UL,AUEB) Natural s 28 June / 57

35 s A Exhaustability Since the resource is exhaustible in the one-shot game, the eshaustability condition is: 3Hi pq = 2 S 2 S, or 3 β + 2γq 2 S 2 = S (1) For p = 1, β = 1, q = 0.3, γ = 0 -Use A No congestion externalities (UL,AUEB) Natural s 28 June / 57

36 A Exhaustability Natural s For p = 1, β = 1, q = 0.3, γ = Use A Congestion externalities (UL,AUEB) Natural s 28 June / 57

37 s A Exhaustability Congestion Externalities -Use A Individual profits under the presence of this negative externality are given by: ui βp = 2 q 2 S 2 2(β + 2γq 2 S 2 ) 2 while aggregate profits are given by: u T = 3βp 2 q 2 S 2 2(β + 2γq 2 S 2 ) 2 (UL,AUEB) Natural s 28 June / 57

38 s A Exhaustability Congestion Externalities & Technological Spillovers -Use A Figure: network with technological spillovers congestion externalities. (UL,AUEB) Natural s 28 June / 57

39 s -Use A A Exhaustability Congestion Externalities & Technological Spillovers Individual payoffs are given by: ( ) 2 Hi u i = ph i β γh i 2 qs }{{} private cost 3 j = 1 j = i H j }{{} congestion cost 3 g ij H i H j } j = 1 j = i {{ } technology spillover effect + δ Notice that g ij shows the presence of a link between two agents. g ij could take values 0 < g ij < 1. Here g ij = 1 when a collaboration link is formed. Individual harvesting is given by: H i = pq 2 S 2 β + 2(γ δ)q 2 S 2 (UL,AUEB) Natural s 28 June / 57

40 s -Use A A Exhaustability Congestion Externalities & Technological Spillovers Individual payoffs are given by: ũ i = aggregate payoffs: ũ T = βp 2 q 2 S 2 2(β + 2(γ δ)q 2 S 2 ) 2 3βp 2 q 2 S 2 2(β + 2(γ δ)q 2 S 2 ) 2 Notice that: H i > Hi harvesting is higher when agents collaborate share technological advances knowledge. The positive technological spillovers (fully or partly) outweigh the negative congestion effect, lead to higher use of the resource higher individual aggregate profits. (UL,AUEB) Natural s 28 June / 57

41 Natural s -Use A Market Equilibrium Decisions of harvesting agents to create or sever existing cooperation links. This will determine the structure of the network at the end of the period Effi cient Market Structure (MNS) Regulator s Optimum Maximize aggregate payoffs (plus the conservation value of the resource) decide at the beginning of the period to retain or sever cooperation links Socially effi cient Structure. (SNS) If MNS = SNS, the regulator can intervene provide incentives schemes. (UL,AUEB) Natural s 28 June / 57

42 Market Structure Natural s -Use A Assume no cooperation links at the beginning of the period (star-shaped network). û i ( H S ij ), i, j = 1, 2, 3, i = j : maximized payoff of each agent (no links exist) H S : the vector of profit maximizing harvesting when the network is star-shaped. Cooperation: should be profitable for both agents. H : the vector of profit maximizing harvesting at each network structure +ij : link ij is created ij: link is not created, i, j = 1, 2, 3, i = j. (UL,AUEB) Natural s 28 June / 57

43 s If Market Structure ) u 1 (H +12, 13) > û 1 (H S ij u 1 (H +12, 13) > u 1 (H +ij). ) u 2 (H +21, 23) > û 2 (H S ij u 2 (H +21, 23) > u 2 (H +ij). -Use A there will be a link between 1 2 but not with 3. Note that it is possible to have u 3 (H +ij) ) > û 3 (H S ij u 3 (H +13, 23) ) > û 3 (H S ij u 3 (H +23, 13) ) > û 3 (H S ij but there will be no cooperation with 3 since this is not profitable for the other agents. (UL,AUEB) Natural s 28 June / 57

44 Market Structure Natural s -Use A All agents create cooperation links, if ) u i (H +ij) > û i (H S ij, i, j = 1, 2, 3, i = j, No cooperation links are created the star shaped network will remain until the end of the period, if ) u i (H +ij) < û i (H S ij, i, j = 1, 2, 3, i = j All the network structures described above are pair-wise stable (Jackson Wolinsky, 1996). (UL,AUEB) Natural s 28 June / 57

45 s Fully or Partly Connected? Full network Pareto dominates the unconnected network H T > HT (aggregate use of the resource) ũ T > ut (aggregate profits). What if 2 of the agents decide to collaborate without including the 3rd agent in the first step. -Use A Figure: A partly-connected network (UL,AUEB) Natural s 28 June / 57

46 Fully or Partly Connected? Natural s -Use A What if 2 of the agents decide to collaborate without including the 3rd agent in the first step. We show that Ĥ 1 = Ĥ 2 > Ĥ 3 û 1 = û 2 > û 3 collaboration is profitable for the two connected agents. But it is only conditionally profitable for all the agents to move from a partly to a fully connected network: ũ 1,2 > û 1,2 if β > 2γq 2 S 2 ũ 3 > û 3 if β > δq 2 S 2. If ũ 3 > û 3, but û 1,2 > ũ 1,2, only agent 3 has a benefit to join the collaboration, but it is not profitable for 1 & 2. If ũ 3 û 3 > 2(û 1,2 ũ 1,2 ), agent 3 could offer a bribe equal to û 1,2 ũ 1,2 to each one of agents 1 2 make them interested in collaborating with her. (UL,AUEB) Natural s 28 June / 57

47 s Introducing Heterogeneity Assume that transportation is costly cost depends on the geographical distance between the agent the resource. -Use A Figure: Introducing heterogeneity: different geographical distance between the agent the resource. (UL,AUEB) Natural s 28 June / 57

48 Introducing Heterogeneity Natural s -Use A l i (0, 1] :location of the agent i, defined as her distance from the resource, τ : marginal transportation cost. Then, the pay-off of agent i will be: u i = ph i β 2 (E i ) 2 τl i H i γh i 3 j =ih j Individual harvesting is given by: ( [β(p τl i ) γq 2 S 2 H i = Notice that dh i dl i ( ))] p + τ l i l j q 2 S 2 j =i (β γq 2 S 2 ) (β + 2γq 2 S 2 ) < 0 dh i dl j > 0. (UL,AUEB) Natural s 28 June / 57

49 Introducing Heterogeneity Natural s If agents are linked: -Use A Figure: Technological spillovers between heterogeneous agents. (UL,AUEB) Natural s 28 June / 57

50 Introducing Heterogeneity Natural s -Use A H i = If agents are linked, individual harvesting is given by: [β(p τl i ) + (δ γ)q 2 S 2 ( ))] p + τ l i l j q 2 S 2 j =i (β + (δ γ)q 2 S 2 ) (β 2(δ γ)q 2 S 2 ) Note that in this case: d H i dl i ( < 0 (as before), but d H i dl j < 0. (UL,AUEB) Natural s 28 June / 57

51 Introducing Heterogeneity Natural s -Use A H i = If agents are linked, individual harvesting is given by: [β(p τl i ) + (δ γ)q 2 S 2 ( ))] p + τ l i l j q 2 S 2 j =i (β + (δ γ)q 2 S 2 ) (β 2(δ γ)q 2 S 2 ) Note that in this case: d H i dl i ( < 0 (as before), but d H i dl j < 0. With strong positive spillover effects (δ γ) > 0), agent s j harvest affects the use of the resource by agent i positively. (UL,AUEB) Natural s 28 June / 57

52 Introducing Heterogeneity Natural s -Use A H i = If agents are linked, individual harvesting is given by: [β(p τl i ) + (δ γ)q 2 S 2 ( ))] p + τ l i l j q 2 S 2 j =i (β + (δ γ)q 2 S 2 ) (β 2(δ γ)q 2 S 2 ) Note that in this case: d H i dl i ( < 0 (as before), but d H i dl j < 0. With strong positive spillover effects (δ γ) > 0), agent s j harvest affects the use of the resource by agent i positively. Larger distance between agent j the resource reduces j s harvest which affects agent i negatively. (UL,AUEB) Natural s 28 June / 57

53 s -Use A Congestion Spillovers The regulator chooses H 1, H 2, H 3, to maximize total welfare: max W (H i ) = max 3 H 1,H 2, H 3 i=1 harvesting is given by: ph i β 2 H S i = pq2 S 2 β + 4γq 2 S 2 while the value of the network is given by: W (H S i ) = ( ) 2 3 Hi γh i qs j = 1 j = i 3p 2 q 2 S 2 2(β + 4γq 2 S 2 ) H j (UL,AUEB) Natural s 28 June / 57

54 Exhaustability Natural s -Use A exploitation exhaustability (UL,AUEB) Natural s 28 June / 57

55 s -Use A Exhaustability Congestion & Technological Spillovers The regulator chooses H 1, H 2, H 3, to maximize total welfare: [ 3 max ph i β ( ) ] 2 3 Hi + δ g ij H i H j γh i 2 qs H j H 1,H 2, H 3 i=1 harvesting is given by: H S i = 3 j=1,j =i pq 2 S 2 β + 4(γ δ)q 2 S 2 while the value of the network is given by: W ( H S i ) = 3p 2 q 2 S 2 2(β + 4(γ δ)q 2 S 2 ) j=1,j =i When congestion externality dominates, ((γ δ) > 0), harvesting < Decentralized harvesting. (UL,AUEB) Natural s 28 June / 57

56 s -Use A Exhaustability Congestion & Technological Spillovers The regulator chooses H 1, H 2, H 3, to maximize total welfare: [ 3 max ph i β ( ) ] 2 3 Hi + δ g ij H i H j γh i 2 qs H j H 1,H 2, H 3 i=1 harvesting is given by: H S i = 3 j=1,j =i pq 2 S 2 β + 4(γ δ)q 2 S 2 while the value of the network is given by: W ( H S i ) = 3p 2 q 2 S 2 2(β + 4(γ δ)q 2 S 2 ) j=1,j =i When congestion externality dominates, ((γ δ) > 0), harvesting < Decentralized harvesting. When positive externality dominates, ((γ δ) < 0), harvesting > Decentralized harvesting. (UL,AUEB) Natural s 28 June / 57

57 s Exhaustability Structure The value of the optimal network under congestion forces is: W (Hi S 3p ) = 2 q 2 S 2 2(β + 4γq 2 S 2 ) -Use A (UL,AUEB) Natural s 28 June / 57

58 s Exhaustability Structure -Use A The value of the optimal network under congestion forces is: W (Hi S 3p ) = 2 q 2 S 2 2(β + 4γq 2 S 2 ) The value of the optimal network under congestion positive externalities is: W ( H S i ) = 3p 2 q 2 S 2 2(β + 4(γ δ)q 2 S 2 ) (UL,AUEB) Natural s 28 June / 57

59 s Exhaustability Structure -Use A The value of the optimal network under congestion forces is: W (Hi S 3p ) = 2 q 2 S 2 2(β + 4γq 2 S 2 ) The value of the optimal network under congestion positive externalities is: W ( H S i ) = 3p 2 q 2 S 2 2(β + 4(γ δ)q 2 S 2 ) It is clear that: W ( H S i ) > W (H S i ). (UL,AUEB) Natural s 28 June / 57

60 s Exhaustability Structure -Use A The value of the optimal network under congestion forces is: W (Hi S 3p ) = 2 q 2 S 2 2(β + 4γq 2 S 2 ) The value of the optimal network under congestion positive externalities is: W ( H S i ) = 3p 2 q 2 S 2 2(β + 4(γ δ)q 2 S 2 ) It is clear that: W ( H S i ) > W (H S i ). Thus, the fully connected network is the socially effi cient network structure. (UL,AUEB) Natural s 28 June / 57

61 s Exhaustability Structure -Use A The value of the optimal network under congestion forces is: W (Hi S 3p ) = 2 q 2 S 2 2(β + 4γq 2 S 2 ) The value of the optimal network under congestion positive externalities is: W ( H S i ) = 3p 2 q 2 S 2 2(β + 4(γ δ)q 2 S 2 ) It is clear that: W ( H S i ) > W (H S i ). Thus, the fully connected network is the socially effi cient network structure. Since moving from the partly to the fully connected network is not always profitable for all the agents involved, the regulator should intervene implement policies that will achieve the socially effi cient market structure (UL,AUEB) Natural s 28 June / 57

62 s -Use A Conservation Use of the Connected The regulator chooses H 1, H 2, H 3, to maximize total welfare taking into account that there is welfare loss when the stock of the resource decreases, i.e ( ) max W P 3 3 (H i ) = max u i (H, g) + κ S H i H 1,H 2, H 3 i=1 harvesting is given by: H P i = (p κ)q2 S 2 β + 4(γ δ)q 2 S 2 while the value of the network is given by: ( 2βκ + q W ( H i P 2 S [3(κ 2 + p 2 ) + 2κ(4S(γ δ) 3p)] ) S ) = 2(β + 4(γ δ)q 2 S 2 ) H P i < H S i the higher the value of the preserved resource, the higher the distance between the two optimal harvests. (UL,AUEB) Natural s 28 June / 57 i=1

63 s -Use A harvesting is given by: Conservation Use of the H P i = (p κ)q2 S 2 β + 4γq 2 S 2 Unconnected while the value of the network is given by: ( 2βκ + q W (Hi P 2 S [3(κ 2 + p 2 ) + 2κ(4Sγ 3p)] ) S ) = 2(β + 4γq 2 S 2 ) Notice that H P i < H P i harvest is higher in the fully connected network (UL,AUEB) Natural s 28 June / 57

64 s -Use A harvesting is given by: Conservation Use of the H P i = (p κ)q2 S 2 β + 4γq 2 S 2 Unconnected while the value of the network is given by: ( 2βκ + q W (Hi P 2 S [3(κ 2 + p 2 ) + 2κ(4Sγ 3p)] ) S ) = 2(β + 4γq 2 S 2 ) Notice that H P i < H P i harvest is higher in the fully connected network but W (H P i ) W ( H P i ) depending on the value of κ, collaboration between agents (that increases resource exploitation) could lead to either higher or lower welfare. (UL,AUEB) Natural s 28 June / 57

65 s -Use A harvesting is given by: Conservation Use of the H P i = (p κ)q2 S 2 β + 4γq 2 S 2 Unconnected while the value of the network is given by: ( 2βκ + q W (Hi P 2 S [3(κ 2 + p 2 ) + 2κ(4Sγ 3p)] ) S ) = 2(β + 4γq 2 S 2 ) Notice that H P i < H P i harvest is higher in the fully connected network but W (H P i ) W ( H P i ) depending on the value of κ, collaboration between agents (that increases resource exploitation) could lead to either higher or lower welfare. For suffi ciently high κ values, the fully connected network leads to lower welfare (UL,AUEB) Natural s 28 June / 57

66 s -Use A harvesting is given by: Conservation Use of the H P i = (p κ)q2 S 2 β + 4γq 2 S 2 Unconnected while the value of the network is given by: ( 2βκ + q W (Hi P 2 S [3(κ 2 + p 2 ) + 2κ(4Sγ 3p)] ) S ) = 2(β + 4γq 2 S 2 ) Notice that H P i < H P i harvest is higher in the fully connected network but W (H P i ) W ( H P i ) depending on the value of κ, collaboration between agents (that increases resource exploitation) could lead to either higher or lower welfare. For suffi ciently high κ values, the fully connected network leads to lower welfare Socially effi cient network structure: Unconnected (UL,AUEB) Natural s 28 June / 57

67 s Natural resource management problems Externalities Different Structures. -Use A (UL,AUEB) Natural s 28 June / 57

68 s -Use Natural resource management problems Externalities Different Structures. Socially Effi cient Structure Policies to form or eliminate links between agents. A (UL,AUEB) Natural s 28 June / 57

69 s -Use A Natural resource management problems Externalities Different Structures. Socially Effi cient Structure Policies to form or eliminate links between agents. Strategic Heterogeneity (particular characteristic of environmental networks) was shown to provide new insights in network formation. (UL,AUEB) Natural s 28 June / 57

70 s -Use A Natural resource management problems Externalities Different Structures. Socially Effi cient Structure Policies to form or eliminate links between agents. Strategic Heterogeneity (particular characteristic of environmental networks) was shown to provide new insights in network formation. The regulator who focuses more on the conservation of the resource rather than economic development defines different optimal network structures. (UL,AUEB) Natural s 28 June / 57

71 s -Use A Natural resource management problems Externalities Different Structures. Socially Effi cient Structure Policies to form or eliminate links between agents. Strategic Heterogeneity (particular characteristic of environmental networks) was shown to provide new insights in network formation. The regulator who focuses more on the conservation of the resource rather than economic development defines different optimal network structures. analysis can be used to numerous environmental problems. (UL,AUEB) Natural s 28 June / 57