Co-management and the possibility of cooperative selfenforcement

Transcription

1 Co-management and the possibility of cooperative selfenforcement Lone Grønbæk & Marko Lindroos

2 Tragedy of the commons: History of shared resources The UN Convention on the Law of the Sea (UN 1982) resulted in establishment of 200 nautical miles Exclusive Economic Zones (EEZs). A fishery resource that crosses the EEZs of one or more neighbouring states or the open sea is a transboundary or shared resource. Still management problems > non-cooperative solution. Management organisations are created (UN 1995) > a step towards cooperation. 2

3 Motivation Cooperative games in resource economics ES IS Symmetric Players Coalition formation / agreements Incentives to Free Ride 3

4 Motivation Cooperative games in resource economics ES IS Symmetric Players Coalition formation / agreements Incentives to Free Ride Existing Theory: Only two-player coalition stable Counter-Example: Groundfish trawl fishery of British Columbia 4

5 23 January 2017 Modelling Basics The simple fisheries model Benefit functions Biomass evolution 5

6 Game Theory and Fisheries Open Access Inefficient Warming (1911) Gordon (1954) Involves applying game theory for analysing the relevant problems Sole Owner Efficient Gordon (1954) Scott (1955) Source: Kronbak & Lindroos, 2010, p.557 6

7 23 January 2017 Renewable Resource Games Games with externalities A game with externalities: A merger of two players/coalitions affects the payoff of players/coalitions outside the merger. 7

8 23 January 2017 Renewable Resource Games Games with externalities A game with externalities: A merger of two players/coalitions affects the payoff of players/coalitions outside the merger. 8

9 23 January 2017 Renewable Resource Games Games with externalities A game with externalities: A merger of two players/coalitions affects the payoff of players/coalitions outside the merger. Externalities can be positive or negative. In resource games positive externalities creates free rider incentives Classic TU-games does not take externalities into consideration. 9

10 Objective The objective is to: analyze stability issues in a repeated game version of a coalition game in partition function form. n player symmetric game in partition function form Inspired by Pintassilgo and Lindroos 2008 Repeated game Inspired by Hannesson

11 23 January 2017 Partition function games Definitions Implications: - Member of exactly one coalition - Symmetric players => Coalition defined by its size 11

12 23 January 2017 Partition function games Definitions Definition 2.2. The partition function each coalition structure. maps a vector of payoff values to Definition 2.3. The per-member partition function yields the payoff of a coalition of size n i in the coalition structure C. 12

13 23 January 2017 Partition function games Stability Issues A coalition, S i with n i members, is Internal Stable iff External Stable iff 13

14 23 January 2017 The Model The objective function for coalition S i s.r. 14

15 23 January 2017 Being a member of the coalition Information as a club good The coalition is a set of information flow. Members of the coalition benefits from this information not being available outside of the coalition. Excludable Non-Excludable Rival Private Goods Common Goods Non-Rival Club Goods Public Goods Two can do the job more effectively than one plus 1 2 > 1+1 Scale parameter on costs 15

16 Free-riding A deviating player achieves higher profits when deviation is not detected. With positive externalities, this profit will be higher than the profits of the standard non-cooperative game. A deviating player will be detected after a number of periods, τ. After τ th period the other players would respond to the deviation. 16

17 23 January 2017 Free-riding Grand Coalition Deviation Coalition + 1 singleton. t-1 t t+τ Time 17

18 23 January 2017 { { { Free-riding Grand Coalition Deviation Coalition + 1 singleton. t-1 t t+τ Time Full info. Ass. info. Full info. 18

19 Free-riding Optimal effort for the free rider in a given period of deviation not being detected Trivial conclusion: 19

20 Free-riding Optimal effort for the free rider in a given period of deviation not being detected Trivial conclusion: Deviator applies: 1. higher share of effort then the player would have applied being a member of the grand coalition, 20

21 Free-riding Optimal effort for the free rider in a given period of deviation not being detected Trivial conclusion: Deviator applies: 1. higher share of effort than the player would have applied being a member of the grand coalition, 2. not as high as the sum of all players effort in the grand coalition. 21

22 Free-riding Optimal effort for the free rider in a given period of deviation not being detected Trivial conclusion: Deviator applies: 1. higher share of effort then the player would have applied being a member of the grand coalition, 2. not as high as the sum of all players effort in the grand coalition. 3. The effort for the deviator increases the more players there are in the game 22

23 23 January 2017 Propositions Proposition 3.1 There exist a critical level of beta to sustain an internal stable/spne full cooperative repeated game for a given number of players, n, when information in a coalition is treated as a club good. 60 maximum number of players in equilibrium

24 23 January 2017 Propositions Proposition 3.1 There exist a critical level of beta to sustain an internal stable/spne full cooperative repeated game for a given number of players, n, when information in a coalition is treated as a club good. Proposition 3.2 There exist a discount rate such that it is possible to sustain an internal stable/spne full cooperative repeated game for a given number of players, n, when information in a coalition is treated as a club good. 24

25 23 January 2017 Conclusion Presents analytical results for stability issues in a repeated coalition game. When a deviating agent is excluded from a club good the games turns into a variant of an asymmetric game. This is the reason for the stability of coalitions larger than two players. 25

26 Next steps Discuss and analyze the repeated structure the time issue, the discount factor and pay-offs over time Discuss the issue of a second deviator is it possible? And when? Include elements from behavioral economics: Hyperbolic discounting Loss-aversion 26

27 Thank you!

28 23 January 2017 Modelling Basics Renewable Resources In order to investigate the economics of renewable resources it is necessary to describe the pattern of biological growth of the resource. ( ) = rx t ( 1- X t K) F X t Where X is the stock size at time t F is the growth function. r is the intrinsic growth rate K is the maximum size of the stock (carrying capacity) 28

29 23 January 2017 Modelling Basics Renewable Resources Logistic Growth F(X) Relationship between stock size and the rate of change of population due to biological growth. X min X MSY K Stock Three properties: 1. K is max. stock size that can be supported in the milieu. 2. Growth, F, is a quadratic function of the resource stock, X. The max. amount of growth (X MSY ) will occur when stock size is half of K. 3. Growth is zero only at a stock size of zero and a stock size of K. For all intermediate values, growth is positive. 29

30 Rent elimination in Open Access Revenue and Cost of harvest intensity ( ) Fishing The Tragedy of the Commons Cost Revenue - Entry continues until all rents are dissipated (profit per boat => zero). - Stock size will tend to be lower, and harvest rates will tend to be higher compared with a restricted access fishery. - Extinction is more likely, but not necessarily happen 30 SO = Sole Owner (Private E 0 E 1 E 2 E 3 E 4 harvest intensity Property) E OA OA = Open Access E SO

31 The Model Assume A set of n ex ante symmetric players, P; P=(1,2,,n) Classical Gordon-Schaefer harvest model Identical and constant unit costs per effort Constant price Identical players implies that a coalition can be defined by its size. 31

32 Full coop vs Non-coop EFFORT LEVELS 32