Game Theory and International Environmental Agreements IEA

1

• Game Theory and International Environmental
  Agreements (IEA)
• christine.heumesser_at_boku.ac.at

2
Outline of lecture

• Introduce 3 games which reflect challenges an IEA
  is facing.
• Outline methods of operation of Game Theory
  (equilibrium concepts, simultaneous and
  sequential moves, mixed strategies, repeated
  games and games with many players)
• Show how Game Theory can serve as tool/framework
  to approach international environmental problems

3
Game theory and International Environmental
Agreements

• International environmental problems and their
  treaties
• i.e.
• Climate change (Kyoto Protocol)
• Ozone layer depletion (Montreal Protocol)
• Acid rain (Sulphur Emissions Reduction Protocol)
• Biodiversity loss (Convention on Biological
  Diversity)

4
Game theory and International Environmental
Agreements

• Typical features of many environmental problems
  (Public good, Externalities, Free riding) can be
  handled by means of game- theoretic models and
  framework.

5
Game theory and International Environmental
Agreements

• Externalities occur when the production or
  consumption decision of one agent has an impact
  on the utility or profit of another agents in an
  unintended way and when no compensation/payment
  is made by the generator.
• Provision of a public good usually leads to
  Market Failure
• no international institution to correct this
  instead voluntary international cooperation
  efforts to provide the public good.

6
Game theory and International Environmental
Agreements

• Following Questions arise

7
Game Theory?

• Sub discipline of Mathematics
• Focuses on games where
• There are 2 or more players
• Some choice of action where strategy matters
• Outcome for each player depends on the strategy
  chosen by all other players
• offers an approach to model the strategic
  interactions among economic agents
• attempts to capture behavior in strategic
  situations, in which an individual's success
  depends on the choices of others

8
Game Theory?

• Many economic issues involve strategic
  interaction.
• Behavior in imperfectly competitive markets,
  e.g. Coca-Cola versus Pepsi.
• Behavior in auctions, e.g. Investment banks
  bidding
• Behavior in environmental/economic negotiations
• Got popular in 1944 after the publication of
  Games and Economic Behaviour by John von
  Neumann and Oskar Morgenstern
• Several game theorists won the Nobel Prize,
  u.o.
• Robert Aumann, Thomas Shelling, John Harsanyi,
  John F. Nash Jr. (A beautiful mind by Silvia
  Nasar), Reinhard Selten

9
Game Theory?

• Three Elements of a Game
• 1) The players
• how many players are there?
• does nature/chance play a role?
• 2) A complete description of the strategies of
  each player
• 3) A description of the consequences (payoffs)
  for each player for every possible profile of
  strategy choices of all players.

10
Game Theory?

• Further assumptions for following games
• (4.) Assumption that each player is rational
• (5.) Common knowledge that each player is
  rational
• (6.) Perfect information the payoff functions
  are common knowledge.
• In an EQUILIBRIUM, each player of the game has
  adopted a strategy that they are unlikely to
  change

11
Games which depict an IEA

• Prisoners Dilemma

Prisoner 2

• Normal form representation agents choose their
  strategy simultaneously
• individual optimal strategy yields a result,
  which is, seen as a whole, not optimal

Not confess
Confess
Not confess
Prisoner 1
Confess
12
Games which depict an IEA
Pollution Game 1
Country 2

• In this game strictly dominated strategy is
  abate (not confess)
• Strictly dominated strategy a strategy which is
  never played
• Non-cooperative solution (pollute, pollute)

Abate
Pollute
Pollute
Country 1
Abate
13
Equilibrium Concepts

• Strictly dominated strategies are not always
  given

Player 2
L C R

• None of these strategies are strictly dominated
• We need another equilibrium concept
• Each player chooses the best possible strategy
  (best response)given the strategy of the other
  player
• -gt NASH EQUILIBRIUM

T M B
Player 1
14
Equilibrium Concepts

• Nash Equilibrium
• In the n-player normal-form game a strategy is a
  Nash Equilibrium if it is for each player the
  best response to the strategies specified for the
  other players.
• In the previous games the non-cooperative
  solutions (pollute, pollute) and (confess,
  confess) are Nash equilibria.
• Each normal form game has at least one Nash
  equilibrium.
• What happens if there are several Nash
  equilibria?

15
Games which depict an IEA

• Pollution Game 2 (analogue to Chicken Game)

• Game has been restructured such that abate is an
  equilibrium strategy for one of the agents.
• When country x plays pollute, country y can only
  play abate.
• 2 NASH equilibria
• Cooperative solution (abate, abate) not stable
• How can we find out
• which equilibrium will be played?

Country 2
abate
Pollute
Pollute
Country 1
abate
16
Games which depict an IEA

• Pollution Game 2 (analogue to Chicken Game)

• Which equilibrium will be
• played?
• Extensive form game
• sequential choice leads
• to a unique Nash Equilibrium
• Backwards induction
• First-Mover advantage

pollute
Country 2
(-4, -4)
pollute
abate
(5, -2)
Country 1
(-2, 5)
pollute
abate
(3, 3)
abate
17
Games which depict an IEA

• First-mover advantage
• The lady who pushes her childs stroller across
  the intersection in front of a car that has
  already come to a dead stop is in no particular
  danger as long as she sees the driver watching
  her even if the driver prefers not to give her
  the right of way she has the winning tactic
  Schelling (1966). Arms and Influence. New have
  Yale University Press, pp 117-118

18
Games which depict an IEA

• Pollution Game 2 (analogue to Chicken Game)
• How to figure out which strategy will be played
  when the game is played simultaneously?
• Assume a probability distribution over each
  strategy.

Country 2
y
1-y
gt Nash equilibrium in mixed strategies.
x
Country 2
1-x
19
Games which depict an IEA

• Pollution Game 3 (analogue to the Assurance
  Game)

Country 2

• Cost of contribution 8
• Benefit of contribution (only if both countries
  contribute) 12
• Threshold effect only when the contribution to
  a public good reaches a certain level (2 players
  contributing) then benefits will flow.
• again, there are 2 Nash equilibria
• Cooperative solution is stable

Do not contribute
Contribute
Do not contribute
Country 1
Contribute
20

• different payoff structures lead to different
  equilibria.
• How can international treaties be structured,
  such that the mutually preferred outcome is an
  equilibrium?

21
Repeated games

• Until now we only looked at one-shot games, what
  happens when games are played repeatedly?
• Players have to take into account the future
  actions of other players
• Players act differently also cooperative
  solutions are possible.
• Outcome depends on the future valuation of the
  players (discount rate)
• Infinitely repeated games
• Finitely repeated games

22
Repeated games (Infinitely repeated games)

• There are two possible actions good and bad
• Examples of strategies
• Stable (always plays bad)
• Pendulum (alternately good and bad, irrespective
  of opponent)
• Trigger (starts of nice and plays good as long as
  opponent plays good if disappointed plays bad
  forever after)
• Imitate (starts off with good and then observes
  opponent and imitates his action of previous
  period)
• These are strategies where cooperation can be
  sustained.

23
Repeated games (Infinitely repeated games)

• Examples
• Stable vs. Trigger

Pendulum vs. Imitate
Trigger vs. Trigger
24
Multiple players

• Prisoners Dilemma with multiple players, N 10
• Pollution abatement costs 7 and confers a benefit
  of 5 to countries

Number of abating countries other than i
Net benefit when polluting NBP a bK Net
benefit when abating NBA c dK a 0, b
5, c -7, d 5
gt nations will follow their Self-interest and
pollute
25
Multiple players

• Prisoners Dilemma with multiple players, N 10
• Another payoff structure (a12, b 3, c -7, d
  7)

Number of abating countries other than i

• Threshold if less than 3 players abate no one
  will abate
• If more than 3 players abate,
  everyone will abate
• 2 Nash Equilibria

26
Multiple players and partial agreements

• If multiple players are involved also partial
  cooperation is possible.
• In this case, an agreement must be self-enforcing
• Self enforcing no participant has an incentive
  to deviate and no non-participant has an
  incentive to accede to the agreement.

27
Which conclusions can be drawn from Game Theory
for the functioning of IEAs?

• Signatories and non-signatories would both do
  better if all cooperate (like in the prisoners
  dilemma)
• Non signatories do better than the signatories,
  because they free-ride (similar to the chicken
  game)
• Full cooperation is not usually stable (it is not
  self enforcing)
• Fraction of members decreases when there are many
  countries affected.
• Breadth versus depths of an agreements

28
Which conclusions can be drawn from Game Theory
for the functioning of IEAs?

• Predictions for self-enforcing agreements are
  rather pessimistic.
• Since treaties must be self-enforcing, they must
  do more than simply telling countries what to do.
  Treaties must manipulate the incentive structure
  of countries (Barrett, 2003 18)
• How can the incentive structure be manipulated?

29
Which conclusions can be drawn from Game Theory
for the functioning of IEAs?

• Existence of an external institution which
  coordinates the process.
• Leadership role by one important nation.
• Define minimum participation threshold.
• side payments to induce cooperation of the non
  contributors (Montreal protocol)
• Establish more agreements than only one. For
  instance for each group of countries which has
  particular characteristics Kyoto protocol and
  developing countries
• Linkage of negotiations and linked benefits.

30
Literature suggestions

• Introduction to Game theory
• Gibbons, Robert (1992). A Primer in Game Theory.
  Harvester Wheatsheaf
• Binmore, Ken (1991). Fun and Games. A text on
  game Theory. D.C. Heath
• Game Theoretic Literature on IEAs
• Barrett, Scott (1994a). Self-Enforcing
  International Environmental Agreements. Oxford
  Economic Papers, 46, 878-894.
• Barrett, Scott (1998b). Political Economy of the
  Kyoto Protocol. Oxford Review of Economic
  Policy, 14, 20-39
• Barrett, Scott (2003) Environment Statecraft.
  The strategy of environmental treaty making.
  Oxford University Press
• Cesar, H. and de Zeeuw, A. (1996). Issue linkage
  in global environmental problems. In Xepapadeas,
  A., ed. Economic Policy for the Environment and
  Natural Ressources. E. Elgar, Cheltenham.
• Carraro, Carlo and Dominico Siniscalco (1993).
  Strategies for the International Protection of
  the Environment. Journal of Public Economics,
  52, 309-328.
• Carraro, Carlo (ed., 2003) Governing the Global
  Environment. E. Elgar, Cheltenham,
• Finus, M. (2003). Stability and design of
  international environmental agreements The case
  of transboundary pollution. In Folmer, H. and
  Tietenberg, T. ed. International Yearbook of
  Environmental and Resource Economics, 2003/4, E.
  Elgar, Cheltenham
• www.feem.it Fondazione Eni Enrico Mattei has
  many working papers on this topic.

31
Literature suggestions

• Experimental Game Theory
• Axelrod, Robert (1986). The evolution of
  cooperation. New York Basic Books
• Benz, Matthias and Meier, Stephan (2008). Do
  People Behave in Experiments as in the Field?
  Evidence from Donations. Experimental Economics.
  Volume 11, Number 3
• Camerer, Colin (2003) Behavioral game
  theory   experiments in strategic interaction.
   New York, NY   Russell Sage Foundation
• Diekmann (1993) .Cooperation in an Asymmetric
  Volunteers Dilemma Game Theory and Experimental
  Evidence. International Journal of Game Theory.
  Volume 22, Number 1
• Fischbacher, Urs Gächter, Simon Fehr, Ernst
  (2001). Are people conditionally cooperative?
  Evidence from a public goods experiment. pp
  397-404
• Fischbacher, Urs and Gächter, Simon (2005).
  Heterogeneous social preferences and the dynamics
  of free riding in public goods. IEW Working
  Paper, iewwp 261, Institute for Empirical
  Research in Economics- IEW
• Fehr, Ernst and Fischbacher, Urs (2004). Social
  norms and human cooperation. Trends in Cognitive
  Science, Volume 8, Issue 4, pp. 185-190
• Schelling, Thomas (1997).  The strategy of
  conflict Cambridge, Mass.  Harvard Univ. Press 
• Sigmund, Karl and Nowak, Martin (1999).
  Evolutionary Game Theory. Current Biology, Volume
  9, Issue 14, p. 503-505