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What aspects of environmental problems are applicable to game theory, where the outcome of a decision by one player depends on the decisions of other players

Where pollution splills over national boundaries expenditures by one country on pollution abatement will give benefits not only to the abating country but to others as well. Similarly if a country chooses to do nothing to abate pollution it can obtain benefits if others do so (the free rider problem). Examples include ocean acidification, infectious diseases and climate change.


Explain a simple prisoner's dilemma game for pollution

1. Each player has a simple binary choice selecting to either pollute or abate
2. The game is played once and the players are identical
3. Pollution abatement is assumed to be a public good so that abatement by either country benefits both
4. Before starting the game neither player was abating pollution
5. Hence if neither country abates then costs are zero and net benefits are zero
6. The results are that pollute, pollute is a dominant strategy for either player. It is also a nash equilibrium. It is an inefficient outcome.


What is a chicken game and what are its main results?

A chicken game is a game with a form of prisoner's dilemma game and is a game of daring. By doing nothing both countries are exposed to serious pollution damage and suffer from this at an extra cost. The results are that neither player have a dominant strategy and two nash equilibria emerge.

The indeterminacy that results from a chicken game could be solved through a commitment/reputation mechanism provided that the announcement of a nation commiting to a decision is credible.


What does a leadership game represent and what problems arise?

A leadership game is one in which the pollute, pollute combined strategy yields different outcomes for each nation (-1, -4) because the absolute cost of pollution for some countries is greater than others. The result is then pollute, abate. This can cause a free rider problem and creates an asymmetry in the pay-off matrix.


What is an assurance game?

A game in which each nation contributes to a global public good. If one or neither country contributes then there is no benefit for either country due to the existence of a threshold effect. The threshold effect is that only when the provision of the public good reaches a certain level is there a benefit from the public good. The result is that neither country has a dominant strategy however a cooperative solution is one of the nash equilibria that emerges. If the game is played repeatedly then there is a strong presumption that both countries would contribute.


What are the pay off generating functions in an international game with multiple players?

NBP = a + bK
NBA = c + dK