Game Theory in Climate Change Economics

菁英小记者_Sihan zhao 编辑_刘煜

Introduction

Climate change is one of the most important global challenges today,yet governments have failed to respond to it.In this paper,we review the fundamental concepts of game theory and then apply them to study why countries struggle to mitigate climate change.

Sources: Game theory background is taken from [1].Climate change background is taken from [2].

Game Theory Background

Game theory is a theoretical tool that analyzes strategic interactions among at least two players,such as people,firms,countries,and so on.A game is composed of several fundamental components: utilities,players,and strategies.In economics,utility identifies each player’s preference.It may represent money or profit,happiness,or satisfaction gained from the process or the result of a game. Each participant can choose a strategy from a given set.Once every player has chosen a strategy,the game specifies the resulting utility for each player.Players try to choose their strategy such as to maximize their utility.The basic assumption is that players are rational and all the utilities are known to all players.

For example,the well known Prisoners’ Dilemma where two criminals were arrested for committing a crime.However,the authorities lacked enough evidence to convict them.Therefore they were interrogated in separate rooms where they were both asked to defect.If neither criminal admits the crime,they will both be charged with a minor offense.But,if both criminals defect,then they will receive a reduced term for their cooperation.If criminal A defects and criminal B does not,then criminal A will be released,while B will be sent to jail due to A’s testimony,which also applies if B defects and A does not.In this example,strategy C represents corporation,while strategy D represents defect for both players.In this payoffmatrix,the first entry in each box represents the payoff for player A and the second entry in the boxes represents the payoff for player B.

Dominance

Dominance is a property that takes place when a strategy earns a better utility than another strategy for one player,no matter which strategies the opponents choose.This property can be best explained through this payoff matrix example.In player 1’s situation,A is a better strategy than strategy B because the payoff 3 in the first entry of the upper left box is better than payoff 1 in the first entry of the bottom left box,while the payoff 5 in the first entry of the upper right box is better than the payoff 4 in the first entry of the bottom right box.Therefore,player 1 will select strategy A instead of strategy B no matter which strategy player 2 selects.As a result,strategy A dominated strategy B: strategy U is a dominating strategy.While in player 2’s situation,none of the strategies are dominated or dominating because strategy C is better when player 1 selects A but D is better when player 1 selects B.

Iterated Dominance

The iterated dominance procedure (also called iterative removal of strictly dominated strategies) is a procedure that eliminates all dominated strategies until both players reach the ultimate best response.First,the players will cross out all the dominated strategies,remaining with the non-dominated strategies.We call R1 this set of non-dominated strategies.Then,we repeat the process.Throughout this procedure,players are interacting in “reducing” the game.Both players will continue with the process of eliminating the other dominated strategies under the current situation after the game is “reduced” to a smaller set of strategies,leading to R2.Then continuing on,both players will identify smaller and smaller strategy sets,R3,R4,and so on until no more strategies can be reduced.This process is known as the iterated dominance procedure.For some but not all games,it leads to a single strategy profile R.

Continuing on with the game,both players deduce that strategy A and X are out of consideration.Knowing that player 1 will play B,the best response for player 2 is to play Z.Therefore,strategy Y is dominated by strategy Z for player 2.As a result,strategy B and Z in the right lower box is the resulting strategy profile R that survived the procedure.

Best Response

Nash Equilibrium

Nash Equilibrium is a strategy profile where each player plays the best response to the other players.In this circumstance,no player would regret their choice of strategy,or be incentivized to deviate from it,even after learning the strategies of the other players.Nash equilibria often exist in games even when there are no dominated strategies and thus the iterated dominance procedure is not useful.Especially in games which have a unique Nash equilibrium,that profile is often seen as a reasonable prediction of the outcome among rational players.

This concept of Nash Equilibrium is one of the contributions in the field of Game Theory presented by John Nash,a Nobel winner for economics.For example,a game occurs in the setting in which the players know each other before the game.They are able to form accurate beliefs on each other,thus both are able to prepare a best response based on previous understanding of the other.

Tak ing the famous Pr isoners’ Dilemma into examination,in which both players face either defect or confess.Despite the other player’s strategy,strategy D is the best response for both players.Therefore,strategy D is the Nash Equilibrium of the Prisoner’s Dilemma.

Application to Climate Change Mitigation

The Climate Change Issue

Greenhouse gasses (GHGs) are gasses that impact the earth's absorption and release of energy,thus disturbing the energy balance on earth.There are a few well known greenhouse gasses: carbon dioxide,methane,and nitrous oxide,which are generally generated from burning fossil fuels,chemical reactions,and industry plants.As known,the sun emits radiation to earth's atmosphere,where the emitted greenhouse gasses trap the heat inside the atmosphere,which leads to global warming.We refer to [2]for background on the physics of climate change.

Climate change is a problem that arises because every nation allocates resources for their self-interest.At the same time,it affects all nations collectively.Historically,governments have struggled to respond to climate change.There are two fundamental problems that impact the mitigation of climate change:

Every country makes decisions to allocate resources for their own benefits and to take a share from the atmosphere,which is an open-access resource.Openaccess resources are defined as resources that are not the private property for any individual to demonstrate full control over,it is free for everyone to use: no country can restrict another country’s access.

Greenhouse gasses are a negative externality issue,which occurs when the production or consumption decisions of an individual agent impose an unintended consequence on the utility of another agent,while a reparation will not be made by the generator of the side effect to the party being affected.Being a negative externality issue,the emissions of greenhouse gasses impose a negative,unintended damage on others.Markets fail in the presence of negative externalities because the consequences are not taken into account before actions are taken,since there will not be a remuneration or penalty for the externality.Indeed,even though the effects of climate change affect everyone and the future generations,there is no immediate cost for the unintended consequences.When countries are producing GHG emissions,they would only consider their individual costs and utility,ignoring additional side effects on others.

Economists have been conceptualizing climate change mitigation as a good that can be produced and consumed.In order to supply this product,a nation must contribute effort.Consuming the product is passive.If a nation decides to reduce the quantity of GHG emitted,all nations will benefit from slowing climate change.On the other hand,the country that has decided to reduce its emissions loses utility due to the mitigation effort (reduced consumption,financial costs,etc).

Below,we study a model for this situation in the market system and to show how the negative externality issue leads agents to make far less efforts to mitigate climate change than would be socially optimal.