Unit 4: Strategic Interaction and Social Dilemmas
The Stern Review on the Economics of Climate Change (2006) highlighted the critical need for prompt action to
address climate change, arguing that the benefits of early intervention far surpass the costs of inaction. This stance
was reaffirmed by the UN Intergovernmental Panel on Climate Change (IPCC) in 2014, which advocated for
substantial reductions in greenhouse gas emissions through the adoption of new energy technologies, reducing the
impact of agriculture, and enhancing the efficiency of existing technologies.
Despite this, the global response has been marked by conflicting national interests and varying levels of
commitment. The 2015 Paris Agreement made significant strides by setting the goal of limiting global temperature
rise to 1.5°C and requiring countries to implement domestic measures to reduce emissions. However, by 2022, the
UN warned that these efforts remained inadequate and needed to be significantly strengthened over the next eight
years to meet the necessary scale and pace of emission reductions.
Climate change is a classic example of a social dilemma, where individual actions, driven by personal interests, lead
to collectively suboptimal outcomes. This concept was famously discussed by Garrett Hardin in "The Tragedy of the
Commons" (1968), which illustrated how common resources (e.g. the earth’s atmosphere or fish stocks) are prone
to overexploitation unless access is regulated.
Historically, societies have developed various mechanisms to address such dilemmas. For instance, altruism
(individuals who are willing to bear a cost to benefit somebody else) and government policies have played crucial
roles. Governments have successfully implemented quotas and taxes to manage resources and waste, whilst local
communities have also established institutions to regulate behaviour.
Successful international agreements, like the Montreal Protocol, demonstrate that collective action can effectively
tackle global environmental issues. The challenge remains to apply similar principles to climate change. Game theory
can help understand social interactions and why social dilemmas occur, providing insights into potential solutions.
However, the complexity of climate change requires more than just altruistic behaviour; it necessitates robust
government policies and international cooperation.
Game Theory: A Model of Social Interactions:
Social interactions involve multiple people whose actions affect both their own and others' outcomes. When
participants are aware of how their actions affect others and vice versa, it's called a strategic interaction. A strategy
is an action plan chosen with this mutual dependence in mind. Game theory, a branch of mathematics, models these
strategic interactions by specifying the players, feasible strategies, order of play, information available, and pay-offs
for each action combination.
To illustrate, consider two farmers, Anil and Bala, deciding whether to grow rice or cassava. Anil's land is suitable for
both crops, while Bala's land is better for rice. They sell their crops at a village market where prices depend on the
supply of each crop. They choose independently without coordinating, reflecting real-world scenarios like climate
change where many individuals act independently.
This situation can be modelled as a game:
• Players (who is interacting): Anil and Bala.
• Feasible strategies (what actions are open to the players): Growing rice or cassava.
• Order of play (when the players chose their action): Simultaneous decisions.
• Information (what each player knows when making their decision): Each farmer knows the pay-offs for all
possible outcomes.
, • Pay-offs (what the outcomes will be for each possible combination of actions): Incomes from selling crops,
influenced by market prices.
The model assumes a one-shot, simultaneous
game where both farmers know the outcomes
of each strategy combination. If both grow the
same crop, market saturation lowers their total
income. Optimal pay-offs occur when Anil grows
cassava and Bala grows rice, leveraging their
land's suitability.
Game theory helps predict their choices and the
resulting outcomes, offering insights into
Figure 4.1: Planting rice or cassava: social Figure 4.2: The pay-offs from crop
choice.
strategic decision-making in various social
interactions between Anil and Bala.
interactions, including global challenges like
climate change.
The Nash Equilibrium: The Best Response in the Rice-Cassava Game:
Game theory helps describe and predict outcomes of social interactions by using the concept of best response,
which is the strategy that yields the highest payoff for a player, given the strategies of other players. In the context
of a game between two farmers, Anil and Bala, deciding whether to grow rice or
cassava, the pay-offs for each farmer depend not only on their own choices but also
on the choices of the other farmer, as shown in a pay-off matrix.
If Bala chooses Rice, Anil’s best response is Cassava—that gives him 6, rather than
4.
If Bala chooses Cassava, Anil’s best response is Rice—giving him 6, rather than 5.
If Anil chooses Rice, Bala’s best response is to choose Rice too (4 rather than 3).
Lastly, if Anil chooses Cassava, Bala’s best response is Rice again (he gets 6 rather
than 2).
Figure 4.2b: Finding best responses
Anil and Bala's pay-off matrix reveals that Anil's best response to Bala growing rice
in the rice–cassava game.
is to grow cassava. Conversely, Bala’s best response to Anil growing cassava is to
grow rice. This combination, where Anil grows cassava and Bala grows rice, is an equilibrium because neither farmer
would want to change their decision after seeing the other’s choice. This is called a Nash equilibrium or dominant
strategy equilibrium, where each player's strategy is the best response to the other's strategy and is beneficial for
both.
The Nash equilibrium for this game is (Cassava, Rice), indicating Anil chooses Cassava and Bala chooses Rice. This
equilibrium occurs because Bala, regardless of Anil’s decision, benefits more from choosing Rice, which in turn
makes Anil’s best response to choose Cassava. Thus, independently pursuing their self-interest leads both farmers to
the highest possible pay-off.
This game exemplifies an "invisible hand game," where players independently acting in their own self-interest are
guided to an outcome that is jointly optimal. This reflects Adam Smith’s idea that individual self-interest can lead to
socially desirable outcomes. However, this is not always the case, as some games like the prisoners’ dilemma show
that self-interested decisions can lead to suboptimal outcomes for all involved.
The Stern Review on the Economics of Climate Change (2006) highlighted the critical need for prompt action to
address climate change, arguing that the benefits of early intervention far surpass the costs of inaction. This stance
was reaffirmed by the UN Intergovernmental Panel on Climate Change (IPCC) in 2014, which advocated for
substantial reductions in greenhouse gas emissions through the adoption of new energy technologies, reducing the
impact of agriculture, and enhancing the efficiency of existing technologies.
Despite this, the global response has been marked by conflicting national interests and varying levels of
commitment. The 2015 Paris Agreement made significant strides by setting the goal of limiting global temperature
rise to 1.5°C and requiring countries to implement domestic measures to reduce emissions. However, by 2022, the
UN warned that these efforts remained inadequate and needed to be significantly strengthened over the next eight
years to meet the necessary scale and pace of emission reductions.
Climate change is a classic example of a social dilemma, where individual actions, driven by personal interests, lead
to collectively suboptimal outcomes. This concept was famously discussed by Garrett Hardin in "The Tragedy of the
Commons" (1968), which illustrated how common resources (e.g. the earth’s atmosphere or fish stocks) are prone
to overexploitation unless access is regulated.
Historically, societies have developed various mechanisms to address such dilemmas. For instance, altruism
(individuals who are willing to bear a cost to benefit somebody else) and government policies have played crucial
roles. Governments have successfully implemented quotas and taxes to manage resources and waste, whilst local
communities have also established institutions to regulate behaviour.
Successful international agreements, like the Montreal Protocol, demonstrate that collective action can effectively
tackle global environmental issues. The challenge remains to apply similar principles to climate change. Game theory
can help understand social interactions and why social dilemmas occur, providing insights into potential solutions.
However, the complexity of climate change requires more than just altruistic behaviour; it necessitates robust
government policies and international cooperation.
Game Theory: A Model of Social Interactions:
Social interactions involve multiple people whose actions affect both their own and others' outcomes. When
participants are aware of how their actions affect others and vice versa, it's called a strategic interaction. A strategy
is an action plan chosen with this mutual dependence in mind. Game theory, a branch of mathematics, models these
strategic interactions by specifying the players, feasible strategies, order of play, information available, and pay-offs
for each action combination.
To illustrate, consider two farmers, Anil and Bala, deciding whether to grow rice or cassava. Anil's land is suitable for
both crops, while Bala's land is better for rice. They sell their crops at a village market where prices depend on the
supply of each crop. They choose independently without coordinating, reflecting real-world scenarios like climate
change where many individuals act independently.
This situation can be modelled as a game:
• Players (who is interacting): Anil and Bala.
• Feasible strategies (what actions are open to the players): Growing rice or cassava.
• Order of play (when the players chose their action): Simultaneous decisions.
• Information (what each player knows when making their decision): Each farmer knows the pay-offs for all
possible outcomes.
, • Pay-offs (what the outcomes will be for each possible combination of actions): Incomes from selling crops,
influenced by market prices.
The model assumes a one-shot, simultaneous
game where both farmers know the outcomes
of each strategy combination. If both grow the
same crop, market saturation lowers their total
income. Optimal pay-offs occur when Anil grows
cassava and Bala grows rice, leveraging their
land's suitability.
Game theory helps predict their choices and the
resulting outcomes, offering insights into
Figure 4.1: Planting rice or cassava: social Figure 4.2: The pay-offs from crop
choice.
strategic decision-making in various social
interactions between Anil and Bala.
interactions, including global challenges like
climate change.
The Nash Equilibrium: The Best Response in the Rice-Cassava Game:
Game theory helps describe and predict outcomes of social interactions by using the concept of best response,
which is the strategy that yields the highest payoff for a player, given the strategies of other players. In the context
of a game between two farmers, Anil and Bala, deciding whether to grow rice or
cassava, the pay-offs for each farmer depend not only on their own choices but also
on the choices of the other farmer, as shown in a pay-off matrix.
If Bala chooses Rice, Anil’s best response is Cassava—that gives him 6, rather than
4.
If Bala chooses Cassava, Anil’s best response is Rice—giving him 6, rather than 5.
If Anil chooses Rice, Bala’s best response is to choose Rice too (4 rather than 3).
Lastly, if Anil chooses Cassava, Bala’s best response is Rice again (he gets 6 rather
than 2).
Figure 4.2b: Finding best responses
Anil and Bala's pay-off matrix reveals that Anil's best response to Bala growing rice
in the rice–cassava game.
is to grow cassava. Conversely, Bala’s best response to Anil growing cassava is to
grow rice. This combination, where Anil grows cassava and Bala grows rice, is an equilibrium because neither farmer
would want to change their decision after seeing the other’s choice. This is called a Nash equilibrium or dominant
strategy equilibrium, where each player's strategy is the best response to the other's strategy and is beneficial for
both.
The Nash equilibrium for this game is (Cassava, Rice), indicating Anil chooses Cassava and Bala chooses Rice. This
equilibrium occurs because Bala, regardless of Anil’s decision, benefits more from choosing Rice, which in turn
makes Anil’s best response to choose Cassava. Thus, independently pursuing their self-interest leads both farmers to
the highest possible pay-off.
This game exemplifies an "invisible hand game," where players independently acting in their own self-interest are
guided to an outcome that is jointly optimal. This reflects Adam Smith’s idea that individual self-interest can lead to
socially desirable outcomes. However, this is not always the case, as some games like the prisoners’ dilemma show
that self-interested decisions can lead to suboptimal outcomes for all involved.
