Chapter 4 - Social Interactions & Game Theory Cartes

Beneficial Self-Interest (The Invisible Hand)

Under proper market conditions, individual self-interest can promote societal welfare (e.g., entrepreneurship, technological innovation, specialization).

Harmful Self-Interest (Social Dilemmas)

When individuals pursue private gains without accounting for external effects on others, individual rationality leads to collective failure.

A social dilemma

A social dilemma is a situation in which actions taken independently by self-interested individuals result in an outcome that is inferior to another feasible outcome that could have been achieved if people had acted cooperatively.

Climate Change & Fossil Fuels

Individual nations benefit from cheap fossil fuels, but global carbon emissions create severe climate externalities.

Traffic Congestion

Every driver prefers taking their car, creating gridlock for everyone.

Tragedy of the Commons

Common property or shared environmental resources (e.g., global fisheries, pastures) are overexploited because no single user bears the full cost of depletion.

Free Riding

Individuals benefit from a public good (e.g., street lighting, national defense, group projects) without contributing to its cost.

Social Interaction

Any situation involving two or more individuals where each person's actions affect both their own outcome and others' outcomes.

Strategic Interaction

A social interaction where players are explicitly aware of how their actions affect others and how others' actions affect them.

Strategy

An action or complete plan of action that a player can choose when engaging in a game.

Four elements of a game

Players, Feasible Strategies, Information, Payoffs

Players

Who is involved in the interaction?

Feasible Strategies

What actions can each player take?

Information

What does each player know when choosing their action?

Payoffs

What numerical outcome/utility does each player receive for every possible combination of strategies?

Best Response

The strategy that yields the highest payoff for a player, given the specific strategy chosen by the other player(s).

Dominant Strategy

An action that yields the highest payoff for a player regardless of what strategy the other player chooses.

Dominant Strategy Equilibrium

An outcome of a game in which every player chooses their dominant strategy.

Nash Equilibrium

A set of strategies (one per player) such that each player's strategy is a best response to the strategies chosen by all other players.

IPC (Integrated Pest Control)

Environmentally friendly, inexpensive, but requires effort.

Terminator (Chemical Pesticide)

Highly effective for the user, but pollutes the shared groundwater supply.

Characteristics of the Prisoners' Dilemma

Dominant Strategy, Suboptimal Equilibrium, Pareto Inefficiency

Why Does the Prisoners' Dilemma Occur?

Self-Regarding Preferences, Lack of Accountability / Externalities, Non-Binding Commitments

Self-Regarding Preferences

Players care only about their own payoffs.

Lack of Accountability / Externalities

Neither player pays for the environmental damage caused by Terminator.

Non-Binding Commitments

Players cannot enforce an agreement to use IPC beforehand.

Lab Experiments

Highly controlled environments, replicable, isolated variables.

Field Experiments

Real-world settings observing actual human decisions.

Selfish Preferences

U (A) = y (A) (Anil's utility depends only on his own income; indifference curves are vertical lines).

Altruistic Preferences

U (A) = f(y (A), y (B)) (Anil cares about Bala's payoff; indifference curves are downward-sloping and convex).

Inequality Aversion

A dislike of outcomes where payoffs are distributed unequally.

Reciprocity

A desire to be kind to those who are helpful and to punish those who act uncooperatively.

Social Norms

Shared understandings of acceptable behavior within a community.

One-shot game

In a one-shot game, players interact once and never meet again.

Repeated games

In repeated games, ongoing interactions allow players to build reputations, reward cooperation, and enforce peer punishment.

Without Punishment

Initial contributions average around 50%, but decay over repeated rounds toward 0% as contributors react against free-riders.

With Peer Punishment

When contributors can pay $1 to impose a $3 penalty on free-riders, contributions rebound dramatically and remain near 100% across global experiment sites.

Sequential games

In sequential games, players take turns making decisions (represented using a Game Tree).

Rules of the Ultimatum Game

Proposer receives a sum of money (e.g., $100) and proposes a split y to the Responder.

Responder can either Accept (both get the proposed split) or Reject (both receive $0).

Self-Interested Responder

Will accept any offer y > 0 (since y > 0).

Self-Interested Proposer

Anticipates this and offers the minimum possible amount epsilon o 0, keeping $100 - epsilon.

Offers

Proposers routinely offer 40% extto 50% of the pie.

Rejections

Responders routinely reject offers below 30%, preferring to receive $0 in order to punish unfair Proposers (reciprocity & inequality aversion).

Cross-Cultural Evidence

Tested across US university students and Kenyan farmers; offers reflect local social norms of fairness.

Impact of Competition

Adding a second competing Responder causes rejections to plummet, moving the outcome close to the self-interested prediction.

Coordination Trap

If both countries act out of narrow self-interest, (BAU, BAU) is a Nash Equilibrium. Once stuck there, neither country can unilaterally switch to Restrict without suffering the "WORST" payoff.

Role of Institutions

International climate treaties (e.g., Paris Agreement) change the rules, expectations, and payoffs, enabling countries to coordinate and shift to the superior Nash Equilibrium (Restrict, Restrict).

Strategic Interactions

Modeled as games with players, strategies, information, and payoffs.

Social Dilemmas

Occur when dominant strategies or self-interested Nash equilibria produce Pareto-suboptimal outcomes.

Overcoming Dilemmas

Achieved through social preferences (altruism, reciprocity), peer punishment, repeated interactions, and institutional policy.