Game Theory and Social Interactions

Week 4: Social Interactions

• This lecture will explore the area of game theory.
• Game theory will be used to understand how people interact based on constraints, motives, and beliefs on what others will do.
• Equilibrium outcomes will be examined in games such as the invisible hand, prisoners' dilemma, ultimatum, and public goods.

Overview

• Economy is built on direct and indirect interactions among people.
• Social interactions can result in mutual gains such as gains from trade.
• Distribution of gains often causes conflict.
• Individual pursuit of self-interest can yield socially beneficial outcomes, like the "invisible hand" theory.
• Social dilemmas exist where cooperation is better than individual action; non-cooperation leads to worse outcomes for all.
• Social dilemmas occur because people don't consider external effects of their actions on others.
• Free riding arises when people benefit from others' contributions without contributing themselves.
• Public goods are cooperative projects where free riding prevents efficient market outcomes.

Social Dilemmas

• Social dilemmas refer to situations where individual actions driven by self-interest result in socially suboptimal outcomes, such as climate change, traffic jams, and the tragedy of the commons.
• These dilemmas frequently arise, reducing the quality of life for individuals and communities.
• Public policies are often needed to address these dilemmas.

Resolving Social Dilemmas

• Altruistic preferences involve individuals caring about the implications for others
• Community institutions allow local groups to create rules to regulate behavior such as customary rules in Valencia, Spain.
• Public policies such as taxes, government spending, laws, and regulations, such as fishing quotas, help resolve social dilemmas.

Game Theory

• Game theory presents strategic interaction models.
• It mathematically models interactions between rational decision-makers to analyze social interactions in economics, biology, politics, and military strategy.
• Social interaction is when one person's actions affect other people's outcomes.
• Strategic interaction involves participants being aware of the ways their actions affect others and vice versa.
• Strategy refers to an action a person may take when they are aware of the mutual dependence of results for themselves and others.

Game Elements

• A game describes social interactions through players, feasible strategies, information, and payoffs.
• Players are those involved in the interaction.
• Feasible strategies are the actions each player can take.
• Information is what each player knows when choosing their action.
• Payoffs are the outcomes for every possible combination of actions.

Crop Choice Game

• Two framers make a decision to plant either rice or cassava.
• Specialization provides a benefit from producing only one crop due to tools and investment.
• Anil's land better suits cassava and Bala's land is better suited for rice.
• The benefit of interaction: If they don't engage in strategic interaction, but produce both crops for subsistence, there benefits with be lower.
• Price determined by supply: If they both bring the same crop to market the price of that crop will fall due as there will be a glut.
• Each farmer doesn't know what the other chooses in advance
• Payoffs depend on market prices and quality of land
• Preferences and beliefs: Players seek to maximize their own payoff, are rational egoists, and believe the other's preferences are the same.

Payoff Matrix

• Illustrates payoffs (numbers) for all strategy combinations by two or more players.

Best Responses

• Payoff matrixes analyze players' actions based on knowledge of what the opposing player will do.
• Best response is the strategy yielding the highest payoff, given other players' strategies.

Dominant Strategy

• This is the action that provides the highest payoff for a player, no matter what the other players do.
• Note that a dominant strategy need not always exist - it depends on how the payoffs are arranged.

Dominant Strategy Equilibrium

• This is an outcome of a game when every player opts for their dominant strategy, resulting in a self-perpetuating situation.

Invisible Hand

• Self-interest pursuit, disregarding others can be considered morally bad, can result in socially desirable outcomes.
• Both players ended up both getting the highest payoff in pursuing their self-interest (4)
• This strategy yielded the largest total payoffs for the two farmers combined (social optimum 4+4)

The Prisoner's Dilemma

• This is a textbook example where self-interest leads to non-optimal outcomes.
• Optimal outcome requires cooperation between the two players but co-operation is difficult and requires trust.
• The dominant strategy, which results in both getting 10 years in jail, is not optimal, as they could have kept silent, resulting in 1 year each.

Golden Balls Game

• A video shows an application of the Prisoner's Dilemma
• The participants must choose between splitting the cash or taking all the cash and they risk losing everything depending on what the other person decides

Pesticide Game (Application of prisoners' dilemma)

• Two farmers, Anil and Bala, must decide what pesticide to use.
• The options are Terminator which is cheaper, but contaminates the water, and Integrated Pest Control (IPC) which is no water contamination.
• It is a prisoners' dilemma type game as pursuing self interest results in dominant equilibrium where A and B both user Terminator.
• However, if they trusted each other and cooperated they would both use IPC and achieve a socially optimal outcome.

Altruism Impact

• Social preferences, like altruism, mean people care not just for themselves, but also for others, potentially altering game outcomes.
• If Anil cared sufficiently about the harm that he would inflict on Bala by using Terminator when Bala was using IPC, then IPC would have been Anil's best response to Bala's IPC.

Altruistic Preferences as Indifference Curves

• Economic models using the feasible frontier-indifference curve assume self-interested preferences.
• Altruism, or care for the welfare of others, is one such social preference.
• Say, if Anil was given a ticket for the national lottery, and it won a prize of 10 000 rupees, as he could also share some of it with his neighbour Bala.
• Graphically – the points along the feasible frontier shows a zero sum game: Moving along the frontier the sum of any loss for Anil and any gain for Bala is zero.
• An individuals indifference curve would be less steep if there were those for those they loved.

Impact of Altruism on the Prisoner's Dilemma

• Altruism involves someone caring about others' well-being, which can change game outcomes.
• With altruism, downward-sloping indifference curves shift to (I, I) as preferred, even if it means a lower individual payoff but higher collective benefit.

Public Goods

• Public goods are those for which one person's use doesn't reduce availability to others.
• Four small farmers share the benefits of a common irrigation system.
• Farmers contribute a personal cost ($10 each) to maintain the system to improve crop flow.
• For each $10 contributed the improved flow of waters benefits all four farmers, due to improve crop yield.
• Each farmer receives a benefit of $8 for every $10 contributed.

Public Goods Game

• Take one farmer, Kim, who can either contribute (cooperate) or not contribute (defect).
• Option 1: If Kim makes no contribution herself, her total payoff is $16
• Option 2: If Kim decides to contribute, she will receive an additional benefit of $8 but she will incur a cost of $10, so her total payoff is $14.
• She will have an incentive not to contribute the the public good and be a free rider - gaining a payoff of $16 instead of $14

Free-Rider Problem

• In these situations, Kim's payoff is lower if she contributes, creating a free-rider problem due to monetary incentives.
• The result is a prisoner's dilemma, where self-interest leads to less than optimal outcomes.
• Dominant strategy equilibrium in which no one contributes - However, if all cooperated, everyone benefits.
• Altruism could help to solve the free rider problem: As Economist Elinor Ostrom showed sustainable use of common property may be enforced by actions that clearly deviated from the hypothesis of material self-interest.

Summary of Games Analyzed

• Crop choice game (Invisible hand): Dominant strategies result in mutually beneficial outcomes.
• Pesticide game (Prisoner's dilemma): Dominant strategy equilibrium results in a sub-optimal outcome for all players.
• Irrigation game (Public goods): Individuals' incentive to free ride leads to a sub-optimal outcome.

Note on Repeated Games

• Earlier examples have been "one-shot" games, while ongoing relationships are a social interaction not captured.
• In real life there are ongoing relationships: There is a chance all the farmers will be thinking about the next season.
• Repeated interactions boost positive outcomes via social norms, reciprocity, and peer punishment.
• Selfish behavior in one instance can have consequences for future interactions, maybe altering strategy.

Ultimatum Game and Social Preferences

• This is a sequential game in which two players (Proposer and Responder) decide how to divide a cash prize.
• The game examines social preferences.

Game Structure Explained

• The Proposer is given money and decides how much to offer the Responder.
• The Responder accepts or rejects the offer.
• If the offer is rejected, both individuals get nothing.
• If it is accepted, the split is implemented and both individuals get something.

Responders

• A responder focused solely on rational self-interest always accepts a positive offer over nothing.
• Social preference involves a Responder potentially sacrificing payoff to punish a Proposer's unfair offer, acting on violated fairness norms.
• Experimental data shows people act with social preferences and will pay to penalize unfairness.

Responder’s Reciprocity Motive

• This is a preference to be kind to helpful individuals and withhold help to people who are unhelpful.
• Rejection means both sides get nothing, implies satisfaction from punishing the Proposer outweighs accepting the offer.

Respondent's Rejection Equation

• An equation example is a 50-50 norm.
• Total satisfaction relies on satisfaction at rejecting an offer and gain from accepting an offer.

Calculated Minimum

• Acceptable responders reject offers with a lower value that satisfaction from rejection.
• $25 would be the lowest amount a responder would accept if offered by the proposer.
• A more caring Responder about reciprocity would prompt higher offers from the Proposer.

Experimental Results from Ultimatum Game

• In these games the responder would accept any offer with self-interest.
• Experiments have shown that low offers are often rejected as a punishment.
• Kenyan farmers are unwilling to accept low offers while US students are more willing to accept the lower offers.

Expected Payoffs

• Calculation example shows (payoff if accepted) * (probability of acceptance).
• An Example is that in Kenya: 60-40 split maximizes Proposer's payoff, whereas In the US: 70:30 optimizes it.

Concluding Note: Unintended Consequences

• Day-care fines (approx. $3) replaced social incentives, increasing lateness.
• Before lateness fees were priced at zero and after they were about $3. As a result frequency doubled.
• Before most people just had it in them that is was the right thing to do/moral obligation
• Imposing fines can signal as a "market", where tardiness has a purchasable price.
• Replacing these incentives is where the fines and prices have effects - creating a new social norm where parents continued to pick up late even when fines were removed.