Eco slides W5 - Lecture notes 5 PDF

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Week 5_ Unit 4 SOCIAL INTERACTIONS

OUTLINE A. Introduction B. Game theory and social dilemma C. Resolving social dilemmas

A. Introduction

The Context for This Unit • Previous models of choice did not depend on others’ decisions. (Unit 3) • Individuals motivated by self-interest can produce outcomes that are beneficial for society e.g. entrepreneurship, innovation. (Unit 1)

• However, self-interest can also be harmful to society. • Why do these problems arise? • What can we do about it?

This Unit • Social dilemma occur when people do not take adequate account of the effects of their decisions on others, whether these are positive or negative. • Actions taken independently by self-interested individuals result in a socially suboptimal outcome e.g. traffic jams, climate change. •

•

Tragedy of the Commons: Common property or common resources are often overexploited Free riding: Benefiting from the contributions of others to some cooperative project without contributing oneself.

• We look at situations resulting in social dilemmas and how people solve them (or not solve them). • We will use the tools of game theory to model social interactions and explain social dilemmas.

B. Game theory and social dilemma

Social and Strategic Interactions • Social interaction: A situation involving more than one person/party, where one’s actions affect both their own and other people’s outcomes. • Strategic interaction: A social interaction where people are aware of the ways that their actions affect others. • Strategy: Action(s) that people can take when engaging in a social interaction. • Game: A model of strategic interaction that describes the players, the feasible strategies, the information that the players have, and their payoffs. • Game theory is a set of models of strategic interactions. It is widely used in economics and elsewhere in the social sciences.

Invisible Hand Game (1) • Two farmers decide which crop to specialize in. • They interact only once (one-shot game). • They decide simultaneously. 1. Players – Anil and Bala. 2. Feasible strategies – Rice or Cassava 3. Information – Each farmer does not know what the other chose. 4. Payoffs – depend on market prices and quality of land.

Invisible Hand Game (2) • Best response: Strategy that yields the highest payoff, given the other player’s strategy •

If Bala grows rice, Anil’s best response is to grow cassava. If Bala grows cassava, Anil’s best response is to grow cassava. What are Bala’s best responses?

• Dominant strategy: A best response to all possible strategies of the other player (does not always exist!) •

Anil’s dominant strategy is to grow cassava. Bala’s dominant strategy is to grow rice.

Invisible Hand Game (3) • Dominant strategy equilibrium: An outcome of a game in which everyone plays their dominant strategy •

When Anil and Bala each play their dominant strategy, the outcome is (Cassava, Rice).

• Although they independently pursued their self-interest, they were guided ‘as if by an invisible hand’ to an outcome that was in both of their best interests.

The Prisoners’ Dilemma (1) • All conditions of this game are the same as the invisible hand game except for strategies and payoffs. • Anil’s dominant strategy is to use Terminator. Bala’s dominant strategy is also to use Terminator.

• The dominant strategy equilibrium is (Terminator, Terminator), which is not the socially optimal outcome.

The Prisoners’ Dilemma (2) • The prisoners’ dilemma is a game in which the payoffs in the dominant strategy equilibrium are lower for each player, and also lower in total, than if neither player played the dominant strategy. • In the prisoners’ dilemma, the socially optimal outcome is not achieved. • The contrast between the invisible hand game and the prisoners’ dilemma shows that self-interest can lead to either favourable or unfavourable outcome.

Nash equilibrium Nash equilibrium: A set of strategies (one per player), such that each player’s strategy is the best response to the strategies chosen by everyone else. In a Nash equilibrium, no player has an incentive to deviate unilaterally. NOTE: There may be more than one Nash equilibrium in a game.

Why did we predict this outcome? 1. Players did not place any value on the other’s payoffs. • What if the farmers also care about others’ payoffs? 2. Nobody could make players pay for the consequences of their actions on others. • What if games are repeated, or it is possible to punish free-riders? 3. Players could not coordinate their actions beforehand. • Change the rules of the game (institutions and policies)

C. Resolving social dilemmas

Social Preferences: Altruism • Social dilemmas arise when players only care about their own payoffs. • However, in experiments, many players show altruism by choosing the dominated strategy (e.g. IPC, Deny) in the prisoners’ dilemma game. • Altruism is an example of social preferences, preferences that place a value on what happens to other people, even if it results in lower payoffs for the individual. •

Spite and envy are also social preferences.

• What if Anil and Bala had altruistic preferences?

Altruism in the Prisoners’ Dilemma (1)

• If Anil does not care about Bala’s wellbeing, his indifference curves are vertical, so (T, I) is his most preferred outcome.

Altruism in the Prisoners’ Dilemma (2) • When Anil cares about Bala’s wellbeing, indifference curves are downward-sloping and (I, I) is his most preferred outcome. • If Bala feels the same way, then the two would both choose IPC, resulting in the outcome that both prefer the most. • If people care about one another, social dilemmas are easier to resolve. • However, altruism may not be sufficient with a large group of people.

Social Preferences: Other Types • Reciprocity: Being kind/helpful to others who are kind/helpful, and vice versa. • Fairness (inequality aversion): Disliking outcomes in which some individuals receive more than others • We evaluate whether others have been ‘kind’ or ‘helpful’ according to social norms (common understanding of how to act in situations when one’s actions affect others). These motives affect outcomes in the public goods game and the ultimatum game.

Learning about Preferences Economists sometimes use experiments to learn about preferences.

1. Lab experiments: • Can control participants’ decisions and their outcomes. • Can create a control/treatment group for comparison. • Results can be replicated. • Can control for other variables. 2. Field experiments: • Lab experiments may not predict real-world decision making. • More realistic context in which people make decisions.

Public Goods Game (1) • There are a group of farmers. • Each farmer decides whether to contribute to the public good (e.g. irrigation project) •

Public good is a good for which use by one person does not reduce its availability to others.

• Contributing has a personal cost ($10), but everyone benefits ($8 each).

Public Goods Game (2) • If the farmer only care about their own payoffs, free riding is a dominant strategy for each farmer. •

If all contributed, each gets $22.

• There is a dominant strategy equilibrium: no one contributes and earns zero payoffs, which is a social dilemma. • Public goods game is a prisoners’ dilemma game with more than two people.

Repeated games • Anil and Bala’s game is a one-shot game. • But ongoing relationships are an important feature of social interactions. • Behaving selfishly in one period has consequences in future periods, so it may no longer be a dominant strategy. • Better outcomes can arise in repeated interactions due to social norms, reciprocity, and peer punishment. • We will explore repeated interactions in the public goods game.

Public Goods Game: Experimental Data (1) • The experiments were conducted in cities around the world. • Participants are randomly sorted into small groups of four people. • Participants play 10 rounds of a public goods game, where they decide on a contribution from their $20 to a common pool of money (a public good). • For every dollar contributed, each person in the group receives $0.40, including the contributor. • For example, if you do not contribute, and the other three in your group contribute $10 each, you will get $32 (the initial $20 + 0.4 x $30), and the other three will get $22 ($32 – contribution $10).

Public Goods Game: Experimental Data (2) • Contributions were high in the first period, although they vary across cities. • But contributions remain positive until the tenth period, although they decrease over time. People are not solely selfinterested. • It appears as if participants are punishing free riders by decreasing contributions. Reciprocity is a better explanation than altruism here.

Public Goods Game: Experimental Data (3) • Now participants can identify and anonymously make freeriders pay $3, which cost themselves $1. • With the punishment option available, the contributions increased in most cities. • This experiment illustrates the way that, even in large groups of people, a combination of repeated interactions and social preferences can support high levels of contribution to the public good.

The Ultimatum Game (1) • The most common tool to study social preferences is a two-person one-shot sequential game known as the ultimatum game. • Proposer is given $100 and is told to give a part of $100 to Responder. • Responder can accept or reject the offer. • This game is a strategic interaction.

The Ultimatum Game (2) • The ultimatum game provides insights about sharing the economic rents that arise in an interaction. •

e.g. sharing profit between employer/ employees

• In a world of people who only care about their own payoffs, we can predict: • •

Responder will accept any offer because something is better than nothing. Knowing this, Proposer would offer the minimum possible amount.

The Ultimatum Game: Experimental Data (1) • However, this prediction does not match the experimental data. • Better offers, fewer rejections. • Results differ across the two populations. • Proposer may be motivated by altruism, fairness, social norms, or reciprocity. • Offers are consistent with social preferences, but also with expected payoff maximization.

The Ultimatum Game: Experimental Data (2) • What if we introduce two Responders, instead of one? • Proposer offers a two-way split of $100 to two Responders. • If no one accepts, no one gets anything. • If one accepts, but not the other, that Responder and the Proposer get the split, and the other Responder gets nothing. • If both Responders accept, one is chosen at random to receive the split.

The Ultimatum Game: Experimental Data (3) • The Responder in a competitive situation cannot be sure if rejecting the offer will punish the Proposer, because the other Responder may accept the low offer. • Introducing competition between responders moves outcomes closer to the selfinterested outcome. • Changes in the rules of the game matter.

Coordination Issues • When there is more than one Nash equilibrium and individuals choose independently, the socially optimal outcome may not be selected. • Society could be “stuck” in a suboptimal outcome (rice, cassava) since there is no incentive to unilaterally change one’s action.

Summary 1. Social interactions can be modeled as games. • Players choose best responses to others’ strategies. 2. The invisible hand game illustrates how markets may channel individual self-interest to achieve mutual benefits 2. Social dilemmas e.g. prisoners’ dilemma can be resolved by social preferences, peer punishment, or binding agreements. • The rules of the game also matter for outcomes.

3. Multiple Nash equilibria can cause coordination problems....