Collective Action

Social Choice Approach• How the society manages itself?

– Self-intrested, rational agents

• Aggregating rational individual preferences into rational social preferences.

• Rationality: Consistency & Transitivity

• Why do we want to have a social preference?– To determine the outcome– Need a normative justification for choosing a particulat

outcome.

Rational Man & Introduction to the Game Theory

• Situations in which decision makers interact?• Range of situations to which game theory can be

applied:– Firms competing for business,– Political candidates competing for votes,– Jury members deciding on a verdict,– Animals fighting on a prey,– Bidders competing in an auction,– Legislators voting behaviour under pressure from interest

groups,– Role of threats and punishment in long term

relationships…

Game – theoretical Modelling

• Usefulness – > relevant assumptions, purpose dependent,– Shorterst route from Florence to Venice, flatness– Shortest route from Bejing to Havana,

sphericalness,– Climbing to Everest?

• Uncomplicatedness – > only necessary ingredients..

The Theory of Rational Choice• The Decision – maker chooses the best action

according to her preferences, among all the actions available to her.

• The theory is based on a model with two components– Actions: a set consisting of all the actions that, under some

circumstances, are available to the decision maker. Eg. Consumer choice

– Preferences and Payoff Functions: when presented with any pair of actions, decision maker knows which of the pair she prefers + consistent preferences• Preferences are represented with payoff functions, which

associates a number with each action in such a way that actions with higher numbers are preferred. Eg. Utility function (also called Preference Indicator Function)

Strategic Game with Ordinal Preferences

• A Strategic Game consists of:– Set of Players,– Set of Actions for each Player,– For each Player, preferences over the set of action

profiles..

Prisoner’s Dilemma -1-• Two suspects in a major crime are held in

separate cells. There is enough evidence to convict each of them of a minor offence, but not enough evidence to convict either of them of the major crime unless one of them acts as an informer against the other (finks). If both stay quiet each will be conviced of a minor offense and spend 1 year in prison. If one and only one of them finks, she will be freed and used as a witness against the other who will spend 4 years in prison. If they both fink, each will spend 3 years in prison.

Prisoner’s Dilemma -2-

• The situation may be modelled as a strategic game:– Players The Two suspects,– Actions Each Player’s set of actions is (Quiet, Fink),– Preferences Each Suspect’s action profiles from

best to worst: • (Fink, Quiet) => she is freed,• (Quiet, Quiet) => she gets 1 year in prison,• (Fink, Fink) => she get 3 years in prison, • (Quiet, Fink) => she gets 4 years in prison.

Prisoner’s Dilemma -3-

• There are gains from cooperation,• Each player has an incentive to free ride..

Working on a Joint Project -1-• You are working with a friend on a joint project.

Each of you can either work hard, or goof off. If your friend works hard, then you prefer to goof off (the outcome of the project would be better if you worked hard too, but the increment in its value to you is not worth the extra effort). You prefer the outcome of your both working hard to the outcome of your both goofing off (in which case nothing gets accomplished), and the worst outcome for you is that you work hard and your friend goofs off (you hate to be exploited).

Working on a Joint Project -2-

• If your friend has the same preferences, then the game that models the situation you face is:

Some Other Examples

• Duopoly

• Arm’s Race: – Build bombs & Not to build bombs

• Bach or Stravinsky• (Battle of Sexes)• Happier compared tot he situation being alone

What actions will be chosen by the Players in a Strategic Game?

• Nash Equilibrium – In the theory of rational decision maker, each

player chooses the best available action.– In a game, the best action for any given player

depends on the other player’s actions.– So when choosing an action, the player must have

in mind the actions the other players will chose. (She must form a blief!)

– Each players’ blief is derived from her past experience.

What actions will be chosen by the Players in a Strategic Game?

• Nash equilibrium is an action profile a* with the property that no player i can do better by choosing an action different from a* given that every other player adheres to a* too.

• Nash equilibrium action of each player is the best action for each player not only if the other player chooses her equilibrium action but also if she chooses her other action.

• Nash Equilibrium ia designed to model a steady state among experienced players.

• Some games have a single Nash Equilibrium, some possess no Nash Equilibrium, and others have many Nash Equilibria.

Examples of Nash EquilibriumPrisoner’s Dilemma

• The action pair (Fink, Fink) is the unique Nash equilibrium because given that player 2 chooses Fink, player 1 is better off choosing Fink than Quiet.

• No other action profile is a Nash equilibrium:– (Quiet, Quiet) When Player 1 chooses Quiet, Player

2’s payoff to Fink exceeds her payoff to Quiet, and vice versa,

– (Fink, Quiet) When Player 1 chooses to Fink, Player 2’s payoff to Fink exceeds her payoff to Quiet,

– (Quiet, Fink) When Player 2 chooses to Fink, Player 1’s payoff to Fink exceeds her payoff to Quiet

Examples of Nash EquilibriumBattle of Sexes

• (Bach, Bach) If Player 1 switches to Stravinsky, then her payoff decreases from 2 to 0; If Player 2 switches to Stravinsky, then her payoff decreases from 1 to 0. => A deviation by either player decreases her payoff, thus (Bach, Bach) is a Nash equilibrium!!

• (Bach, Stravinsky) If Player 1 switches to Stravinsky, then her payoff increases from 0 to 1. Player 2 can increase her payoff by deviating too. => not a Nash equilibrium!

• (Stravinsky, Bach) If Player 1 switches to Bach then her payoff increases from 0 to 2 . => Not a Nash equilibrium!

• (Stravinsky, Stravinsky) If Player 1 switches to Bach, then her payoff decreases from 1 to 0. If Player 2 switches to Bach, then his payoff decreases from 2 to 0. A deviation by either player decreases his/her payoff. => Nash Equilibirum!!

Coordination Game

• Battle of Sexes Again: Two people wish to go out together. They agree on the more desirable concert – both prefer Bach. The game has two Nash equilibria: (Bach, Bach) and (Stravinsky, Stravinsky).

• If either pair is reached, there is no reason for either player to deviate from it.

Majority Rule -1-

• Three contestant are left and they must choose who is next to go, depending on their preferences about each other.

• Using majority rule, we get the following complete and transitive social preference: A>J>M

Majority Rule -2-

• Next day stg changed in John’s preferences.• Again using majority rule: M>A>J>M… • Majority rule has the problem that sometimes

it aggregates the preferences of rational individuals into a social prefrence that is not transitive.

Cooperation and Collective Action

• How society manages itself?• Self-interested, rational agents are the

elements of the society.• Managing social life involves cooperation

between individuals.• What makes certain groups more capable of

sustaining more cooperative outcomes than other groups?

Hobbes, T.• To manage society you must enforce order.• Some kind of social mechanism to put restraints:

Leviathan!– An entity which could detect deviations and punish

them.• But who checks over Leviathan?• Is all cooperation in life enforced by a third

entity?• Can we have selfish individuals but nevertheless

cooperate?

Selfish Cooperation -1-

• Each person has a tree yielding two units of coconuts each day. Every day each person decides whether to go to other trees in the island to collect more coconuts or go to the other person’s shelter and steal his supplies. Going to look for trees and climbing the trees is costly. It costs 1 unit of effort to produce 2 units of coconuts. When stealing you exert no effort and you steal all the 3 units the other has.

Selfish Cooperation -2-

• What is the equilibrium of this game?• It is a dominant strategy to steal!• What is the Nash equilibrium if the game is

repeated?• The benefit of defection is smaller than the

benefit of cooperation.

Olson’s Logic of Collective Action• When there is a temptation to shirk or free ride

on other’s actions, three things enable cooperation:– External Enforcement: Costly, imperfect monitoring,

enforcers’ incentives.– Internalised Values– Rational Cooperation: If interaction is repeated

regularly, cooperation can be sustained as long as people are patient enough. Current cooperation is sustained by the prospect of future cooperation. Defection is deterred by the threat of future non-cooperation.

Problems of Collective Action

• Need patience and/or not to big incentives to defect,

• Need to be able to monitor defection and to be able to enforce punishment,

• Need the interaction to be repeated often enough.

• Eg. Workers going on a strike, people demonstrating against WTO in Seattle..

Collective Action Paradox

• In any reasonable model of collective action, accounting for uncertainty, as the group grows large, the fractions of individuals who partake in collective action shrinks to zero.

What is Special About a Group?• Anonymity: Actions may be anonymous and hard

to monitor. Therefore external enforcement and repeated interaction cooperation may be hard to sustain.

• Coordination: There may be different ways to achieve the collective goal, but it may be hard to coordinate on which one to take.

• Conflict of Interest: There may be a conflict of interests as to what is the appropriate action to take. Should we take violent actions or should we protest quietly within the laws of demonstration.

The Problems are Greater the Larger are the Groups!• In large groups, monitoring individuals’ actions

and punishing them are almost impossible. Day to day interaction is not guaranteed in large groups, most interaction is more local.

• An individual’s defection or free riding has small implication for the group’s goal but the individual often cannot be excluded from the benefit.

Olson’s Claim -1-

• Small groups are privileged with respect to large groups in that their political organisation is easier and thus they are able to achieve better outcomes than large groups.– Member actions are observable,– Easier to monitor and enforce order,– There is day to day interaction between

participants and thus we can sustain behaviour on the basis of repeated action.

Olson’s Claim -2-

• Logic also applies within groups: If group members are unequal in important ways, these inequalities may actually help the group achieve their actions. But this comes at the price of unequal contributions to the group goals. A large powerful member is more likely to make a big difference and will be under pressure to contribute. The small and less powerful members will thus be able to exploit the big and powerful members.

Two Shortcomings of Olson’s Theory

• Doesn’t take account of the role of leaders (Wagner’s theory of leadership),

• Non materialistic motivations. I join because I believe in the cause (modelling religions as social institutions that internalise values).