Lec12 - Conditional cooperation and the strategy method

Voluntary contribution mechanisms (VCM) design

Subjects in group of size n

Money payoffs proportional to points

Each player i endowed with E token

• divide between private account (each token = 1 point for i)

• and public account (earns m points per token regardless of who put it in the account)

VCM strategy

If each player i wants to maximise own points:

• dominant strategy for i to set contributions (c_i) = 0 to public account

• All players get E

Social optimum is for all players to contribute all E to public account

• all receive mnE points

Typical parameter: 1 > m > 1/n

VCM typical findings

m usually set around 0.4-0.6 (and m > 1/n)

If 1-shot game:

• ~20% contribute 0 to public account

• subjects contribute ~40-60% of endowment to public account

If repeated games (with feedback on contributions):

• Contribution rates decay towards 0

Reasons / theories for contributing to VCM

Error / learning - Players may be confused in early rounds

Strategic - Players may think contributing in early rounds of repeated game will raise future contributions of others

Preference accounts - Subjects may not be motivated only by their own money payoffs

• Utility doesnt just depend on own money payoff

Altruism / warm glow - Warm glow gained from ‘moral’ behaviour

• BUT doesnt explain decay or why some FR in 1st round

Fischbacher et al. (2012) - OV (FGQ)

Focus on repeated game in C-experiment (10 round repeated VCM)

• strangers matching protocol

• Each subject’s beliefs elicited in each round about others members contributions

  • mall reward for being right, or nearly - incentivised

P-Experiment used to classify subjects into preference types

Paper draws on:

• FG(2010) - decay caused by disappointed expectations among subjects - conditional cooperators

• FGF (2001) - uses same strategy method

Uses individual-level analysis that categorises each subject into a preference type from P-experiment

Strategy method

Developed by Selten in 1960s

Used in sequential games to elicit a subject’s “choice” for every point in a game tree where it would be that subject’s move

• even thought not all reached in real play

FGF (2001) adapt it to symmetric, simultaneous-play games

• e.g VCM games

How to detect conditional contributors

Need to know what they would want to contribute for different levels of contribution by other players.

• One-shot game: Players move simultaneously, so are not responding to others.

• Repeated game: Only see responses to the behaviour of others that has actually occurred

So use contribution table to let each player announce a “strategy”, for transformed one-shot game in which they move last,

• i.e. Announce a contribution level for each possible average contribution levels of other group members

Different types of strategies

Free-riders: Never contribute.

Unconditional cooperators: Maximal contribution, regardless of average contributions of others.

Conditional cooperators: Contributions vary positively and (weakly) monotonically with average contributions of others.

Perfect conditional cooperators: Contributions equal average contributions of others

Different types of strategies graphically

real subject might not have straight line / monotonic preferences

We assume preferences fixed BUT changes in behaviour caused by changes in beliefs

P-experiment design - FGQ (2012)

One-shot VCM game

Each subject states unconditional contribution + reveals “strategy” by contribution table.

Then 1 subject i chosen randomly from group BUT other group members play their unconditional contributions

• Subject i’s choice determined by their strategy in light of the unconditional contributions of others

• 1 group member uses strategy whereas other 3 use unconditional contribution

Incentive to complete contribution table honestly as any part of contribution table may be used

P-experiment results - FGQ (2012)

55% CC 23% FR Most people CC but not perfect CC

TC increase contributions initially and then decrease as others give higher - strategic contributions

C-experiment aggregate results - FGQ (2012)

Decay in both contributions & beliefs found

contributions slightly below beliefs - causes cyclical decline

C-experiment individual prediction - FGQ (2012)

Subjects “strategy” from P-experiment + stated belief in each round of C-experiment combined to “predict” i’s behaviour in round r of C-experiment

individual level predictions

If predictions accurate then they re-assure about strategy method

• + support “stable preference + changing beliefs” account of falling contributions

Individual prediction graphically - FGQ (2012)

Individual prediction accuracy - FGQ (2012)

Predictions mostly accurate (for CC & FR)

• especially in later rounds

Shows FR dont always FR (strategic contribution)

CC have condensed set of results (+- 4 from 0 deviation)

Contribution table telling the truth in how people would behave in real life

CC vs FR beliefs and real response - repeated game FGQ (2012)

In C-experiment, CC respond like in contribution table

FR still have positive relationship between belief & action

• FR behave as CC in early rounds

CC vs FR beliefs and real response - 1-shot game FGQ (2012)

No incentive for FR to contribute at all strategically in 1-shot game

• FR behave how expected (not CC at all like in repeated)

Dangerous mix and decay

Imperfect CC want to “undercut” contribution they expect from others.

Causes downward spiral of contributions subjects make expect others to make.

Presence of FR hastens this process.

Sustained high contributions to PG games very hard to see in reality

• Constant undercutting from both imperfect CC + FR