5.11 - Intro to public goods games

Experimental games issues

Games may be too complex

• leads to subjects making errors (needs to be accounted for)

• Other subject’s actions may depends on their beliefs about others errors (exploit them)

Nash equilibrium in Game theory measures behaviours and beliefs at the same time and

assumes each player plays as if optimising given correct beliefs about strategies of others

• in reality players can learn and adjust how they play based on how other behave (conditional convergence on a choice)

Control of preferences - GT specifies payoffs in utility whereas experiments only deal with money payoffs (not always equal)

• only equal if players dont care about any other factors (equality or non-monetary aspects of play)

Duhem-Quine problem

single hypotheses cannot be tested in isolation

• If predictions of a game theoretic model seem to fail, are players violating game theory itself or playing different game from one experimenter intended?

Voluntary contribution mechanism (VCM) game structure

Subjects in size n groups

Each player i has an endowment of E tokens

Each player can divide tokens between private account or a joint public account

• Each token i puts in private account earns 1 token for i

• Each token in public account earns m points (identical) for every group member

m - marginal per capita return

benefits of contribution to public account are a pure public good (as identical return for all members)

VCM payoffs

let c_i = token contributed to public account by i

Total points for i = (E - c_i) + mc_i + mQ = (E + mQ) + (m-1)c_i

• Q = tokens contributed to public fund by other members

To max own points if m < 1 → dominant strategy for i is c_i = 0 (dont contribute)

Everyone gets E if all give 0

Everyone gets mnE if all give E

• if mn > 1 then all do better if all give max (E)

• if 1 > m > 1/n then we have an n-player prisoner dilemma game

  • should give max but dont know what others will do so give 0

Typical VCM findings

many studies set m = 0.4-0.6 (and set n so m > 1/n)

If one shot game:

• only ~20% give 0 to public account

• On avg subjects give ~40-60% of E to public account

• Over contribution relative to equilibrium prediction (less than efficient though)

If game repeated with anonymous feedback:

• Contribution rates decay to close to 0

Reasons for why players contribute

Error - player may be confused about game rules

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

Preferences - Altruism + warm glow + conditional cooperation

Compelling explanation must account for decay, not just initial level of contribution

One-sided error problem and solution - Keser (1996)

As dominant strategy to contribute 0, errors and any intended contribution deviate in same direction as cant contribute negative amount (cant distinguish)

• same for efficiency prediction

Keser (1996) - redesign game so NE has contribution > 0 so errors on both sides of NE possible

• Amend VCM so points to i from tokens in private account given by: ax_i - bx_i²

• where x_i = E - c_i

Keser (1996) equilibrium graph

marginal return now a decreasing function

constant marginal cost of keeping

Equilibrium at A (when b positive & a > m)

Keser (1996) - results

Dominant strategy: Keep 13 & Contribute 7

• marginal return shown to subjects in a table

results aggregated across all rounds:

• 27% gave 7 (mode)

• 12% < 7 (FR) & 60% > 7

Over-contribution in VCM games not fully explained by only direction of error possible (errors both ways)

Andreoni (1988) - OV

VCM game with standard payoff structure

aim to separate Learning hypothesis from Strategic hypothesis

• to explain decay

Partners vs Strangers groups

• P stay in same group of 5 for each round BUT strangers random every round

• Strategic hypothesis predicts higher contribution in partners till final rounds

• Learning hypothesis predicts no difference between groups as doesnt affect learning

Includes surprise restart after 10 rounds

• Restart should not stop decay in contributions if LH the reason

Learning hypothesis

Players contribute in early rounds in error, as they have not yet understood the incentives

Contributions decay as they start to understand

Strategic hypothesis

P{layers contribute in early rounds in hope of boosting future contributions of those they will play with later

Contributions decay as final round gets closer

Andreoni (1988) - Results

Restart with partners

• Initial Strong decay from 50%

• post restart decay gone and back to almost start again

  -              Learning hypothesis not shown by data

Strangers contribute more than partners

-              Most replications find the opposite however (IMPORTANT)

Croson (1996)

replication of Andreoni (1988)

Found robust effect of restart

BUT partners contribute more

Yamakawa et al (2016) - design

3 treatments

Human treatment (H) - Standard VCM

• n = 2 & 20 rounds

Computer (C) - 1 human player and 1 computer

• computer choices predetermined & payoff only goes to human

• Design where no motive to contribute (C treatment) - Only error / confusion causing donations

HC - same as C but C acts on behalf of another human who received the payoff

Yamakawa et al (2016) - Rationale

No incentive to contribute in C, so contributions there must be errors.

Comparison of C and HC captures effect of there being a human to receive the computer’s payoffs

• measure of altruism / pro-sociality

Comparison of HC and H captures effect of human co-group-member making decisions round by round.

• no effect of cooperation in early rounds to encourage contribution in later rounds

Yamakawa et al (2016) - results

Unusually stable contribution levels in treatment H till late on, when decay finally sets in

-              Decay delayed (maybe from small n = 2)

Very low contribution levels in treatment C

-              Low confusion even from start

Contribution levels in HC closer to those in C than in H (for nearly all rounds)

-              Their interpretation: shows evidence for importance of “multi-round incentives”

Summary of Why over-contribution

Errors / learning

• play some role but do not seem to be whole story

• Keser 1996 - Predominance of over-contribution

• Restart effect for partners - Andreoni 1988

• Low contributions for C treatment - Yamakawa 2016

Strategic

• Some evidence

• Yamakawa 2016 - supports this theory

• Partners vs strangers has mixed results

  • some evidence that strangers give less