Group exercises, where people engage and transact, can be designed in ways that uncover conflicts of self-interest and co-operation. An example is where different participants seek to profit from a common, limited resource, like harvesting fish from a lake.

Narrow self-interest leads to the resource getting depleted. True self interest would lie in co-operation, where each person draws a limited quantity and allows the resource to regenerate.

A well-known exercise to analyse behaviour is the Public Goods Game, where players are each given a personal, starting endowment. They may now make contributions to the public pool.

The pool is then multiplied by some number and equally divided among the players. As a player receives an equal share of the pool regardless of what she put in, it would be in her interest to contribute the least, even nothing.

This, however, would soon be understood by all players and this is not the behaviour we see in practice. What we see is that players make contributions, induced in part by aversion to being seen as “free-riders” and in part because of the multiplier. In one form of the game, there are four players who start with twenty tokens each.

Each one then receives 0.4 tokens for each token that is contributed to the pool. As this amounts to a return of 0.4 on an investment of a full token, it may be better to hold on to one’s tokens.

Putting in all the tokens, however, would result in 80 tokens in the pool and a return of 32 tokens to each player. But if one player held back, there would still be 60 tokens in the pool, with 24 tokens given to each player, and the one that held back would have 20+24! Michael Muthukrishna, Patrick Francois, Shayan Pourahmadi and Joseph Henrich, from schools of psychology and economics from London, Vancouver, Massachusetts and New York, report in the journal, Nature Human Behaviour, that their trials with variations of the PGG included penalties for non-co-operative behaviour and then an element of corruption, which eroded the penalising action. The first variation of the PGG is where players can penalise, or punish low contributors, but at a cost to themselves.

The cost that must be borne moderates the level of punishment, but the practice does increase the level of co-operation. And then, there is the reverse factor of co-operators or large contributors being penalised, because they are seen as progenitors of punishments. The paper in Nature Human Behaviour examines a particular form, the Institutional PGG where an individual is chosen as a leader, to mete out punishment to those who contribute less. When all the contributions have been received, a portion is extracted as the tax, and this is used to administer punishments.

The punishment consists of reducing tokens, according to the part of the tax income that the leader uses for punishing, multiplied by a factor. The level of tax and the multiplier are measures of the leader’s power to punish. The multiplier of the contributions, which yields what is returned to the members, represents the economic level of the community.

Trials with IPGG are reported to have shown that punishment generally improves levels of contributions. Another form of IPGG is with rewards given to high contributors, but it is reported that punishing the low contributors is more effective.

With “rational” players, of course, one can imagine that the reward/penalty effect would depend on the level of punishment or reward — whether the penalty negates the benefits of contributing less, or whether the reward compensates the lower personal gains of generous contribution.

Muthukrishna and team next developed the Bribery Game, in which players and leaders have more ways to function. In addition to contributions to the pool (if any), players can choose to deliver tokens to leaders, to improve the leaders’ income.

The leaders can choose to accept or refuse the gifts, like bribes, and respond by punishing or not punishing a player, either one who contributes less, or one who does not offer a bribe.

The team carried out the trials with 274 Canadian participants, men and women, of different ages and ethnicities, in randomly assigned groups of four to seven. In playing the IPGG, the multipliers, of the pool return, which indicated the economic level, and multiplier of the punishment, which reflects the leaders’ potency, were varied from low to high.

And in the BG, a device (transparency), to mitigate corruption, was introduced at three levels — partial transparency (disclosing contributions by leaders), full transparency (revealing all leader behaviour, including bribe taking) and leader investment (forcing leaders to contribute their endowment to the public pool). And the leaders were changed in each iteration of the game. The paper observes that without punishment, the contributions shrink down to zero (excepting infrequent, pathological “givers”), as contributions depend on the power of leaders to punish low contributors.

Leaders, who also pay the tax which is used to empower themselves, could be counted on to use the tax to punish players, first as the tax itself was low, and then, as promoting contributions was good for the leaders too. Strengthening leaders, with tax resource and a robust penalty multiplier would hence promote contributions, in IPGG.

When it comes to the BG, the paper says, there would be no incentive to contribute to the pool or to offer bribes unless players were punished for not doing either. Where the bribe is an option, however, making sure of bribes is more lucrative for the leader than punishing low contribution.

Hence, in contrast to the IPGG, empowering leaders in a bribe-taking environment would lower the contributions to the public pool, the paper suggests.

However, if the players were from an environment where contribution was more rewarding (high pool multiplier) and anti-corruption norms had sway, low contributions would be punished more severely than low bribe offers. “In contrast, growing up in a more corrupt society may lead to a higher preference for eliciting, offering and accepting bribes,” the paper says.

In the trials carried out by the team, it was found that the public contributions dropped by a whole 25 per cent when IPGG was changed for BG, or when bribes became possible. “…When corruption could enter, it did, and co-operation deteriorated,” the paper says. On further analyses of behaviour when the multipliers were varied, by cultural experience and based on past decisions of leaders, it was found that powerful leaders were twice as likely to accept bribes and three times as likely to punish players.

Based on individual data, it was found that leaders who had been exposed to corruption were significantly more likely to accept bribes, and conversely, those with different parental corruption norms were less likely to do so. The next assay was to see the effect of corruption mitigation by transparency.

Here, as shown in the diagram, in a low economic potential (pool multiplier) environment, strong leaders did more to improve public contribution, and full transparency had a positive effect.

In poorer countries where leaders often abuse power and do economic harm, it was still important that leaders be powerful, but with strong anti-corruption measures, like full transparency be put in place.

If the leaders are not powerful, making low public contribution and free-riding would be the rational course, and transparency would only present the same example.

The paper cautiously concludes that while less government action may be the way for areas of high economic potential, poorer regions would benefit from strong government action, but essentially paired with strategies to keep corruption in check.

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