Strategically influencing an uncertain future: Recent developments in strategic decision-making suggest that individuals (or a small group of them), can unilaterally influence the collective outcome of complex social dilemmas

Strategically influencing an uncertain future. Alain Govaert & Ming Cao. Scientific Reports volume 10, Article number: 12169. July 22 2020. https://www.nature.com/articles/s41598-020-69006-x

Abstract: Many of today’s most pressing societal concerns require decisions which take into account a distant and uncertain future. Recent developments in strategic decision-making suggest that individuals, or a small group of individuals, can unilaterally influence the collective outcome of such complex social dilemmas. However, these results do not account for the extent to which decisions are moderated by uncertainty in the probability or timing of future outcomes that characterise the valuation of a (distant) uncertain future. Here we develop a general framework that captures interactions among uncertainty, the resulting time-inconsistent discounting, and their consequences for decision-making processes. In deterministic limits, existing theories can be recovered. More importantly, new insights are obtained into the possibilities for strategic influence when the valuation of the future is uncertain. We show that in order to unilaterally promote and sustain cooperation in social dilemmas, decisions of generous and extortionate strategies should be adjusted to the level of uncertainty. In particular, generous payoff relations cannot be enforced during periods of greater risk (which we term the “generosity gap”), unless the strategic enforcer orients their strategy towards a more distant future by consistently choosing “selfless” cooperative decisions; likewise, the possibilities for extortion are directly limited by the level of uncertainty. Our results have implications for policies that aim to solve societal concerns with consequences for a distant future and provides a theoretical starting point for investigating how collaborative decision-making can help solve long-standing societal dilemmas.

Discussion

Classic theories of strategic decision-making rely on how one’s actions can affect their future. If one would consider to defect by choosing selfishly at some point in time, how large will the consequences of retaliation be? And is the fear of retaliation from others enough to sustain cooperation even when the immediate benefit of defection is large? These strategic trade-offs are commonly referred to as “the shadow of the future” and provide an elegant theoretical explanation for the emergence of cooperative behaviour of rational players in repeated social dilemmas8. However, even with moderate discount factors, the exponential discounting functions used in these theories attribute meaningless significance to the distant future23 and do not take into account empirically observed time-inconsistent valuations, making them less suitable for modelling strategic decisions that affect a distant future. More recently, strategic behaviour has been studied from an alternative perspective by identifying decision-making strategies that can unilaterally exert strategic influence on the long-run collective behaviour. Because they require minimal assumptions on the behaviour of others, such strategies are of particularly interest to human decision-making7. However, also these theories are built upon valuations of future scenarios that, in reality, are riddled with uncertainties in the probability or timing of payoffs that are likely to influence strategic decisions27,42.

Here we have modelled these uncertainties with a discounting method that exhibits the characteristic features of empirically validated delay, probability and social discounting methods1,5. Using the proposed framework, existing theories of strategic decision-making can be recovered in deterministic limits and new insights are obtained into the interaction between uncertainty, discounting and the possibilities for strategic influence. Namely, in social dilemmas, uncertainty leads to generosity gaps that require generous strategic influence to be adjusted to the longer term. These potentially long periods of time in which no generous payoff relation can be enforced may also contribute to the empirically observed inconsistencies in strategic influence and cooperation levels over time25,26. On the other hand, our results indicate that the slower discounting becomes, the more certain an extortioner needs to be about an increasingly distant future: sufficient patience thus requires sufficient certainty. These findings illustrate the difficulties one can expect when attempting to exert strategic influence in the real world and provide new insights for decision-making experiments in more controlled environments. From a more technical point of view, our extension to time-varying strategies that is found in the Supplementary Information section 2, provides a novel perspective for the study of reciprocity in changing environments43.

In this paper, we interpreted the beta distribution as a common uncertain belief in the discount factor or continuation probability which is a rather restricting assumption. However, we believe arguments can be made for interpreting the beta distribution as an approximation of the distribution of discount factors in a large group of individuals21,44. In this case, (1) can be seen as a weighted average discounting function used in collaborative decisions45,46. In this context, our framework can be used to theoretically study the strategic behaviour of groups making collective decisions and how the group composition can affect their cooperative behaviour.

Regardless of the interpretation, our work shows that strategic efforts to solve social dilemmas must be adjusted to the uncertainty in the valuation of the future, because only then can strategic influence help to solve today’s societal concerns.