Contribution-Based Grouping under Noise

Abstract

Many real-world mechanisms are "noisy" or "fuzzy", that is the institutions in place to implement them operate with non-negligible degrees of imprecision and error. This observation raises the more general question of whether mechanisms that work in theory are also robust to more realistic assumptions such as noise. In this paper, in the context of voluntary contribution games, we focus on a mechanism known as "contribution-based competitive grouping". First, we analyze how the mechanism works under noise and what happens when other assumptions such as population homogeneity are relaxed. Second, we investigate the welfare properties of the mechanism, interpreting noise as a policy instrument, and we use logit dynamic simulations to formulate mechanism design recommendations.Keywords: voluntary contributions; behavioral economics; noise; heterogeneity; mechanism design; welfare; efficiency; equality JEL Classification: C73; D02; D03; D63 MotivationTypically, individual decisions in social-dilemma interactions are not perfectly observable in the real world. Applied mechanism designers should keep this in mind when implementing mechanisms, in particular in the context of interactions that have the strategic nature of voluntary contribution games where imperfect observability is ubiquitous. 1 Real-world institutions are usually "noisy" or "fuzzy", operating with non-negligible degree of imprecision. By contrast, theory investigations of mechanisms for the most part study perfect mechanisms. In this paper, as a first step towards performing robustness checks of mechanisms under relaxed assumptions more generally, we investigate the mechanism of contribution-based competitive grouping (as introduced by [5]): we relax some assumptions and investigate what happens when there is (i) noise, (ii) heterogeneity and (iii) different action spaces.The paper is structured as follows. Next, we introduce our model. In Section 3, we first analyze how the existence of Nash equilibria depends on (iii) the strategy space of the game and on (ii) the underlying population homogeneity/heterogeneity in terms of contribution budgets. Then, we assess their robustness when we allow more and more (i) monitoring noise. In Section 4, we investigate how a social planner, interpreting monitoring noise and/or the other model characteristics as policy instruments, would trade-off efficiency and equality to maximize social welfare. Finally, we use agent-based simulations to study the logit dynamics of the game in order to quantify the effect of noisy monitoring. 1 For other social-dilemma contexts, see, for example, [1,2] for imperfect public monitoring, [3] for noisy prisoners' dilemmas and [4] for team-production games with group-level information. Our results are summarized as follows. In terms of the existence of Nash equilibria, the zerocontribution outcome is always a Nash equilibrium and becomes the unique one under too much noise. High-contribution equilibria exist if three things come together: the rate of return of the underlyin...

Payoff-based learning best explains the rate of decline in cooperation across 237 public-goods games

“…For example, apparently stable contributions in a cooperative game could signal a level of norm-compliance, or merely that individuals are struggling to learn how to maximize their payoff. Likewise, studies testing how 'cooperators' behave when grouped together risk confounding social preferences with changes to the payoff mazimizing equilibrium, and thus how individuals learn about payoffs [57][58][59][60][61] . A behavioural approach when measuring social preferences, with control treatments and appropriate null hypotheses, can be used to distinguish between alternate hypotheses.…”