Relational quality and uncertainty in common pool water management: an exploratory lab experiment

If there is one certainty for the sustainable management of water resources is that facing uncertainty is an unavoidable matter. A concern that, in addition to the best available scientific knowledge and models, requires deep insights about the socio relational processes that underlie decision-making. Our objective here is to better understand if and how the socio relational environment in which decisions are made shapes decision-making under uncertainty in common pool water resource management. Our goal is twofold: methodological and analytical. It consists in designing experiments for carrying out uncertainty analysis to explore the influence that the relationships established among decision actors have in making decision choices under uncertainty in management processes. To this end, we developed one experimental game protocol, representing a typical water management scenario: irrigation, which we use to test two different conjectures about the combined effects of uncertainty and relationships. In doing so, we play close attention to the quality of relationships developed among players (acting as water managers), and how these relationships are structured and organized. Initial tests confirmed the importance that the relationships established among players have for coping with uncertainty in managing water resources.


Supplementary Information for Relational Quality and Uncertainty in Irrigation Water Management: an exploratory lab experiment
Supplementary S3. Operationalization of the concepts of uncertainty and relationships Operationalization of uncertainty: Uncertainty stands for what players do not know regarding the management of the CPR system, concerning the water resource, the canal, and others´ behaviours. So, uncertainty refers to lack of knowledge about what others are doing (e.g., water extractions, gains and investments, or use of ultimatum), the state of the water system (e.g., water available for extraction) and the technical system (e.g., canal´s level of maintenance). Each treatment varies in what information is disclosed to participants and when, as indicated below. Average gain is disclosed in T1 and T2 during Phase 3, reducing the uncertainty regarding how much others are gaining and how much water they are using.
Furthermore, it is important to mention that even though these are designed as deterministic (nonstochastic) games, players at time t do not know, for example, how much water there will be at time t+1. For example, a period of drought is simulated, by lowering the input of water to the canal during the last phase of the game, which players do not know about (see Supplementary Figure S6 A).

Operationalization of relationships:
The development of relationships in the experiments is made possible through organized interactions carried out via communication among players. In the experiments interactions are configured, structured and timed differently through the treatments (unlimited or structured 1-to -1, all-to-all communication, carried out via online chat), as indicated in the design of the treatments per game in the section below.
The quality of relationships is established through elicitation of the following qualitative variables: 1. player´s level of satisfaction regarding their own performance and gains; 2. their perception of others in connection to themselves and. of themselves in connection to others (based on attributes, such as: trust, caring, understanding, fairness, competitiveness, cooperativeness, enviousness and selfishness), 3.their experience communicating with others, and 4. the relevance players assign to uncertainty, regarding initial water inputs, how much water others extract, how much they invest in the canal and ultimatum use. This information is elicited via a questionnaire (Supplementary Questionnaire S5) rating answers in a 5 items likert scale. It is assumed that players do not know each other before the game, so there is no previous relationship formed among them, or past common history of collaboration.

Supplementary Information for Relational Quality and Uncertainty in Irrigation Water Management: an exploratory lab experiment Supplementary S4. Practical procedure
A total of 75 subjects (53% women) participated in the experiment. Participants were students from University of Montpellier, randomly selected from a pool of volunteers 1 , from various educational backgrounds and without previous experience. The experiment was computerized and took place in the experimental economics laboratory of Montpellier (LEEM), which is composed of 20 terminals isolated from each other by boxes. Players could communicate only through the computer no visual contact or direct communication was possible. The experimental session lasted for 2 hours including instructions and payment. A total of 3 experimental sessions were held. The game was played by 15 groups of 5 subjects each, with 5 groups allocated to each of the 3 treatments. Subjects were allocated to treatments following a 'between design' (different subjects for each treatment). We are aware that 5 groups per treatment falls below the standard of 8 or 10 groups per treatment used as a rule of thumb in lab experiments, but we consider that for our explorative purpose, a broader spectrum of treatments rather than groups/individuals per treatment, was more suitable to identify trends and compare different situations. We expected that the combined effects of relationships and knowledge, we are looking to identify, will be apparent in even small samples.  Tables   Table A. Estimations of ordered logit regressions by position and communication process  Table C. Answers to questionnaire. Averages per treatment and phase, and their differences Table D. Average ratings of uncertainty items in the two phases, and their differences