Prisoner’s Dilemma, Chicken, Stag Hunts, and other two-person two-move (2 × 2) models of strategic situations have played a central role in the development of game theory. The Robinson–Goforth topology of payoff swaps reveals a natural order in the payoff space of 2 × 2 games, visualized in their four-layer “periodic table” format that elegantly organizes the diversity of 2 × 2 games, showing relationships and potential transformations between neighboring games. This article presents additional visualizations of the topology, and a naming system for locating all 2 × 2 games as combinations of game payoff patterns from the symmetric ordinal 2 × 2 games. The symmetric ordinal games act as coordinates locating games in maps of the payoff space of 2 × 2 games, including not only asymmetric ordinal games and the complete set of games with ties, but also ordinal and normalized equivalents of all games with ratio or real-value payoffs. An efficient nomenclature can contribute to a systematic understanding of the diversity of elementary social situations; clarify relationships between social dilemmas and other joint preference structures; identify interesting games; show potential solutions available through transforming incentives; catalog the variety of models of 2 × 2 strategic situations available for experimentation, simulation, and analysis; and facilitate cumulative and comparative research in game theory.

The growth of groundwater irrigation poses opportunities and challenges, particularly in Africa where substantial potential exists for increased groundwater irrigation but has been constrained by limited access to energy, technology for pumps and drilling, markets, and other factors. Conventional groundwater governance concepts for state-led regulation or co-management are problematic for conditions where state capacity or political support for regulation to reconcile conflicting interests is limited. Experience in Africa and elsewhere does offer examples that may help recognize feasible patterns for collective action that can influence the equity, efficiency, and sustainability of groundwater development. An extended ladder of participation helps look beyond state-led water governance and co-management to a more diverse range of opportunities for supporting local autonomy and initiative to expand opportunities and solve problems in groundwater development. Collective action in groundwater governance can include well spacing; sharing of wells, pumps, and pipes; protecting domestic water sources; crop coordination; groundwater recharge; water imports; and aquifer management. Even where non-state organizations and collective action play primary roles in water governance, they may still be empowered by, receive advice from, or share information with government agencies and other actors. Polycentric groundwater governance can be supported by improving information, facilitating cooperation, endorsing standards, providing a legal framework for resolving conflicts and constituting governance agreements, and through polycentric social learning. Polycentric institutional artisanship by water users and their organizations can help find feasible solutions for improving groundwater governance.

Groundwater is a vital common pool resource for water supply, irrigation, and ecosystems, but can be difficult to govern due to invisibility, conflicting interests, and limitations of available institutions. While there are many policy and technical instruments (tools) available, efforts to apply them are often ineffective. This special issue of the International Journal of the Commons presents a set of papers with insights into policy instruments and other methods for groundwater governance. The relevance and effectiveness of tools and combinations of tools (toolboxes) in addressing problems that emerge from groundwater use is related to how they fit with diverse physical and social contexts. Drawing on research and applied experience, including that presented in this issue, we outline a conceptual framework for groundwater governance that emphasizes attention not just to knowledge, but also to motivations, and to agency for effective coordination among key actors. Articles in the special issue analyze groundwater governance in areas of Africa (east, south, and north), Central Asia, India, and the United States. The articles cover a range of scales from small groups playing experiential games to international agreements about transboundary aquifers. Several papers illustrate the crucial role of knowledge about groundwater, and the need for governance instruments and interventions to go beyond only changing knowledge. Three papers focus on groundwater games and their use to understand and change behavior, especially when combined with other tools that facilitate collective deliberation and action. Several papers illustrate how understanding of the ways people care about and practice care for groundwater illuminates examples and capabilities for groundwater governance. Highlights There are many institutional tools for governing groundwater, but no panaceas, and successes are rare Effective groundwater governance requires that key stakeholders have combinations of knowledge, motivation, and agency to act together effectively Groundwater co-management can combine stakeholders’ knowledge, values, and collective action with external science, resources, and authority Participatory processes can craft combinations of tools to fit contexts and pursue shared gains