Consider the stylized case of two farmers who have recently acquired neighboring parcels of land that share a common aquifer. Both need irrigation for their crops and must decide whether to invest in high-capacity (H) or low-capacity (L) irrigation equipment. This decision involves substantial sunk costs that lock them into their chosen capacity for a long time. Importantly, the two farmers do not know each other and cannot coordinate their decisions, leaving each to act independently based on their own expectations and incentives. If both farmers choose H, they each earn USD 2 per unit of profit from their irrigated crops. However, pumping from the shared aquifer increases groundwater depth, leading to higher energy costs, which grow quadratically with the volume of water extracted . In contrast, if both farmers choose L, they extract less water, avoiding significant increases in pumping costs, and each earns USD 3 in profit due to a better balance between costs and crop production benefits. If one farmer selects H while the other opts for L, the H farmer can produce more crops with lower average pumping costs due to reduced aquifer depletion from the L farmer's restraint, resulting in a profit of USD 4. Conversely, the L farmer suffers reduced crop yields without the full associated cost savings, earning only USD 1.

The payoff matrix for this scenario is represented in Fig. 1. Clearly, the optimal outcome (henceforth referred to as the first best) is for both farmers to select L. This option maximizes total welfare, generating the highest combined profit for both farmers. It also happens to maximize individual profit as each farmer would prefer earning USD 3 over any other possible outcome. However, when deciding which option to choose, a rational farmer will evaluate their best course of action in response to the other farmer's choice. In the payoff matrix shown in Fig. 1, if farmer B chooses H, the best response for farmer A is to also choose H (USD 2 vs. USD 1). If farmer B instead chooses L, the best response for farmer A remains to choose H (USD 4 vs. USD 3). The same reasoning applies to farmer B in response to farmer A's choices, making H the dominant strategy for both farmers, regardless of the other's decision. This leads to a situation known in game theory as a Nash equilibrium, where both farmers rationally select H as a best response to either of the other farmer's possible choices. In this example, this best-response equilibrium causes the farmers to choose H despite their mutual best interest being for both to select L. It causes profit losses for both farmers and prematurely depletes the resource in a situation that is akin to the tragedy of the commons famously described by in the context of overgrazed pastures.

This stylized example is extremely simplified. It neglects important factors such as environmental variability , groundwater flows , differences in payoffs between farmers , and the actual depletion of the shared resource , all of which have been shown to amplify misaligned incentives in the farmer irrigation problem. The example also mistakenly equates welfare maximization to the raw maximization of irrigation profits, which disregards important environmental, ecosystem, and social impacts that arise as opportunity costs to using the water for irrigation. It also assumes a single-shot game with no communication or coordination between the players, which is unrealistic . Despite these simplifications, the example effectively illustrates the fundamental commitment problem that arises when players generate private profits while externalizing part of the cost of their actions onto others (here, in the form of increased pumping costs due to falling groundwater levels). In this situation, nobody can credibly commit to restricting their pumping to levels that all know to be both collectively and individually optimal. Even if both farmers genuinely wish to act responsibly, neither can trust with certainty that the other will to do the same, leading to a situation where individual optimization does not aggregate into a collectively optimal outcome (hence the “tragedy”). These characteristics are emblematic of many contemporary water resource challenges beyond irrigation, including those related to climate change adaptation and mitigation , multipurpose reservoir management , transboundary aquifers and rivers , or household-level sanitation .

The type of market failure illustrated in the stylized example has been alternatively described as a prisoner's dilemma , a tragedy of the commons , or a collective-action free-rider problem , and it arises across a wide range of goods beyond water resources. These goods, referred to as common-pool resources, are defined by two key characteristics: they are rivalrous, meaning that one user's consumption reduces the availability for others, and they are non-excludable, meaning that it is difficult or impossible to prevent access to users who do not adhere to established rules. Such goods defy governance by traditional institutions: centralized authorities often lack the localized information necessary to allocate resources effectively (e.g., pumping costs determined by local hydrogeologic conditions in groundwater management), while markets struggle to establish and enforce property rights. Yet, in her seminal book Governing the Commons , Nobel Laureate Elinor Ostrom famously argued that alternative approaches to governance must have been historically effective in managing common-pool resources, otherwise these resources would have been depleted long ago. Ostrom studied traditional institutions that had evolved over centuries to manage such resources sustainably, reasoning that only effective institutions could persist as those that failed would collapse along with the resources they governed. Her analysis spanned diverse contexts, from Swiss alpine pastures and Japanese forestry to Spanish and Philippine irrigation systems. Through this work, she identified eight principles shared by successful institutions (Table 2). These principles are hallmarks of systems capable of sustainably managing common-pool resources. To address the diversity of institutional arrangements and their contexts, also developed a coherent framework, often referred to as institutional grammar, to codify and analyze the structures underlying these governance systems (Table 3).

The light version (v0) of the game has a setting that is comparable to the River Basin Game . Students decide how much water to withdraw each year from a shared aquifer, which is recharged annually and experiences losses in natural discharge. Each unit of water withdrawn generates a fixed revenue for the player, but costs increase incrementally with the total volume withdrawn by all players that year (the first unit costs C0, the second unit costs C0+1, and so on; see Sect. S1). This structure is designed to simulate the increasing pumping costs associated with declining groundwater levels, where the cost of the first unit of water each year depends on the state of groundwater storage. Groundwater levels, in turn, are determined by historical withdrawals, recharge, and discharge fluxes. Recharge is constant and set to be proportional to the number of players in the game, while discharge is proportional to the amount of water stored in the aquifer during a given year (i.e., the aquifer behaves like a linear reservoir). Through this setup, students experience the overuse incentives characteristic of common-pool resources, which arise due to communal costs and coordination challenges. The game also demonstrates how these effects are exacerbated by the “memory effect” of depletable resources, where excessive consumption can impact communal costs far into the future. The four solution concepts addressing these effects (the Nash equilibrium and the first best, each under myopic and steady-state conditions) are derived for the game's default parameters and are presented in Sect. S1 in the Supplement.

The full version (v1) of the game is similar to Irrigania in that each student manages nine fields and must decide whether and how to irrigate. The three irrigation options are designed to illustrate fundamental challenges in agricultural water management:

Rainfed (no irrigation) fields incur no costs and can yield high profits in good years but are subject to climate uncertainty. This uncertainty is simulated in the game through randomly drawn “good” or “bad” years. The game can simulate climate change by allowing the probability and expected returns in good and bad years to change over the course of the game.

Unlike Irrigania, students can also decide whether and what to plant on each field. Instead of the default crop, players may choose to leave a field fallow to secure a fixed wage (representing outside work). This wage is stable, unaffected by environmental uncertainty or the decisions of other players, but is lower in terms of expectation than any crop option. In contrast, players may choose to plant a higher-value crop, which doubles both the revenue and costs for that field. That option effectively increases a player's potential productivity, allowing them to simulate up to 18 fields if all nine players are dedicated to high-value crops. This dynamic setup allows students to explore trade-offs between risk, cooperation, and resource sustainability through agricultural decision-making within the framework of shared-resource constraints. The game also provides flexibility for instructors to progressively activate choice options, enabling students to focus on individual trade-offs. For example, deactivating all irrigation options allows students to manage risk and environmental uncertainty (choosing between rainfed crops and a fixed outside wage) without the influence of common-pool overuse incentives or resource depletion. This flexibility makes the game an effective tool for integration into a broader curriculum on water resource management (see Sect. 5).

The distinction between private and public information is a unique feature of both versions of the game that sets them apart from their predecessors. This aspect is central to the game's ability to simulate institutional design. In the default mode of both versions, students have access to limited information to guide their decisions. Specifically, they are provided with the initial costs of both irrigation options, the historical sequence of “good” and “bad” years in prior periods, and the average profit across all players from the previous period as a benchmark for evaluating their performance relative to the group. However, information about the specific actions of other players remains private. This information asymmetry introduces coordination and commitment challenges that are at the core of the tragedy of the commons (see Sect. 2). The game allows students to address these challenges by designing institutions around certain types of information that they might collectively decide to make public.

In the light version (v0), the water use decision of one randomly selected player can be revealed to the group after each period.

The light version of Thirsty Earth (v0) is entirely programmed within the Google Sheets environment to maximize portability, accessibility (for both instructors and students), and adaptability, making it ideal for use within the context of a short module on water governance and management in a hydrology or environmental science class. The game supports up to 50 players, divided into up to five distinct “villages”, each sharing an aquifer. Unlike the River Basin Game , these villages are not hydrologically linked to each other. The game environment consists of three components (Fig. 2):

Main sheet. This Google Sheet is intended for the instructor to use to pilot the game. All tabs and cells are locked except for three colored cells in the MAIN tab (T2, T3, and T4), allowing the instructor to initialize the game, move to the next game period, and make the water use decision of a randomly selected player public if required by the student-designed institutions. The spreadsheet also contains a series of tabs that include license information, the model based on linking players' choices to profits and groundwater stocks, and tabs for managing interfaces with other components. All of these tabs are read-only, but their content is available for download.

The instructor initializes the game by setting cell T2 to 1 on the MAIN tab of the main sheet. If applicable, the instructor may also activate the “Sample Player Info” feature (cell T5) to display the water use decisions of randomly selected players from each village during each period, which students can use to design institutions that regulate water use. Students access the display sheet to register for the game via the provided Google Form link. Once registered, students appear in the Roster tab of the display sheet and are assigned a village letter and player number. The game proceeds through eight rounds of student submissions. Each round begins with students submitting their water consumption decisions through the Google Form linked on the display sheet. The instructor monitors submissions on the MAIN tab, but this information remains private. Once all decisions are submitted, the instructor advances the game by incrementing the “previous period” cell (T3) by 1. This action updates the display sheet with the average water cost for the completed period, which students use to calculate their profits. It also shows the average profit for each village, the water consumption decision of a randomly selected player from each village (if enabled), and the cost of the first unit of water for the next period, helping students strategize their next decisions. Students then submit their decisions through the new Google Form link that appears on the display sheet, and the instructor increments the “previous period” cell (T3) on the main sheet again, repeating the process for each round. After the eighth period, the game concludes, and the display sheet summarizes the total water use and profits for each player, providing an overview of both individual and collective performance.

The full version (v1) of Thirsty Earth builds upon the principles of the light version but is implemented as a web-based graphical user interface (GUI) to provide a more advanced, flexible, and interactive gameplay experience. The game supports up to 99 players, grouped into equally sized, independent “villages” of at least three students who share a common aquifer and surface water irrigation infrastructure. The full version introduces additional features, such as the ability to purchase multiple information bits to address social dilemmas, dynamic decision-making at the field level (three land uses × three irrigation options), and turn-based multi-player gameplay supported by a dedicated server and gaming environment. These features make the full version ideally suited to repeated game plays, for example, within a semester-long class on water resource management. Such a format allows the game to be used successively to introduce students to distinct challenges in water resource management (environmental uncertainty, common-pool overdraft, and resource depletion), explore their compounding effects, and brainstorm institutional approaches to mitigate them. A semester-long structure suggested in Sect. 5 ensures that sufficient time is available for both students and instructors to familiarize themselves with the more complex gameplay and to fully leverage the game's capabilities.

In terms of architecture, the game platform is built using the boardgame.io engine and React JavaScript, supported by a cluster of Docker containers, including an R-based model server and a PostgreSQL database. This architecture allows for real-time, turn-based interactions and comprehensive tracking of game data. However, residual challenges related to platform stability, gameplay synchronization, and reliance on client-side data storage remain (see full technical description in Sect. S3). The game environment consists of two distinct sequences of screens, for the instructor and the players, which move throughout the different phases of gameplay as follows (Fig. 3).

Setup phase. Instructors create a game through the web application by setting parameters such as the number and size of villages (minimum of three players per village), the number of game periods, the types of choices available to students, and other game-specific coefficients of the profit functions. Default parameter values are optimized to highlight the three core trade-offs intended for students to explore, as detailed in Sect. S2. The setup interface also includes a link to teaching materials and game documentation. Once the game is created, the interface generates a unique game ID for students to log in on the game portal. The instructor assigns players to villages and, if relevant, assigns specific purchased information bits to each village. Any unfilled player slots can be filled with automatized “BOT” players who follow the Nash equilibrium strategy, optimizing their choices across all fields and periods under the assumption that all players adopt the same strategy and that all of the land use and water options are available to all players. Once all players are assigned, the instructor starts the game.

In the long-form teaching module, Thirsty Earth was used to support Sustainable Development in a Changing World, an introductory water policy course designed to introduce engineering students to the multifaceted challenges of water resource management and governance. The game served as the centerpiece of a water governance module that typically spanned 7–9 h long lectures, depending on whether the three governance challenges covered by the game (environmental uncertainty, common-pool overuse, and resource depletion) were introduced progressively. The module was structured as follows:

Preparatory readings and introductory lecture. Students were assigned seminal readings on common-pool resource governance e.g., chapters from and wrote reflections in an interactive online forum, with half of the class responding to the other half's posts. This was followed by a lecture introducing the three governance challenges addressed in Thirsty Earth and the concepts outlined in Sect. 2.1.

In the short-form curriculum, Thirsty Earth was typically integrated as a two-lecture module within an upper-level undergraduate hydrology class. The light version of the game (v0) was played twice. The first lecture usually included an introduction to the game, followed by an initial gameplay session and an in-class discussion. Students were then provided with a written solution to the game (Sect. S1) and were tasked with reviewing it before the second lecture. The second lecture generally began with a brief introduction to Ostrom's design principles and institutional grammar, followed by a short deliberation session in which students, grouped by game village, designed institutional rules. To simplify the task, the private information available to students for public enforcement was limited to identifying the water consumption of a randomly drawn player – a feature now integrated into the light version of the game. After agreeing on institutional rules formulated using the ADICO framework, students played the game a second time. The session concluded with a discussion comparing the outcomes of the two gameplay sessions, emphasizing the critical role of well-designed institutions in ensuring infrastructure effectiveness and supporting sustainable resource management.