Allocate indivisible items while tracking utility, envy, and the difference between equality and fairness.
Select an unallocated item for Player 1; the computer or Player 2 then selects.
Use this guide to understand what changes in each play mode and difficulty level, and which fairness concepts to observe.
You control Player 1. After each of your choices, the computer gives Player 2 the remaining item that Player 2 values most. This mode demonstrates strategic picking against a greedy opponent and shows that maximizing your immediate utility may not produce an envy-free allocation.
Two people alternate on the same device. Player 1 chooses first, then Player 2, until every item is allocated. This mode is useful for discussing negotiation, truthful preferences, strategic denial, and whether players pursue personal utility or a mutually acceptable outcome.
The simulation completes automatically. Each computer selects its highest-valued available item. Use this mode to observe the outcome of two greedy agents, compare total utility across repeated allocations, and check whether locally rational decisions create global fairness.
A short, fully visible allocation with four items. Both players’ values are shown, making it easy to calculate utilities manually and understand the envy-free test. This is the best introductory level.
A larger visible allocation with six items. More choices create greater opportunity costs and stronger strategic conflicts. Players must consider not only the best current item but also what valuable items may remain for later turns.
The numerical values are hidden during play, although the game still uses private value profiles internally. Decisions must be made under incomplete information. This level highlights uncertainty, preference elicitation, trust, and the limitations of evaluating fairness when valuations are private.
| Mode | Level 1 | Level 2 | Level 3 |
|---|---|---|---|
| Human vs Computer | Learn the basic alternating-pick mechanism against a predictable greedy opponent. Compare your bundle with the computer’s bundle using visible values. | Plan several turns ahead. Taking the highest-value item now may allow the computer to capture multiple valuable items later. | Play against a greedy opponent without seeing valuations. Focus on decision-making under uncertainty and the risk of mistaken assumptions. |
| Human vs Human | Discuss every choice openly and verify the envy-free condition by hand after four selections. | Explore bargaining, blocking, reciprocity, and strategic sacrifice in a longer allocation. | Keep preferences private or reveal them selectively. Compare perceived fairness during play with computed fairness after the allocation. |
| Computer vs Computer | Observe a quick greedy baseline and check whether it is envy-free. | Study how a longer greedy sequence changes total welfare and the balance between players. | Observe an automated allocation with private values. Use repeated new allocations to see how hidden valuations can produce very different fairness outcomes. |
Begin with Human vs Computer — Level 1, continue with Human vs Human — Level 2, and finish with Human vs Human or Computer vs Computer — Level 3. This sequence moves from visible and simple preferences to strategic interaction and incomplete information.