Lagerspiel

Lagerspiel, literally "storage game" in German, is a term used in game theory and operations research to describe a class of strategic interactions in which multiple agents compete for access to a shared storage or warehousing capacity. The concept models how actors allocate limited space, handling resources, or time slots within a common facility, and is used to study the resulting incentives, allocations, and potential inefficiencies.

In a typical Lagerspiel, there is a fixed capacity (for example, warehouse space, dock time, or handling equipment) and a set of players who decide on their storage demand or bid for capacity. Each player’s actions translate into a potential benefit (e.g., inventory availability, service level) and a cost (e.g., storage cost, retrieval delay). The capacity constraint means that total requested capacity may exceed what is available, requiring an allocation rule to determine actual usage. Games can be static or dynamic, and information may be complete or incomplete.

A common allocation rule is proportional sharing: when demand exceeds capacity, each player receives a share of the capacity proportional to their bid or reported demand. For example, with capacity C and bids b1 and b2 from two players, each receives ai = (bi / (b1 + b2)) * C if b1 + b2 > C; if the total demand fits, each receives their requested amount. This mechanism leads to strategic considerations about bidding, timing, and information disclosure.

Applications include warehouse and logistics planning, cloud storage allocation, and disaster-relief logistics, where efficient and fair distribution of scarce storage and handling resources is essential. Related concepts include congestion games and resource allocation mechanisms in operations research.