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Game theoretic analysis of the substitutable product inventory problem with random demands. (English) Zbl 0638.90031
Summary: This article uses game theoretic concepts to analyze the inventory problem with two substitutable products having random demands. It is assumed that the two decision makers (players) who make ordering decisions know the substitution rates and the demand densities for both products. Since each player’s decision affects the other’s single-period expected profit, game theory is used to find the order quantities when the players use a Nash strategy (i.e., they act rationally). We prove the existence and uniqueness of the Nash solution. It is also shown that when one of the players acts irrationally for the sole purpose of inflicting maximum damage on the other, the maximin strategy for the latter reduces to using the solution for the classical single-period inventory problem. We also discuss the cooperative game and prove that the players always gain if they cooperate and maximize a joint objective function.
Reviewer: Reviewer (Berlin)

##### MSC:
 90B05 Inventory, storage, reservoirs 91A40 Other game-theoretic models 91A05 2-person games 91A10 Noncooperative games 91A12 Cooperative games
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