Some Algorithms of Matrix Game Solutions

Jane Friedkin and Hans Johnson
Troy High School

Abstract

In practice we often deal with the problems which need to make decisions under conditions of uncertainty, i.e. there are situations when two (or more) sides have different purposes, and the results of any actions of each side depend on the activities of the partner. Such situations arise in a game of chess, checkers, dominoes, etc., refer to the conflict. The result of each player’s stroke is dependent on a reciprocal course of the enemy, the goal – winning one of the partners. Conflict situations, arising in the economy are very frequent and have a diverse nature. These include, for example, the relationship between the supplier and the consumer, buyer and seller, the bank and the client. In all these examples, a conflict situation is generated by the difference between the interests of the partners and the desire of each of them to make optimal decisions that implement the goals the most. At the same time everyone has to reckon not only with their objectives but also with the objectives of the partner, and take into account the unknown in advance decisions that these partners will take.

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