Economic and Game Theory
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Have two problems related to game theory, guess to use the zero-sum games and mixed strategy game, with the rule of dominance as well. However, had some problems to solve it. Would like to ask for your kind help for the solution. Problems as follows:
A contract of affreight is being offered to two competing ship owners. The strategies and payoffs are shown in the table below:
Ship owner B B1 B2 B3 Ship ownerA A1 45 50 25 A2 80 55 35 A3 70 40 60
what is the optimal strategy for both?
Ferry A Ferriers (FAF) company each Monday advertises a weekend special fare as a means of attracting trippers away from its Zee Ferries( ZF) competitor. If FAF offers a low fare when ZF also offers the same low fare, ZF will gain 200 of FAF trippers, and if FAF offers free child with one adult passenger when ZF offers the same. ZF will gain 100 of FAF's trippers. On the other hand, If ZF offers low fares when FAF is offering free child, FAF will gain 150 of ZF's trippers. Similarly, ZF expects to lose 150 trippers if it offers free child when FAF is offering low fares.
What is the optimal mix of offer strategies for the two companies and what is the expected value of this strategy in the long run?
Thanks very much for your help in advance and appreciate your reply.