Reference no: EM13838200
Companies 1 and 2 are fighting over a market segment initially held by Company 2. Company 1 has $K in reserves and company 2 has $L. Whenever the market is served by one company, the competing company can launch a price war by reducing the price. The outcome of the price war is that the attacking company loses $1, the incumbent company loses $2, the attacking company wins the market share and, so long as it has funds left, maintains the market share. The management of each company is interested in maximizing profits, but also regards the holding of the market share as worth more than $1, but less than $2. If, after an attack, neither company has any reserve funds left, then the payoff for each company is 0. Analyze this situation as an extensive game (game tree) and, using backward induction, predict the winner as a function of K and L. [Hint: run the game with a few different starting points (K,L), such as (8,8), (8,7), (7,8), (7,7),(7,6), (6,7), (6,6), and use as a function stating whether K, L are even or odd, and ?,?,>,< to one another]. What does your result suggest about first mover’s advantage and incumbency? What application can be made to market share and price wars?
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