Game Trees in Business Strategy: Difference between revisions
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Sometimes one player has a dominant stratgy but the other does not. Suppose that 60 percent of potential buyers will pick Time and 40 percent of buyers will pick Newsweek. Now the table of Time's sales is as follows. Neither rows dominates the other. In other words, Time's best choice is not indepedent to Newsweek's choice. If Time chooses the immigration story, Newsweek does better by choosing the gas price story, and vice versa. Now Newsweek can assume that Time will choose the immigration story and pick the gas price story, which is their own best reponse, since Time has a dominant strategy. | Sometimes one player has a dominant stratgy but the other does not. Suppose that 60 percent of potential buyers will pick Time and 40 percent of buyers will pick Newsweek. Now the table of Time's sales is as follows. Neither rows dominates the other. In other words, Time's best choice is not indepedent to Newsweek's choice. If Time chooses the immigration story, Newsweek does better by choosing the gas price story, and vice versa. Now Newsweek can assume that Time will choose the immigration story and pick the gas price story, which is their own best reponse, since Time has a dominant strategy. | ||
Revision as of 09:08, 5 May 2006
Why Studying Business Strategy? | Game Trees in Business Strategy | Bargaining | Notes
Game Trees
Two Kinds of Strategic Interation: Sequential & Simultaneous
The essence of a game of stratefy is the interdependence of the players' decisions. Theses interactions arise in two ways. The first is sequential; each player makes alterning moves. The players must look ahead to how his current actions will affect the future actions of others, and his own future actions in turn. The second is simultaneous; the players act at the smae time, not knowing what the others' current actions. When you play a strategic game, you must determine whther the interation is simultaneous or sequential.
Sequential-move games
Rule: Look Ahead & Reason Back
The general principle for sequential-move games is that each player should predict the other players' future responses, and use them in calculating his own best current move. Therefore, players should anticipate where their initial decisions will ultimately lead, and use this information to calculate the best choice. Most strateifc situations involve a long sequence of decisions with several alternatives at each. Games trees of the choice in the game gives a visul aid for successful application of the rule of looking ahead and reasoning back.
Consider a business example that has a game tree. Suppose the market for MP3 players in Canada is dominated by Apple's iPod, and a new firm, iRiver is deciding whether to enter this market. If iRiver enters, iPod has two choices: accommodate iRiver by accepting a lower market share, or fight a price war. If iPod accommodates the entry, each makes a profit of $1,000,000. But if iPod starts a price war, this causes iRiver to lose $2,000,000 and iPod to lose $1,000,000. If iriver does not enter the market, its profit is zero. Here is the game tree and the profit for each outcome.
What should iRiver do? The outcomes "accommodation" and "price war" as alternatives arse by chance. If probabilities of the two are thought equally likely, each gets a probability of 1/2. then calculate the average profit that iRiver can expect from entry by multiplying each profit or loss with the corresponding probability. IRiver gets (1/2)($1,000,000)-(1/2)($2,000,000)=-$500,000. Since this is a loss, you would recommend iRiver to keep away from Canada.
But how can we get the probability estimates? The probabilities come from iRiver's beliefs about iPod's profits in each of these cases by using game theory. In order to estimate what iPod will do, iRiver must first estimate iPod's profits in the different scenarios. Then the players look forward and reason backward to predict what the other side will do.
Simulataneous-move games
Dominant Strategies
Every week, Time and Newsweek compete to have more eye-catching cover story. A dramatic and interesting cover will attract the attention of potential readers. The two magazines are engaged in a strategic game, but this game is quite different from the previous game. The game between iRiver and iPod had a sequence of alternating moves. IRiver decided whether or not to enter the market. By contrast, the actions of O and Peopleare simultaneous. By the time each discovers what the other has done, it is too late to change anything.
In the competition between Time and Newsweek assume that there are two major news stories: immigration protests and high gas price. Among newsstand buyers, suppose 70 percent are interested in the immigration protests story and 30 percent in the high gas price story. Therefore, if Newsweek uses the immigration story, then if Time uses the gas price story, Time will get the entire gas price market, which is 30 percent of all readers. By contrast, if Time uses the immigration story, Time and Newsweek share the immigration market, which is 35 percent each. If Newsweek uses the gast price story, then Time gets 15 percent, using the same story, and 70 percent with the Immigration story.
Here is simple table which shows the logic of this reasoning. Two columns correspond to NewsWeek's choices, and two rows correponds to Time's choices. The numbers show the percentage of the total potential readership. The first row shows Time's sales from choosing the immigration story and Newsweek's alternative choices. The second row shows Time's sale's from choosing the gas price story with Newsweek's choice. For example, when Time has the gas price story and Newsweek has the immigration story, then Time gets 30 percent of the market. The dominant strategy is easy to find. The first row is better than the second row. Each entry in the first row is bigger than the second row.
On the other hand, this table below shows Newsweek's sales. The first solumn is better than the second column. Once again, immigration story is dominant strategy for Newsweek, too. Games in which each side has a dominant strategy are simple. Each player's choice is his dominant strategy, irrepective of what the other does. However, the outcome is not the best result, and this competition takes them to a mutually worse outcome. This case is similar to prisoners' dilemma. They can either achieve the better outcome with cooperation or disastrous outcome.
One-Side Dominant Strategies
Sometimes one player has a dominant stratgy but the other does not. Suppose that 60 percent of potential buyers will pick Time and 40 percent of buyers will pick Newsweek. Now the table of Time's sales is as follows. Neither rows dominates the other. In other words, Time's best choice is not indepedent to Newsweek's choice. If Time chooses the immigration story, Newsweek does better by choosing the gas price story, and vice versa. Now Newsweek can assume that Time will choose the immigration story and pick the gas price story, which is their own best reponse, since Time has a dominant strategy.
