Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life

See “Tree Diagram.”

A dominant strategy is “one course of action that outperforms all others no matter what the other players do” (59). A dominant strategy, then, is at least as good as, and often better than, all other plans. When players arrive at such a strategy, their calculations simplify: They follow the dominant strategy in every such situation. A dominant strategy is not the one that dominates other players but the one that dominates all choices for a given player. It doesn’t necessarily guarantee a win but it’s the best option in every scenario. 

A dominated strategy is one that is worse or no better than all other strategies for a given player. These options should be dropped from consideration; if another strategy becomes the new dominated strategy, it, too, should be removed, and so on until all such strategies are eliminated as options. If, during this process, a strategy emerges that’s dominant, it should be adopted. (See “Dominant Strategy.”)

An equilibrium arises when two players try to predict each other’s moves, then predict each other’s responses to those moves until their thinking converges at the same strategy. Here, the endless loop of circular reasoning about each other’s strategies comes to an end, both parties are safe from loss, neither can gain an advantage, and neither party can be tricked into settling because the other side ends up in the same place: “Given what the other is doing, neither wants to change his own move. Game theorists call such an outcome an equilibrium” (76). 

A game is a situation of strategic interdependence: the outcome of your choices (strategies) depends upon the choices of another person or persons acting purposively. The decision-makers involved in a game are called players, and their choices are called moves (85).

Games are everywhere, from hands of poker to business competition to political campaigns to world wars. Games can be understood and played scientifically through game theory. 

Game theory is the science of making strategies; it contains specific approaches to different types of competition. Game theory is the main subject of Thinking Strategically. First developed during the mid-1900s, game theory has grown into a large field used by businesses, sports teams, government planners, military operations, and other organizations. Individuals also can use game theory in their daily lives to improve decision-making at work, play, and home. 

See “Tree Diagram.” 

The min-max theorem states that, in a zero-sum game between two players, “one player should attempt to minimize his opponent’s maximum payoff while his opponent attempts to maximize his own minimum payoff” (178). They soon reach an equilibrium where their minimum gain is the maximum allowed by the other side. 

A prisoner’s dilemma is an agreement between two or more players to make sacrifices for their common good, but which tempts each player to cheat and take advantage of the other side’s loyalty. The classic example is where two suspects, interrogated separately by police, have agreed beforehand to stonewall investigators and receive small prison sentences, but each can reduce his sentence further by selling out the other partner. If, however, both confess and sell out the other, both get harsh sentences: “When neither confesses, the outcome is better for both. The problem is how to attain such cooperation given the competition to obtain an especially good deal for oneself” (91). Prisoner’s dilemmas occur commonly in business, politics, and social life at any time that a group effort tempts members to betray the agreement for a better result.  

Games are either sequential or simultaneous. In a sequential game, players take turns making moves. A tennis match is a good example. “In a game of sequential moves, there is a linear chain of thinking: If I do this, my rival can do that, and in turn I can respond in the following way” (85). Sequential strategies are best charted on a game tree. Simultaneous play involves two or more players moving at the same time: “one must see through the rival’s action even though one cannot see it when making one’s own move” (85). Politicians who must announce their campaign strategies on the same day, or businesses who launch competing products at the same time, are examples of simultaneous play. Simultaneous strategies can best be evaluated by constructing a table that shows one player’s options as columns and a second player’s options as rows, with results of each combination of moves shown in the table’s squares. 

A Schelling point, or focal point, is a place where people searching for each other but not in communication are likely to meet. Developed by games strategist Thomas Schelling, such a location is the place people will go to when they reason out that it’s where the other person will search for them. The classic example is Grand Central Station, where the solution to “Meet me in New York” is likely to be found. Schelling points also occur in other activities—for example stock picking, where investors try to guess what shares other players want to buy and then purchase some while they’re still cheap. 

A strategic move “is designed to alter the beliefs and actions of others in a direction favorable to yourself. The distinguishing feature is that the move purposefully limits your freedom of action” (120). If an army invades, the defenders burn everything, making the invasion worthless. If a company raids another company for its talented employees, the employees all quit, making the attack pointless. A politician promises not to raise taxes, limiting his options but attracting tax-weary voters. The point of a strategic move is to demonstrate to the opposition that the player won’t capitulate. Such a move becomes credible if the player also commits in advance to spend resources. Strategic moves must be announced in advance, or they have no effect. Strategic moves that respond to another’s moves are called “response rules” and take two forms—threats, to compel or deter behavior; and promises, to encourage cooperation.  

A strategy is a plan for winning a contest or executing a complex plan. It helps guide the player as the game or activity unfolds. Strategies vary greatly, depending on game conditions: A sequential game requires different approaches than a simultaneous game; some games require prior commitments; some work better if the player goes second; and so on. Modern strategists rely heavily on game theory, and they often use tree diagrams or tables to plan their moves. 

In game theory, a table, or matrix, is a chart made of rows and columns, the rows representing the options for one team and the columns the options for the other team in simultaneous play. For example, competing news magazines Time and Newsweek each have the same two options for their cover story, an AIDS update or a national budget crisis, and each wants to know their best outcome as a percentage of total readership they attract based on all the possible situations. Newsweek can list its options in two columns and put Time’s options into two rows; this creates a table with four squares. If Newsweek’s first column is “AIDS” and Time’s first row also is “AIDS,” then the upper-left box in the table will contain the result if both magazines choose “AIDS” as their cover stories. If 70% of readers prefer to buy a magazine with the “AIDS” story on the cover, then the upper-left box will show the number “35” because the two magazines will split that 70% of readers. The other squares in the table will show the percentage number for each of the other three options. 

Tit-for-tat is a game strategy that “cooperates in the first period”—that is, when the tit-for-tat player goes first—“and from then on mimics the rival’s action from the previous period” (106). If the other player cheats, the tit-for-tat player cheats; if the other player cooperates, the tit-for-tat player cooperates. This strategy punishes opponents if they cheat and rewards them if they cooperate, which guides opponents toward cooperation. Tit-for-tat is “as clear and simple as you can get. It is nice in that it never initiates cheating. It is provocable, that is, it never lets cheating go unpunished. And it is forgiving, because it does not hold a grudge” (107). Tit-for-tat beats other systems for winning prisoner’s dilemma contests. In the real world, though, automatic retaliation can insult the other player, leading to endless feuds. Players work around this limitation by adding a rule that breaks a series of retaliations with an offer to cooperate. 

A tree diagram helps a strategist plan moves in a sequential process or game. It contains a line for every possible move, with additional lines branching off from each move; this “describes one’s options at each junction” and “looks like a tree with its successively emerging branches” (35). A tree diagram organizes a jumble of possible choices into a chart for easy reading. One person can use a tree diagram called a “decision tree” to plan, for example, a vacation. For two or more persons, as in sports, the diagram becomes a “game tree,” which players use to anticipate their opponent’s likely next move and plan their response. Strategists tend to read tree diagrams backwards, from the most-desired outcome to the moves that lead up to it. 

Named for its inventor, economist William Vickrey, in this auction, “Each person places his bid in a sealed envelope, and the highest bidder is sold the item at the second highest bidder’s price” (322). This motivates bidders to offer a bit more than they might. A Vickrey auction does in reverse what some hiring auctions do for work contracts: The lowest bidder gets paid the second-lowest bidder’s offer. Both systems make bidding more accurate and slightly improve the auctioneer’s results.