Business leaders and, indeed, people in general, differ greatly in what they are able to accomplish with given amounts of resources. Consequently, small armies led by brilliant military strategists sometimes defeat large armies commanded by unimaginative generals. Skilled poker players may be consistent winners even if, on average, they are dealt poor cards, while mediocre players usually walk away from a game as losers despite average or better cards. And one firm may fail miserably, while an apparently similar firm prospers. Luck is sometimes a decisive factor, but even more frequently, correctly forecasting the behavior of your friends or rivals and then developing an effective strategy is the key to success or failure.

 

            Economists who consider strategic behavior[1]  stress that: (a) a single firm's actions may affect industrial concentration, (b) dynamic decisions (decisions made over time) are invariably rational, and (c) differential information shapes firm behavior and market structure.

 

            This first point leads to the idea that, either individually or jointly, firms often pursue strategies to bar entry into their industry; potential competition often determines incumbent firms' current pricing and output policies. For example, banks located close to each other may unite to oppose the chartering of a new bank, citing the low interest rates they charge, lack of "need" for another bank, their willingness and ability to accommodate all "creditworthy" applicants for loans, and their service to the community.

 

            The second point is that firms, like all economic agents, make sequential rational decisions over time. What you will do in a particular situation depends on what you learned from experience after making decisions in similar situations. Firms consider the previous reactions of their rivals when planning a business strategy. Dynamic game theory models of rational decisions extend the boundaries of earlier theory. We will examine some of these conclusions in a moment and introduce several simple game theory models to give you a flavor of how it addresses some complex questions.

 

            The third point recognizes that bargaining parties may have different information about potential transactions that often affect incentives and decisions. For example, a firm's manager may know that a huge layoff is scheduled as soon as a contract is completed, but try to keep workers from looking for other jobs through false reassurances that the firm has a pending new contract to be fulfilled. This type of knowledge asymmetry is common. Traditional models that treat information as free and perfect, or which assume that all transactors share the same information base, typically yield different conclusions than models that recognize asymmetric information.

 

            Our next step is to describe game theory and look at a simple prisoners' dilemma model where both players move simultaneously. We then introduce a dynamic "product standards" game that illustrates the frequent benefits of being able to move first.

 

Strategy in Game Theory

The absence of overt or tacit collusion leads to rivalrous behavior that business leaders think of as competition. Pure competition is an impersonal process in which firms adjust outputs to a market determined price. Oligopolists who compete in a noncooperative fashion have more weapons at their disposal, including adjustments of prices, outputs, product lines and capacity, advertising, and their rates of technological innovation. This diversity of possible strategies among oligopolists led to the development of game theory in 1944 by the mathematician John von Neumann and the economist Oskar Morgenstern.

Game theory is the study of strategic interactions among interdependent decision makers.

 

            Game theory has been extended beyond oligopolistic behavior and is now applied to such areas as poker, courtship, athletic competition, collective bargaining, and national defense. A game requires pairing the costs and benefits of all possible strategies adopted by one player (participant) with all possible strategies adopted by an opponent. The payoff to each player depends on the strategies of other players, but players can select only their own strategy, not the strategies of other players. Then each set of possible outcomes is analyzed to ascertain an equilibrium, which occurs when every player optimizes, after adjusting for the likely strategies of other players.

 

            Winners' gains exactly offset losses to losers in such zero-sum games as poker. Most examples of game theory in economics are non-zero-sum games. Gains typically exceed losses in positive-sum games; exchange according to comparative advantage is an example. When two countries produce and trade products according to comparative advantage , citizens of both countries gain as more total goods are consumed. Violence is generally a negative-sum game; victims of a mugging may suffer bodily damage in addition to monetary loss, while the mugger only gains the money. Net gains may be either positive or negative in some non-zero-sum games, depending on the strategies of the players. For example, all firms in a market can profit if all charge the same high price, but if all charge a low price, all their profits are low.

Prisoners' Dilemma

A classic noncooperative game known as the prisoners' dilemma is often applied to cases of business rivalry, and helps explain why cartel arrangements break down. Suppose that two armed robbers (Able and Charley) are jailed separately and cannot communicate. Each is told that if neither confesses, both will serve a year in prison. If only one confesses and helps to convict the other, the squealer will go free while the silent party will serve 10 years. If both confess, however, both will be sentenced to 4-year terms.

 

            Figure 6 shows a payoff matrix describing each robber's options and payoffs. For example, if both hold out (don't confess), each spends a year in jail (-1, -1). Similarly, their terms are for 4 years (-4, -4) if both confess. What should each player do?

  Figure 6

           

Equilibrium in this prisoners' dilemma occurs if both players follow their dominant strategies. A strategy is dominant if, no matter what strategy your opponents select, your payoff is maximized (or a negative payoff is minimized).

A dominant strategy is a player's best response to any strategy other players might pick.

 

            Consider Able's dominant strategy. No matter which strategy Charley picks, Able gains by confessing, because he goes free if Charley holds out (compared to a year in jail if he, Able, holds out), while saving 6 years if Charley confesses (10 years - 4 years). In fact, both Able and Charley have dominant strategies---confess. Consequently, confess-confess is a dominant strategy equilibrium, because it is each player's dominant strategy. The dilemma facing prisoners is that they seem unable to cooperate so that each gets the shorter sentence---one year each in the case of Able and Charley. Refuting the "honor among thieves" stereotype, almost all prisoners succumb and "rat" on their colleagues.

 

            How does the prisoners' dilemma apply to oligopoly? Consider a cartel that sets output ceilings for each member. Every member will enjoy reasonable profit if no firm cheats by exceeding its quota, but a lone cheater will gain even more profit. If cheating is rampant (and it will be if players follow dominant strategies), all members' profits suffer. The power of the prisoners' dilemma game is reflected in the collapse of OPEC. The dilemma OPEC members faced ultimately brought down energy prices. The prisoners' dilemma model also applies in such areas as bids at an auction, the nuclear arms race, and strikes by unions when collective bargaining breaks down.

 

Cooperation in Game Theory

One obvious question is, "Why don't both prisoners agree not to confess? Then, each spends only a year in jail." Since one robber could potentially go free by confessing when the other doesn't, whether communication beforehand would matter would depend on whether agreements to hold out are binding. Although both might agree not to rat on the other, both eventually confess unless each can enforce their agreement on the other. If, however, agreements are binding, the results of the game differ.

Cooperative games permit players to make binding agreements, and players may form coalitions. Noncooperative games permit neither binding commitments nor coalitions.

            The prisoners' dilemma makes it clear that binding commitments change a game's equilibrium by changing the payoff matrix. For example, if Charley would murder Able if Able confessed and Able knows it, then Able's costs of confessing rise dramatically. This changes the payoffs, so the game is now different. How can players ensure that commitments are binding? Violence is a possibility, but agreements may also be made binding through such mechanisms as legally enforceable contracts, government regulations, or side payments (bribes) from one party to another.

 

            Examples of cooperative games include (a) international trade, (b) collective bargaining, in which firms and unions bargain over employment conditions and, (c) plea bargaining between prosecutors and defense attorneys. Cooperative games break down, however, if a party can gain by violating what was supposed to be a binding agreement. The prisoners' dilemma, hostile corporate takeovers, or pure competition are all examples of noncooperative games.

Moving First

The sequence of moves is unimportant in a simple prisoners' dilemma. No matter which prisoner chooses first, Able always confesses because he knows that if he is silent, he will spend 10 years in jail if Charley follows dominant strategy, rather than 4 years if he (Able) confesses. But the sequence of moves is important in many games. For example, a chess player who starts with the white pieces has the first move---an advantage over an equally talented player who uses the black pieces.

 

            Consider the case of IBM and Compaq in Figure 7. Both manufacturers must select either small (3.5") or large (5.25") disk drives as standard for their own computers, and both gain by using the same sizes. Their payoffs illustrate why making the initial decision or first move can be highly profitable for firms. If IBM (assume it goes first) installs 3.5" disk drives, so will Compaq. If Compaq selected first, it would select 5.25" drives and IBM would install large drives to maximize its profit (payoff). The first firm to introduce its standard clearly sets the industry standard. Each of these equilibria is also an example of a Nash equilibrium. [2]

Figure 7

A Nash equilibrium is a strategy combination where no player has a net incentive to change unless other players change.

 

            In the final equilibrium, either both will use 3.5" or both will use 5.25" drives; each firm will avoid losses by sticking with its now profitable strategy. In the prisoners' dilemma, there was only one Nash equilibrium (confess-confess), but there are two in this case. The final equilibrium turns on which player moves first. Many games have multiple Nash equilibria, and game theorists have developed sophisticated decision rules (beyond the scope of our inquiry) to determine which outcomes are most likely.

 

Dynamic Games

Real life games are seldom one-shot events like the prisoners' dilemma, but involve a sequence of choices over time. Consider the prisoners' dilemma repeated for a number of periods. How can we determine what would be a player's best set of choices over time?[3]

 

            Both Able and Charley would like to cooperate and be silent, but without the ability to enforce agreements, both would ultimately confess. Both also know that in the last repetition of the game, both confessed, so each might as well confess in the next to last period, and so on, until both confess in round one! Thus, both Able and Charley will serve 4   n (the number of periods in the game) years in jail.

 

            Dynamic (repeated) games lead to more sophisticated strategies than do one-shot games. These more sophisticated strategies can result in higher overall payoffs over time (or less jail time in the prisoners' dilemma). Two possibilities for infinitely repeated games are a grim strategy and tit for tat.

Grim Strategy

Second Mover Advantage

The opposite of being first is to wait for an opponent's first move. Although most boxing trainers urge their boxers to "be first," some boxers are natural counterpunchers who wait until their opponents make the first move. Similarly, many people may try to gather information in uncertain situations by letting the opponent move first. For example, people who are negotiating with a used car dealer often gain by refusing to answer the salesperson's "How much are you willing to pay for this car?"---insisting instead that the dealership state a "rock-bottom price" as a starting point for haggling.

            Following a noncommittal policy is known as a grim strategy.

A second mover advantage entails refusal to commit to a position until the other player commits to a position.

 

            Since some move is required in the first round, a prisoner following a grim strategy will begin in a "cooperative" (silent) mode. Prisoners who stick to grim strategies remain silent until the other person confesses but then confess in each subsequent round. If both steadfastly follow grim strategies, both receive minimum sentences.  A grim strategy is at fault when two timid people, both of whom might like a deeper relationship, are each afraid to say, “I love you.”  Their romance is doomed if neither makes a first move.

 

Tit for Tat

Screw up once and I’ll pound you forever.

-R. Byrns (2008Fall 9am Class)

 

Extensive experiments suggest that, in repetitive games, most people ultimately tailor their interactions to their opponents' previous choices. Instead of sticking to a strategy based on how your opponent first commits, you might begin in a cooperative mode, but then repeatedly echo whatever your opponent did in the previous period.

A tit-for-tat strategy begins cooperatively. Thereafter, in any period, tit for tat entails echoing what the opponent did in the previous period.

Tit for tat in everyday life means responding in kind to people's behavior. Whether they treat you well or badly, you treat them in precisely the same fashion. Tit for tat may not result in a stable equilibrium. For example, if one player begins tit for tat cooperatively, but another starts in a noncooperative mode, the players will infinitely flip-flop for as long as the game continues.

 

Asymmetric Payoffs

Game theorists have explored ways to avoid the "ratting" disaster in a prisoners' dilemma. Reputation building convinces opponents that past behavior is a good predictor of future behavior. Since the past entails only sunk costs, why wouldn't each party in a repeated prisoners' dilemma "let bygones be bygones" and make the best decision in each round? Firms, governments, and individuals often nurture reputations for toughness or hard bargaining. Asymmetric payoffs between parties are one possible motive for reputation building.

In an asymmetric payoff, the payoffs from cooperation for at least one party are higher than the payoffs to some other players.

            Silence equals cooperation in the prisoners' dilemma. A party preferring to cooperate only confesses if the other party does. Our example of asymmetric payoffs (Figure 8) involves consumers who decide to purchase only from sellers with "clean" environmental records. These consumers boycott polluters' products. The (0, 0) payoff connotes consumers' refusals to deal with sellers who have ever polluted.

Figure 8

 

            A reputation as a nonpolluter will ensure long-run returns, so nonpollution as a strategy means that consumers will continue to purchase products. Buyers only pick boycott as a defensive action when sellers cheat (save on pollution control costs) and pollute. While pollute-boycott is a Nash equilibrium, it is not a dominant strategy (the only outcome) as confessing is in the prisoners' dilemma. Reputation can be important in many models---including, for example, an oligopolist that builds a reputation for matching price cuts of opponents but not price increases, or entry deterrence decisions, in which a potential new entrant must judge the willingness of incumbent firms to fight market entry.

 

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