Game theory is generally considered to have begun with the publication of von Neumann & Morgenstern's The Theory of Games and Economic Behavior in 1944.

Note: The first payment goes to the row player, the second payment goes to the column player.

If column player is silent what is the best action for the row player?

Well, if the row player is silent then the row player gets -1 (that is, a year in jail); if the row player finks the row player gets 0 (i.e., no time in jail). Therefore, it is best for the row player to Fink.

If the column player finks what is the best action for the row player?

Here if the row player is silent, the row player gets -10 (a decade in jail). If the row player finks, the row player gets -8 (eight years in prison). Therefore, it is best for the row player to Fink.

We can conclude then that the row player in this game situation has a dominant strategy to FINK. That is, no matter what the column player does, FINK is the best response by the column player.

This game is symmetric, so that if we went through the same exercise for the column player, it is easily seen that FINK is a dominant strategy for the column player.

The "payoff" of this game is (-8, -8) and in this case is the dominant strategy (Nash) equilibrium. If both players have a dominant strategy then there is by definition a dominant strategy equilibrium. There are strong reasons to predict this outcome if each player makes their best move.

(It is important to note that the "collective rationality" is for both to remain silent and obtain the payoff (-1, -1), however, the "individual rationality" is for each member to play their dominant strategy. The end result, however, is (-8, -8).

The prisoners' dilemma game is a very powerful illustration (metaphor") for a fundamental conflict that we all know all too well.

What is best for an individual may not be best for a division.
What is best for a division may not be best for a firm.
What is best for a firm may not be best for a strategic group.

What is best for a strategic group may not be best for the industry.

What is best for an industry may not be best for the nation.
What is best for a nation may not be best for the world.

The way an economist generally expresses this idea is that "individual rationality" does not always lead to "collective rationality."

Rationality at lower level "units of analysis" does not always lead to the best outcome for higher level units of analysis.

In the prisoners' dilemma what is best for them as individuals (i.e., individual firms) is to fink and this "individual rationality" is detrimental to their "group" well-being. (-8, -8) is worse than (-1, -1). However, no matter how much they preach the importance of the common good, there is always the possibility that there is no honor among thieves. The (poor) outcome predicted is the prisoners' dilemma.

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Now that we have learned the dominant strategy equilibrium, there is a weaker equilibrium concept called a Nash equilibrium. A Nash equilibrium occurs when at a payoff cell it is the case that neither player would unilaterally change their strategy.

ALL DOMINANT STRATEGY EQUILIBRIUM ARE NASH EQUILIBRIUM BUT NOT ALL NASH EQUILIBRIUM ARE DOMINANT STRATEGY EQUILIBRIUM.

Does the column player have a dominant strategy? YES

Does the row player have a dominant strategy? NO.

Therefore, there is not a dominant strategy equilibrium.

Is there a Nash equilibrium? Yes. At (4, 4) neither player would unilaterally change strategy.

There are also games that have multiple equilibria:

The Battle of the Sexes Game (A cooperative game with conflict)

Characteristics of this game:

The most important thing is that they are together.

But after that, the man wants to go to the prize fight, while the woman wants to go to the ballet.

This game has multiple (Nash) equilibria.

Suppose the game was played sequentially? Would it be better to go first or second?

Sometimes first-mover advantages are played out in terms of dominant designs for technology. The economics of QWERTY.

There is a mixed strategy equilibrium in which each player plays each strategy at random with probability of ½ even and ½ odd for each play.

Variation on Battle of Sexes Game (or Joe Mahoney's sad undergraduate days):

No pure strategy Nash equilibrium.
Would you like to move first or second?

We are back where we began with a Prisoners' Dilemma.

The strategies which are best for the "collective good" are that both firms cooperate. While this is collectively rational, it is unfortunately not individually rational.

Does General Motors have a dominant strategy?

Does Toyota have a dominant strategy?

One way out of the Prisoners' dilemma occurs when the players take steps that change the payoff matrix. Paradoxically, worsening some of one's own payoff possibilities may improve the likely outcome of the game (see Thomas Schelling the Strategy of Conflict)

Cooperation is now General Motor's dominant strategy.

Lesson: The wise manager should think beyond Machiavelli's myopic approach to contracting and should seek both to give AND receive credible (sunk cost) commitments that facilitate ongoing relationships and adaptation.

Schelling, Thomas (1960). The Strategy of Conflict. Cambridge, MA: Harvard University Press.

Chapter 1 International Strategy

"A study of conscious, intelligent, sophisticated conflict behavior ­ of successful behavior ­ is like a search for rules of 'correct' behavior in a contest-winning sense. We can call this field of study the strategy of conflict. The term "strategy" is taken here, from the theory of games, which distinguishes games of skill, games of chance, and games of strategy, the latter being those in which the best course of action for each player depends on what the other players do. The term is intended to focus on the interdependence of the adversaries' decisions and on their expectations about each other's behavior. This is not the military usage." (p.3)

"If we confine our study to the theory of strategy, we seriously restrict ourselves by the assumption of rational behavior ­ not just of intelligent behavior, but of behavior motivated by a conscious calculation of advantages, a calculation that in turn is based on an explicit and internally consistent value system. We thus limit the applicability of any results we reach. If our interest is the study of actual behavior, the results we reach under this constraint may prove to be either a good approximation of reality or a caricature. Any abstraction runs a risk of this sort, and we have to be prepared to use judgment with any results we reach." (p.4)

"...in taking for granted, and working with an image of participants who try to 'win,' a theory of strategy does not deny that there are common as well as conflicting interests among the participants. In fact, the richness of the subject arises from the fact that, in international affairs, there is mutual dependence as well as opposition. Pure conflict, in which the interests of two antagonists are completely opposed, is a special case; it would arise in war of complete extermination, otherwise not even in war. For this reason, 'winning' in a conflict does not have a strictly competitive meaning; it is not winning relative to one's adversary. It means gaining relative to one's own value system; and this may be done by bargaining, by mutual accommodation, and by the avoidance of mutually damaging behavior." (pp. 4-5)

"Thus, strategy -- in the sense in which I am using it here -- is not concerned with the efficient application of force but with the exploitation of potential force. It is concerned not just with enemies who dislike each other but with partners who distrust or disagree with each other. It is concerned not just with the division of gains and losses between two claimants but with the possibility that particular outcomes are worse (better) for both claimants than certain other outcomes. In the terminology of game theory, most interesting international conflicts are not "constant-sum games" but "variable-sum games": the sum of the gains of the participants involved is not fixed so that more for one inexorably means less for the other. There is a common interest in reaching outcomes that are mutually advantageous." (p.5)

"To study the strategy of conflict is to take the view that most conflict situations are essentially bargaining situations." (p. 5)

"A 'successful' employees' strike is not one that destroys the employer financially, it may even be one that never takes place. Something similar can be true of war." (p. 6)

"The idea of 'deterrence' has had an evolution that is instructive for our purpose. ... We have learned that a threat has to be credible to be efficacious, and that its credibility may depend on the costs and risks associated with fulfillment for the party making the threat. We have developed the idea of making a threat credible by getting ourselves committed to its fulfillment ..." (p. 6)

"... a useful distinction can be made between the application of force and the threat of force. Deterrence is concerned with the exploitation of potential force. It is concerned with persuading a potential enemy that he should in his own interest avoid certain courses of activity. ... A theory of deterrence would be, in effect, a theory of the skillful nonuse of military forces, and for this purpose deterrence requires something broader than military skills." (p. 9)

"Deterrence -- to continue with deterrence as a typical strategic concept -- is concerned with influencing the choices that another party will make, and doing it by influencing his expectations of how he will behave." (p. 13)

"... 'strategic behavior' is concerned with influencing another's choice by working on his expectation of how one's own behavior is related to his." (p.15)

"... we might call our subject the theory of interdependent decision." (p. 16)

"Rationality is a collection of attributes and departures from complete rationality may be in many different directions. Irrationality can imply a disorderly and inconsistent value system, faulty calculation, an inability to receive messages or to communicate efficiently; it can imply random or haphazard influences in the reaching of decisions or the transmission of them, or in the receipt or conveyance of information; and it sometimes merely reflects the collective nature of a decision among individuals who do not have identical value systems and whose organizational arrangements and communication systems do not cause them to act like a single entity." (p. 16)

"...the results reached by a theoretical analysis of strategic behavior are often somewhat paradoxical; they often do contradict common sense or accepted rules. ... the same tactic is illustrated by the burning of bridges behind oneself to persuade an adversary that one cannot be induced to retreat." (pp. 18-19)

"... the power of a negotiator often rests on a manifest inability to make concessions and to meet demands. Similarly, while prudence suggests leaving open a way of escape when one threatens an adversary with mutually painful reprisal, any visible means of escape may make the threat less credible. The very notion [proposed is] that it may be a strategic advantage to relinquish certain options deliberately ..." (p. 19)

"... where trust and faith do not exist ... The ancients exchanged hostages, drank wine from the same glass to demonstrate the absence of poison, met in public places to inhibit the massacre of one by the other, and even deliberately exchanged spies to facilitate transmittal of authentic information. Its seems likely that a well-developed theory of strategy could throw light on the efficacy of some of those old devices, suggest the circumstances to which they apply, and discover modern equivalents that ... may be desperately needed in the regulation of conflict." (p.20)

Chapter 2 "An Essay on Bargaining"

"[W]e shall be concerned with what might be called the 'distributional' aspect of bargaining: the situations in which a better bargain for one means less for the other. When the business is finally sold to the one interested buyer, what price does it go for? When two dynamite trucks meet on a road wide enough for one, who backs up? These are situations that ultimately involve an element of pure bargaining -- bargaining in which each party is guided mainly by his expectations of what the other will accept." (p. 21)

"The purpose of this chapter is to call attention to an important class of tactics of a kind that is peculiarly appropriate to the logic of indeterminate situations. The essence of these tactics is some voluntarily but irreversible sacrifice of freedom of choice. They rest on the paradox that the power to constrain an adversary may depend on the power to bind oneself; that, in bargaining, weakness is often strength, freedom may be to capitulate, and to burn bridges behind one may suffice to undo an opponent." (p. 22)

"When one wishes to persuade someone that he would not pay more than $66,000 for a house that is really worth $70,000 to him, what can he do to take advantage of the usually superior credibility of the truth over a false assertion? Answer: make it true. .... [S[uppose the buyer could make an irrevocable and enforceable bet with some third party, duly recorded and certified, according to which he would pay for the house no more than $66,000, or forfeit $5,000. The seller has lost; the buyer need simply present the truth. ... [T]he buyer's true incentive has been voluntarily, conspicuously, and irreversibly changed. [I]f the buyer can accept an irrevocable commitment, in a way that is unambiguously visible to the seller, he can squeeze the range of indeterminacy down to the point most favorable to him." (p. 24)

"What makes many agreements enforceable is only the recognition of future opportunities for agreement that will be eliminated if mutual trust is not created and maintained, and whose value outweighs the momentary gain from cheating in the present instance." (p. 45)

(Comment: In modern strategic management, such agreements are called Self-enforcing agreements. In other words, [imperfect] third-party enforcement is not relied upon.)

Chapter 3 Bargaining, Communication ...

Tacit Coordination

"The follow abstract puzzles are typical of those that can be 'solved' by a substantial proportion of those who try. The solutions are, of course, arbitrary to this extent: any solution is 'correct' if enough people think so." (p. 55)

Problem 1:

Name "heads" or "tails." If everyone in the class names the same you win.

Problem 2:

Circle one of the numbers listed in the line below. You win if all succeed in circling the same number.

Problem 3:

Put a check mark on one of the sixteen dots. You win if you all succeed in checking the same dot.

Problem 4:

You are to meet somebody in New York City. You have not been instructed where to meet; you have no prior understanding with the person on when to meet; and you cannot communicate with each other. Try to make you guesses coincide on both where and when to meet.

Problem 5:

Write some positive number. If you all write the same number, you win.

Problem 6: Name an amount of money. If you all name the same amount, you can have as much as you name.

Problem 7:

You are to divide $100 into two piles, labeled A and B. If you allot the same amounts, you each get $100.

"These problems are artificial, but they illustrate the point. People can often concert their intentions or expectations with others if each knows that the other is trying to do the same. Most situations -- perhaps every situation for people who are practiced at this kind of game ­ provide some clue for coordinating behavior, some focal point for each person's expectation of what the other expects him to expect to be expected to do. Finding the key, or rather finding a key -- any key that is mutually recognized as the key becomes the key -- may depend on imagination more than on logic; it may depend on analogy, precedent, accidental arrangement, symmetry, aesthetic or geometric configuration, casuistic reasoning, and who the parties are and what they know about each other. (p. 57)

"A prime characteristic of most of these 'solutions' to the problems, that is, of the clues or coordinators or focal points, is some kind of prominence or conspicuousness. But it is a prominence that depends on time and place and who the people are." (pp. 57-58)

[an imaginative process of introspection]

Focal Points and Divergent Interests:

"[T]here is abundant evidence that some [focal point] is powerfully present even in explicit bargaining. In bargains that involve numerical magnitudes, for example, there seems to be a strong magnetism in mathematical simplicity. A trivial illustration is the tendency for the outcomes to be expressed in "round numbers"; the salesman who works out the arithmetic for his 'rock-bottom' price on the [used] automobile at $2,507.63 is fairly pleading to be relieved of $7.63." (p. 67)

"If we then ask what it is that can bring their expectations into convergence and bring the negotiation to a close, we might propose that it is the intrinsic magnetism of particular outcomes, especially those that enjoy prominence, uniqueness, simplicity, precedent, or some rationale that makes them qualitatively differentiable from the continuum of possible alternatives. ... The rationale may not be strong at the arbitrary 'focal point," but at least it can defend itself with the argument "If not here, where?" (p. 70)

Focal points enable "intuitively perceived mutual expectations." (p. 71)

Chapter 4 "Toward a Theory of Interdependent Decision"

Games:

1. Games of pure conflict: Zero-sum games (e.g., chess)
2. Games of pure coordination (e.g., charades) ­ in academics "team theory"
3. Games of bargaining with conflict and coordination (e.g., a typical business joint venture).

These three types of games will be called:

Type 1: Zero-sum games

Type 2: Coordination games

Type 3: Bargaining games

"It is to be stressed that the pure-coordination game is a game of strategy in the strict technical sense. It is a behavior situation in which each player's best choice of action depends on the action he expects the other to take, which he knows depends, in turn, on the other's expectations of his own. This interdependence of expectations is precisely what distinguishes a game of strategy from a game of chance or a game of skill. In the pure-coordination game the interests are convergent; in the pure-conflict game the interests are divergent; but in neither case can a choice of action be made wisely without regard to the dependence of the outcome on the mutual expectations of the players." (p. 86)

The individual character of [a firm with a strong cultural] seems to be largely a matter of convergent expectations -- everyone's expectation of what everyone expects of everyone -- with the new arrivals' expectations being molded in time to help mold the expectations of subsequent arrivals. There is a sense of a "social contract," the particular terms of which are sensed and accepted by each incoming generation. (p. 92)

The Empirical Relevance of a Focal Point:

"[M]athematical solutions are one species of a genus of influences that have the power to focus expectations; but they work through the same psychic mechanism -- this power of suggestion that is able to bring expectations into convergence -- as the other species. When husband and wife, separated in a department store, gaily traipse off to the Lost and Found by a tacit and jocular mutual appreciation that it is the 'obvious' place to meet, two mathematicians in the same situation -- each aware that both are aware that both are mathematicians -- might look for a geometrically unique point rather than one that depended on a play of words. ... If the phenomenon of 'rational agreement' is fundamentally psychic -- convergence of expectations ­ there is no presumption that mathematical game theory is essential to the process of reaching agreement, hence no basis for presuming that mathematics is a main source of inspiration in the convergence process." (p. 114)

Chapter 5 Enforcement, Communication, and Strategic Moves

"The commitment is a strategic move, a move that induces the other player to choose in one's favor. It constrains the other player's choice by affecting his expectations. The power to commit one's self in this kind of game is equivalent to 'first move.' And if the institutional arrangements provide no means for incurring an irrevocable commitment in a legal or contractual sense, one may accomplish the same thing by an irreversible maneuver that reduces his own freedom of choice." (pp. 122-123)

[Comment: Sunk cost investments are "irreversible maneuvers"]

"Many interesting game tactics and game situations depend on the structure of communication, particularly in the structure of communication, particularly asymmetries in communication and unilateral options to initiate communication or to destroy it. ... When a man and a wife are arguing by telephone over where to meet for dinner, the argument is won by the wife if she announces where she is going and hangs up. And the status quo is often preserved by a person who evades discussion of alternatives, even to the extent of simply turning off his hearing aid." (p. 146)

Chapter 6 Game Theory and Experimental Research

"[T]he principles relevant to successful play, the strategic principles, the propositions of a normative theory, cannot be derived by purely analytical means from a priori considerations. ... [In a bargaining game], two or more centers of consciousness are dependent on each other in an essential way. Something has to be communicated; at least some spark of recognition must pass between the players." (p. 163)

"[C]onsider the question whether two people, looking at the same ink blot, can identify the same picture or suggestion in it if each is trying and knows that the other is trying to concert on the same picture or suggestion? The answer to this question can be found only by trying. But, if they can, they can do something that no purely formal game theory can take into account; they can do better than a purely deductive game theory would predict. And, if they can do better -- if they can arise above the limitations of a purely formal game theory -- even a normative, prescriptive, strategic theory cannot be based on purely formal analysis." (p. 164)

Chapter 9 The Reciprocal Fear of Surprise Attack

"If I go downstairs to investigate a noise at night, with a gun in my hand, and find myself face to face with a burglar who has a gun in his hand, there is danger of an outcome that neither of us desires. Even if he prefers just to leave quietly, and I wish him to, there is a danger that he may think I want to shoot, and shoot first. Worse, there is a danger that he may think that I think he wants to shoot first. Or he may think that I think that he thinks I want to shoot. And so on. "Self-defense" is ambiguous, when one is only trying to preclude being shot in self-defense." (p. 207)

Chapter 10 Surprise Attack and Disarmament

"If Russia knows we won't attack first, the Kremlin will be very much less apt to attack us ... Our reluctance to strike first is a military disadvantage to us; but it is also, paradoxically, a factor in preventing a world conflict today. We live in an era in which a potent incentive on either side -- perhaps the main incentive -- to initiate total war with a surprise attack is the fear of being a poor second for not going first. 'Self-defense' becomes peculiarly compounded if we have to worry about his striking us to keep us from striking him to keep him from striking us ..." (p. 231)

"There is a difference between a balance of terror in which either side can obliterate the other and one in which both sides can do it no matter who strikes first. It is not the 'balance' -- the sheer equality or symmetry in the situation -- that constitutes mutual deterrence; it is the stability of the balance. The balance is stable only when neither, in striking first, can destroy the other's ability to strike back." (p. 232)

Dixit, Avinash K. and Barry J. Nalebuff (1991). Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life. New York: W.W. Norton.

"The science of strategic thinking is called game theory." (p. ix)

"[T]hink of the difference between the decisions of a lumberjack and those of a general. When the lumberjack decides how to chop wood, he does not expect the wood to fight back; his environment is neutral. But when the general tries to cut down the enemy's army, he must anticipate and overcome resistance to his plans." (p. 1)

[Purposive people's] aims often conflict with yours, but they include some potential allies. Your own choice must allow for the conflict, and utilize the cooperation. Such interactive decisions are called strategic, and the plan of action appropriate to them is called a strategy. ... The branch of social science that studies strategic decision-making is called game theory. (pp. 1-2)

"There are two ways to move second. You can imitate as soon as the other has revealed his approach (as in sailboat racing) or wait longer until the success or failure of the approach is known (as in computers)." (p. 11)

"Why is a planeload of people powerless before a single hijacker with a gun? In both cases, a simultaneous move by the masses stands a very good chance of success. But the communication and coordination required for such action is difficult. ...They are just a prisoners' dilemma with more than two people; one might call this the hostages' dilemma. (p. 17)

Chapter 2 Anticipating Your Rival's Response

The essence of a game of strategy is the interdependence of the player's decisions. These interactions arise in two ways: (1) simultaneous, as in the prisoners' dilemma game; the second is sequential. (p. 33)

Rule #1 Look ahead and reason back. (p. 34)

"For any game with a finite number of sequential moves there exists some best strategy. Of course, just because a best strategy exists doesn't mean that we can easily find it. Chess is the prime example. (p. 42)

"Some simple games can be solved completely. For example, in three-by-three tic-tac-toe, a draw can always be obtained." (pp. 42-43)

"An essential feature of negotiations is that time is money. When negotiations become protracted, the pie begins to shrink. Still, the parties may fail to agree, each hoping that the costs of negotiating will be outweighed by a more favorable settlement. Charles Dickens's Bleak House illustrates the extreme case; the dispute over the Jarndyce estate was so prolonged that the entire estate was swallowed up by lawyers' fees. In the same vein, if failure to reach a wage agreement leads to a labor strike, the firm loses profits and workers lose their wages." (p. 45)

"[F]ew games in life have well-specified rules that the players must obey. The players make their own rules." (p. 50)

Chapter 3 Seeing through Your Rival's Strategy

"[Y]ou must not regard the unknown actions of the other players as being uncertain in an impersonal way like the weather." (p. 57)

Dominant Strategies

"In baseball, when there are two outs and count stands at three balls and two strikes, any forced base runners should run on the pitch. ... [R]unning on the pitch is a dominant strategy. (pp. 58-59)

"A dominant strategy is one that makes a player better off than he would be if he used any other strategy, no matter what strategy his opponent uses." (p. 65)

Rule #2 If you have a dominant strategy; use it. (p. 66)

Rule #3 Eliminate any dominated strategies from consideration, and go on doing so successively. (p. 69)

Rule #4 Having exhausted the simple avenues of looking for dominant strategies or ruling out dominated ones, the next thing to do is look for a Nash equilibrium of the game. (p. 76)

"When we say that an outcome is an equilibrium, there is no automatic presumption that it is best for all the players in the game, let alone for society as a whole." (p. 77)

Which side of the road should you drive on? The game has two equilibria. [We] need a convention. (p. 79)

How a Corporate Raider Can Place Target Shareholders in a Prisoners' Dilemma

A two-tiered bid typically offers a high price to the first shares tendered and a lower price to the later shares tendered. To keep numbers simple, we look at a case in which the pre-takeover price is $100 per share. The first-tier of the bid offers a higher price, $105 per share to the first shareholders until half of the total shares are tendered. The next fifty percent of the shares tendered fall into the second tier; the price paid for these shares is only $90 per share. For fairness, shares are not placed in the different tiers based on the order in which they are tendered. Rather, everyone gets a blended price: all the shares tendered are placed on a pro-rated basis into the two-tiers. (Those who don't tender find all of their shares end up in the second tier if the bid succeeds. A raider who gains control of the company has a right to take the company private and thus buy out all remaining shareholders. By law, these shareholders must be given a 'fair market' price for their stock. Typically, the lower tier of a two-tiered bid is still in the range of what might be accepted as fair market value.) We can express the average payment for shares by a simple algebraic expression: if fewer than 50 percent tender, everyone gets $105 per share; if an amount X > 50% of the company's total stock gets tendered, then the average price paid per share is

$105 (50/X) + $90 ( (X - 50)/X) = $90 + $15 (50/X)

One thing to notice about the way the two-tiered tender offer is made is that it is unconditional; even if the raider does not get control, the tendered shares are still purchased at the first tier price. The second feature to note about the way this two-tiered offer works is that if everyone tenders, then the average price per share is only $97.50. This is less than the price before the offer. It's also worse than what they expect should the takeover fail; if the raider is defeated, shareholders expect the price to return to the $100 level. Hence they hope that the offer is defeated or that another raider comes along.

Tendering to the two-tiered offer is a dominant strategy. To verify this, we consider all the possible cases. There are three possibilities to check.

1. The two-tiered offer attracts less than 50% of the total shares and fails.
2. The two-tiered offer attracts some amount above 50% and succeeds.
3. The two-tiered offer attracts exactly 50%. If you tender the offer will succeed, and without you it fails.

Case #1:
If the two-tiered offer fails, and you did not tender your shares you stay at $100 per share. But if you tender your shares you get $105 per share.

Case #2:
If the two-tiered offer succeeds, and you do not tender your shares you get $90 per share. Tendering gives you at worst $97.50. So again it is better to tender your shares.

Case #3
While other people are worse off if the offer succeeds, you are privately better off. The reason is that since there are exactly 50% tendered, you will get $105 per share.

Because tendering is a dominant strategy, we expect everyone to tender. When everyone tenders, the average blended price per share may be below the pre-bid price and even below the expected future price should the other fail. Hence the two-tiered bid enables a raider to pay less than the company is worth. The fact that the shareholders have a dominant strategy does not mean that they end up ahead. The raider uses the low price of the second tier to gain an unfair advantage. Usually the manipulative nature of the second tier is less stark than in our example because the coercion is partially hidden by the takeover premium. If the company is truly worth $110 after the takeover, then the raider can still gain an unfair advantage by using a second tier below $110 but above $100.

(Editorial Comment:

Note that the target firm's shareholders have been gored on the horns of the prisoners' dilemma by the corporate raider. The target shareholders can fight back by voting in favor of corporate charter amendments that refuse to entertain two-tiered tender offers:

Fair-price amendments restrict the transfer of control of a firm if the bidder makes a hostile two-tier tender offer. This decrease in options for the shareholders can improve their strategic advantage.)

Resolving the Prisoners' Dilemma

Each country has a dominant strategy: produce at the higher of the two available levels. This predicament is another prisoners' dilemma. Its remarkable feature is that both sides play their dominant strategy, thus maximize their payoff, and yet the outcome is jointly worse. Iran and Iraq's situation is analogous to that of the prisoners in our earlier example

How to Achieve Cooperation:

Detection of Cheating. A cartel has to find ways to discover if cheating has in fact occurred, and if so, then determine who has cheated. (p. 95)

Punishment of Cheaters. Behind every good scheme to encourage cooperation is usually some mechanism to punish cheaters. The possibility of punishment arises because the two countries are involved in this game day after day.

There is no solution that achieves reciprocal cooperation in a one-time game. Only in an ongoing relationship is there an ability to punish, and thus a stick to motivate cooperation.

Suppose the game is repeated only a fixed number of times. Right from the start, both players look ahead to predict the last play. On this last play, there will be no future to consider, and the dominant strategy is to cheat. The outcome of the last play is a foregone conclusion. Since there is no way to affect the last play of the game, the penultimate play effectively becomes the last one to consider. Once again, cheating is a dominant strategy, and so on ... This argument unwinds all the way back, so that there is no cooperation even in the first play.

The logic of the argument is impeccable, and yet in the real world we find episodes of successful cooperation. There are various ways to explain this. One is that all actual games of this kind are repeated only a finite number of times, but that number is unknown. Since there is no fixed last time, there is always the possibility that the relationship will go on. Then the players have some incentive to sustain the cooperation for the sake of such future contingencies; if this incentive is large enough, the cooperation will persist. (p. 101)

The Punishment is Guaranteed

The neatest trick is enforcing price collusion through a punishment guarantee, all in the name of competition. Here we turn to New York City and its stereo wars. Crazy Eddie has made his trademark "We cannot be undersold. We will not be undersold. Our prices are the lowest ­ guaranteed. Our prices are insane. His main competitor, Newmark & Lewis, is no less ambitious. With any purchase, you get the store's "Lifetime low-price guarantee." It promises to rebate double the difference if you can find a lower price elsewhere.

Although they sound competitive, these promises to beat the rival's price can enforce discipline in a price-setting cartel. How can this happen? Suppose each VCR costs $150 wholesale, and for the moment Crazy Eddie and Newmark & Lewis are selling it for $300. Crazy Eddie is contemplating a sneaky cut to $275. Without the beat-the-rival promise, Crazy Eddie would hope that his lower price would attract some of the customers who would otherwise have gone to his rival ­ say, because they lived nearer to a Newmark & Lewis outlet, or had bought from them before. Unfortunately for Crazy Eddie, his price cut has the reverse effect. With the Newmark & Lewis price guarantee, these people are now tempted just to walk over to Newmark & Lewis and buy the VCR for $300 and then claim a $50 rebate. This is just as if Newmark & Lewis had reduced its price to $250, automatically undercutting Crazy Eddie. But of course Newmark & Lewis would prefer not to give away the $50. Its response will be to lower the price to $275. In any event, Crazy Eddie is worse off than where he started. So why bother? The price stays at $300.

Although cartels are illegal in the United States. Crazy Eddie and Newmark & Lewis have the makings of one. You can see how their implicit cartel works in terms of the requirements of enforcement we mentioned before: detection of cheating and punishment of cheaters. Newmark & Lewis can more easily detect Crazy Eddie's cheating. The customers who bring them the news of Crazy Eddie's lower price, and ask them to beat that, are acting as unwitting enforcement agents for the cartel. The punishment comes in the form of the collapse of the pricing agreement and consequently lower profits. The "beat the competition" ads also set the punishment in motion, automatically and quickly.

Many "discount" stereo stores charge almost a hundred-percent markup over the wholesale cost of their components. There is method to Crazy Eddie's madness.

A similar device is a most-favored customer clause. E.I. Dupont, Ethyl, and other manufacturers of antiknock gasoline additives were charged with using a 'most-favored customer" clause. This clause says that the seller will offer to these favored customers the best price they offer to anyone. Taken at face value, it seems that the manufacturers are looking out for their favored customers. But let's look deeper. The clause means that the manufacturer cannot compete by offering selective discounts to attract new customers away from his rival, while charging the older price to his established clientele. They must make general price cuts, which are more costly, because they reduce the profit margin on all sales. You can see the advantage of this clause of a cartel: the gain from cheating is less, and the cartel is more likely to hold.

Most-Favored Customer Clause to Facilitate Collusion

The case of General Electric and Westinghouse for turbogenerators

Consider the pricing strategies of General Electric and Westinghouse

We are back where we began with a Prisoners' Dilemma.

The strategies which are best for the "collective good" are that both firms choose "high price." While this is collectively rational, it is unfortunately not individually rational.

Does General Electric have a dominant strategy?
Does Westinghouse have a dominant strategy?

One way out of the Prisoners' dilemma occurs when the players take steps that change the payoff matrix. Paradoxically, worsening some of one's own payoff possibilities may improve the likely outcome of the game (see Thomas Schelling the Strategy of Conflict). First, General Electric passes a "most favored customer clause."

"High Price" is now General Electric's dominant strategy.

If Westinghouse emulates General Electric's actions then this action further transforms the payoff matrix to encourage price collusion.

"Low Price" guarantees to customers are guarantees to be sure, they are guarantees of keeping the customer's price high.

Game theorists from around the world played a repeated Prisoners' dilemma game repeated 150 times. There were many complicated strategies but the winner was Anatol Rapoport, a mathematics professor at the University of Toronto. His winning strategy was tit-for-tat.

This strategy embodies for principles:

1. Clarity: The strategy is as clear and simple as you can get.
2. Niceness. It never initiates cheating.
3. Provocable. It never lets cheating go unpunished.
4. Forgiving. Does not hold a grudge for too long and is willing to restore cooperation.

The problem with "tit-for-tat" is that it can 'echo" is the other player is also playing "tit-for-tat" and you wind up with the "Hatfields and McCoys" scenario of unending conflict.

An alternative guideline:

Begin cooperating.
Continue cooperating.

Keep count of how many times the other side appears to have defected while you have cooperated. If this percentage becomes unacceptable, revert to tit-for-tat. (p. 113)

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.

You might have thought that leaving options open is always preferable. But in the realm of game theory that is no longer true. (p. 120)

Unconditional Moves

Picture a rivalry between the United States and Japan to develop high definition TV.

First, both the U.S. and Japan choose their strategies simultaneously.

Payoffs for High-Definition TV Race:

For the United States, the best situation is when both sides make low effort; they are likely to win at low cost. Low effort is the dominant strategy for the United States.

The problem for the United States is that the Japanese can anticipate this. The Japanese best response is to follow with high effort.

To improve the situation calls for a strategic move. Suppose the United States preempts. If the United States pursues high effort, the Japanese respond with low, and the U.S. payoff is 3. Therefore the United States should announce high, and expect the Japanese to respond low. This is the equilibrium of the sequential move game.

The strategic move that brings the United States this advantage is a unilateral and unconditional declaration of its choice. The choice is not what the United States would have made in simultaneous play. This is where the strategic thinking enters.

To behave strategically, you must commit not to follow your equilibrium strategy of the simultaneous-move game. The strategic move changes Japanese expectations, and therefore their response. Once they believe that the United States is committed to high effort, the Japanese will choose low effort. Of course, after the Japanese choose their path, the United States would do better to change its mind and switch to low effort, too.

This raises several questions: Why should the Japanese believe the U.S. declaration? Would they not anticipate a change of mind? And if they anticipate such a reversal, would they not choose high effort? In other words the credibility of the U.S. unconditional first move is suspect. Without credibility, the move has no effect. (p. 123)

Credibility requires a commitment to the strategic move. (p. 124)

In the race for high definition TV, the United States might commit funds to which interested companies can lay claim in order to make a high R&D effort credible.

Some times the first-mover is in terms of announcing a response move, rather than an action. A parent telling a child "No dessert unless you eat your spinach" is establishing such a response rule. Of course this rule must be in place and clearly communicated before the child feeds its spinach to the dog. Response rules can be threats or promises.

The common feature of all credible threats and promises is this: the response rule commits you to actions that you would not take in its absence. (p. 126)

Credibility requires finding a way to prevent going back.

The Eightfold Path to Credibility

1. Establish and use a reputation.
2. Write enforceable contracts.
3. Cut off communication.
4. Burn bridges behind you.
5. Leave the outcome to chance.
6. Move in small steps.
7. Develop credibility through teamwork.
8. Employ mandated negotiating agents.

Reputation. If you try a strategic move in a game and then back off, you may lose your reputation for credibility.

Contracts. A straightforward way to make your commitment credible is to agree to a punishment if you fail to follow through. If your kitchen remodeler gets a large payment up front, he is tempted to slow down the work. But a contract that specifies payment linked to the progress of the work and penalty clauses for delay can make it in his interest to stick to the schedule. The contact is the commitment device.

Cutting Off Communication. Cutting off communication succeeds as a credible commitment device because it can make an action truly irreversible.

Burning Bridges Behind You. Armies often achieve commitment by denying themselves an opportunity to retreat. This strategy goes back at least to 1066, when William the Conqueror's invading army burned its own ships, thus making an unconditional commitment to fight rather than retreat. Cortes followed the same strategy in his conquest of Mexico.

Leaving the Outcome Beyond Your Control. Automatic response is essential. However, this strategic advantage does not come without a cost. There might be an accident.

Moving in Steps. Although two parties may not trust each other when the stakes are large, if the problem of commitment can be reduced to a small-enough scale, then the issue of credibility will resolve itself. The threat or promise is broken up into many pieces, and each one is solved separately. To avoid the unraveling of trust, there should be no clear final step.

Teamwork. Often others can help us achieve credible commitment. Although people may be weak on their own, they can build resolve by forming a group. The successful use of peer pressure to achieve commitment has been made famous by Alcoholics Anonymous (and diet centers too). The AA approach changes the payoffs from breaking your word. It sets up a social institution in which pride and self-respect are lost when commitments are broken.

Mandated Negotiating Agents. The union leader may secure a restrictive mandate from its members, or put his prestige on the line by declaring his inflexible position in public.

Leasing

If customers expect that IBM is about to lower its price, they will wait to make their purchase. When the majority of customers are waiting, IBM has an incentive to speed up its price reductions and capture the customers sooner. This idea, first expressed by University of Chicago law and economics professor Ronald Coase, is that for durable goods, in effect, a monopolist competes with its future self in a way that makes the market competitive. Leasing serves as a commitment device that enables IBM to keep prices high. The leasing contracts make it much more costly for IBM to lower its price. When its machines are on short-term leases, any price reduction must be passed along to all customers, not just the ones who haven't yet bought. The loss in revenue from the existing customer base may outweigh the increase in new leases.

Unpredictability

"The right amount of unpredictability should not be left to chance." (p.170)

(See page 4 of this handout)

There is an equilibrium pattern of randomness. (p. 172)

There are other cases in which businesses must avoid set patterns and predictability. Some airlines offer discount tickets to travelers who are willing to buy tickets at the last minute. But they won't tell you how many seats are left in order to help you estimate the chances of success. If last-minute ticket availability were more predictable, then there would be a much greater possibility of exploiting the system, and the airlines would lose more of their otherwise regular paying customers.

The most widespread use of randomized strategies in business is to motivate compliance at a lower monitoring cost. This applies to everything from tax audits to drug testing to parking meters. It also explains why the punishment should not necessarily fit the crime. A larger fine is more likely to keep people honest.

Cooperation and Coordination.

"It is not from the benevolence of the butcher, the brewer or the baker that we expect our dinner, but from their regard to their own self interest .... [Every individual] intends only his own security, only his own gain. And he is in this led by an invisible hand to promote an end which was not part of his intention. By pursuing his own interest, he frequently promotes that of society more effectually than when he really intends to promote it."

Adam Smith wrote this in 1776 in The Wealth of Nations. Ever since, these words have been music to the ears of free-market advocates. Some free-marketers are inclined to take the idea beyond the economic realm and like Dr. Pangloss in Candide claim that "everything is for the best in the best of all possible worlds." The sad reality is that Adam Smith's invisible hand has a relatively small span. There is no general presumption that when every person pursues his own self interest, the outcome will be the best of all possible worlds.

Remember that there is no presumption that an equilibrium must be good; we have to find out in each situation whether the outcome is a war of each against all, or the best of all possible worlds, or something between these extremes.

The invisible hand at best applies only to situations in which everything has a price. For example, manufacturers are rarely charged an adequate price for using up clean air, nor compensated for training a worker who might then quit and find other employment. Here pollution is an unpriced item, and the problem is that there is no economic incentive to temper the firm's selfish interest in supplying a large amount of pollution (as a by-product). When a firm trains a worker, this good is not traded on a market, so there is no price to guide the firm's action; the firm must equate its own costs with benefits and cannot capture the willingness of others to pay for this service. Because many unpriced or non-marketed activities matter, it is no wonder that individuals acting selfishly often do too much harm to others, and too little good.

Conventions

Sometimes one convention is much better than another. Even so, that doesn't mean it will always get adopted. If one convention has become established and then some change in circumstances makes another one more desirable, it is especially hard to bring about the change.

The keyboard design on most typewriters is a case in point. In the late 1800s, there was no standard pattern for the arrangement of letters on the type writer keyboard. Then in 1873 Christopher Scholes helped design a "new improved" layout. The layout becomes known as QWERTY, after the letter arrangement of the six letters in the top left row. QWERTY was chosen to maximize the distance between the most frequently used letters. This was a good solution in its day; it deliberately slowed down the typist, and reduced the jamming of keys on manual typewriters. By 1904, the Remington Sewing Machine Company of New York was mass-producing typewriters with this layout, and it became the de facto industry standard. But with today's word processors, this jamming problem is now completely irrelevant. Engineers have developed new keyboard layouts, such as DSK (Dvorak's Simplified Keyboard) which reduces the distance typists' fingers travel by over fifty percent. The same material can be typed in 5-10 percent less time using DSK than QWERTY. But QWERTY is the established system. Almost all typewriters use it, so we all learn it and are reluctant to learn a second keyboard. Typewriter and keyboard manufacturers continue, therefore, with QWERTY. ... No individual user would want to bear the cost of changing the social convention. Uncoordinated decisions of individuals keep us tied to QWERTY. ...

History matters. The historical accident that led to QWERTY capturing nearly 100 percent of typists ends up being self perpetuating, even though the original motivation for QWERTY is long since obsolete.

The QWERTY problem is but one minor example of a more widespread problem. Our preference for gasoline over steam and our preference of light-water nuclear reactors over gas-cooled is better explained by historical accidents than by the superiority of the adopted technologies.

The important insight from game theory is to recognize early on the potential for future lock in -- once one option has enough of a head start, superior technological alternatives may never get the chance to develop.

The point of these stories is that the free market doesn't always get it right. There are two fundamental problems. One is that history matters. Our greater experience with gasoline engines, QWERTY keyboards, and light-water nuclear reactors may lock us in to continued use of these inferior technologies. The other general problem with laissez faire is that so much of what matters in life takes place outside the economic marketplace. Goods ranging from common courtesy to clean air are frequently unpriced, so there is no invisible hand to guide selfish behavior.

Strategy of Voting

The most commonly used election procedure is simple majority voting. And yet the results of the majority-rule system having paradoxical properties, as was first recognized over two hundred years ago by French Revolution hero the Marquis de Condorcet.

In a vote of Bashful against Sneezy, Bashful wins two to one.
Then in a vote of Bashful against Dopey, Dopey beats Bashful two to one.

In a vote of Dopey against Sneezy, Sneezy wins two to one.
Then in a vote of Bashful against Sneezy, Bashful beats Sneezy two to one.

In a vote of Dopey against Bashful, Dopey wins two to one.
Then in a vote of Dopey against Sneezy, Sneezy beats Dopey two to one.

Whoever controls the agenda controls the outcome.