BARGAINING AND BARGAINING TACTICS Topics 10 -11

BARGAINING AND BARGAINING TACTICS Topics #10 -11

A Generalized Chicken Game • Bargaining tactics may be used by P 1 to induce P 2 to “Give In, ” – so that P 1 can safely “Stand Firm. ” – Obviously P 2 can use similar tactics. • Some bargaining situations (like the Game of Chicken) are essentially symmetric, but others clearly are not, – e. g. , hostage holders vs. authorities.

Example of Bargaining Situations (a) General bargaining situations: players have – – (b) (c) (d) (e) (f) (g) (h) (i) a common interest in reaching an agreement but conflicting interests with respect to what particular agreement to reach. An actual chicken game A hostage-holding situation (Small) child-parent bargaining Buyer-seller (e. g. , of a house) bargaining Labor-management collective bargaining The first Berlin Crisis (blockade and airlift), 1948 The second Berlin Crisis (leading to Berlin Wall), 1959 -61 => The Cuban Missile Crisis (1962) – In his speech of October 22, 1962, President Kennedy declared that “our unswerving objective” is to get Soviet missiles removed from Cuba. (j) The general U. S. -S. U. cold war conflict and nuclear balance (k) Other international conflicts

Checkpoint Charlie, Berlin, October 1961

Checkpoint Charlie, Berlin, November 10, 1989

Credible Commitment • P 1 somehow makes an credible commitment to stand firm. – The first player to make a credible commitment to “stand firm” wins. – If it is possible to make such a commitment, • it is essential to disclose this to the other player immediately, • before he can make a similar commitment. • Realistically, it is impossible to make such an absolute and irrevocable commitment. • Therefore attention focuses on tactics (pre-play communications and strategic moves) that enhance the credibility of commitments. – Schelling, Arms and Influence, Chapter 2, “The Art of Commitment”

Pre-Play Communications • P 1 can send messages that • project an image of P 1 to P 2, or • convey to P 2 P 1’s (claimed) image of P 2. – P 1 can project an image that suggests P 1 is crazy, irrational, emotional, and uncalculating and generally that P 1 doesn’t understand the risks of standing firm. – This has been called the “rationality of irrationality” or “the political uses of madness” [Daniel Ellsberg] • (a) P 1 tries to appear to be a “force of nature, ” so the only reasonable response by P 2 is to give in and minimize damage. • (a) P 1 exhibits (apparently) erratic, emotional, selfdefeating, irrational behavior • (b) P 1 get into his car (apparently) stumble-down drunk

Pre-Play Communications (cont. ) – (c) terrorists, escaped prisoners, and most criminals have an inherent bargaining advantage over the authorities in this respect – (d) the child throws a deliberate temper-tantrum [“strategic screaming”] – (g) Mr. K’s [Soviet leader Nikita Khrushchev] “shoe-thumping” and other incidents – Note: such tactics can be dangerous, as they give P 2 an incentive to engage in preventive or pre-emptive action. • P 1 attributes rationality (and perhaps cowardice) to P 2, claiming P 2 understands the risks of standing firm – (g) Mr. K to JFK: “only a madman would fight a nuclear war over Berlin – and I don’t think you’re mad. (But can you be sure I’m not mad — remember my “shoe-thumping” and other erratic behavior? )”

Pre-Play Communications (cont. ) • Messages designed to influence the perceived (not the actual) values of payoffs W, C, L, or P. – P 1 can convey the impression that he regards P 1 is not so bad, so maybe P 1 is no worse than L 1, which implies that P 1 believes that standing firm is a dominant strategy (and thereby compels P 2 to give in). • (b) P 1 claims that his car is crash-proof. – Note: P 1 does not have to persuade P 2 that P 1’s car is crashproof, only that P 1 believes that it is crash-proof. • (c) The hostage holders claim that martyrdom is a ticket to heaven (so P may really be their best outcome, not worst). • (d) The child says “I don’t even want any dessert [so you can’t make me eat my vegetables]. ” • (e) The buyer/seller hides the fact that he is very anxious to buy/sell. • (f) The union/company releases a report purporting to show that they can readily survive a long strike/lockout. • (j) P 1 releases a study showing that his civil and other defensive preparations are so effective that P 1 can survive nuclear war.

Pre-Play Communications (cont. ) • P 1 can convey the impression that he regards L 1 as worse than it really is, so again maybe P 1 is no worse than L 1, which again implies that P 1 believes that standing firm is a dominant strategy (and thereby compels P 2 to give in). – (b) P 1 claims that he believes that to be revealed as “chicken” is a fate worse than death. – (c) The hostage holders reveal that they believe that they are already under a death sentence (e. g. , for prior criminal convictions). – (e) The buyer conveys the impression that his “reservation price” (the highest price he would actually be willing to pay) is lower than it actually is. – (e) The seller conveys the impression that his “reservation price” (the lowest price he would actually be willing to take) is higher than it actually is. – (f) The company reveals that it believes it would go out of business of it gave in to union wage demands.

Pre-Play Communications (cont. ) • P 1 tries to persuade P 2 that C 2 is as good as W 2, so that P 2 will believe that giving in is P 2’s dominant strategy, and that P 1 can therefore safely stand firm. – (a) P 1 assures P 2 that “this is my last demand” — it is not costly for you to give in and it won’t set a precedent for the future [but see below on reputation effects]. – (c) Child to parent: “Let me have this treat just this once — I won’t ask for it again. ” – (k) Hitler at Munich

Pre-Play Communications (cont. ) • P 1 conveys the impression that he believes P 2’s preferences are such that C 2 is as good as W 2 and that giving in is therefore P 2’s dominant strategy, so P 1 can safely stand firm. – (b) P 1 conveys the impression that he believes that P 1 doesn’t care if he is revealed to be “chicken. ” – (e) The seller conveys impression that he believes that the buyer’s reservation price is high. – (e) The buyer conveys impression that he believes that the seller’s reservation price is lower. – (f) The union conveys impression that it believes that management can easily pay higher wages.

A Different Prime Minister Projecting a Different Image

Strategic Moves A strategic move actually changes the payoff values W, C, L, or P. • P 1 changes actual payoff values for P 2 so that “giving in” is more attractive (perhaps even dominant) for P 2. – P 1 takes actions to increase the value C 2, i. e. , makes concessions to P 2. • Note: a problem with this strategic move is that, not only are the concessions (presumably) coming out of P 1’s pocket (reducing the value C 1), but also that P 1 may look too anxious to avoid P 1, so that it seems safer for P 2 to stand firm and aim to get W 2. – P 1 takes actions to increase the value of L 2, e. g. , – to provide P 2 with a “graceful exit” [“no invasion” pledge in Cuban Missile crisis] – to avoid seeking “unconditional surrender” [Allied WWII war goals? ] – to promise to treat surrendering forces humanely, etc. , • thereby – making giving in more palatable to P 2, – which makes it safer for P 1 to stand firm, – further reinforcing P 2’s incentive to give in.

Strategic Moves (cont. ) • P 1 changes actual payoff values for himself so that “standing firm” is evidently more attractive (and perhaps actually dominant) for P 1. – P 1 must take care that such changes are evident to P 2. – P 1 visibly takes actions that increase the value of P 1 (i. e. , make mutual disaster less disastrous for himself). • (b) P 1 actually puts effective safety devices in his car. • (e) The buyer/seller looks around for other willing sellers/buyers. • (f) The union builds up strike fund or enters into swap agreement with other unions. • (f) The company builds up inventories. • (j) The U. S. (or S. U. ) actually invests in a massive civil defense program (or ABM system).

Strategic Moves (cont. ) • Less obviously and more perversely, P 1 visibly takes actions that reduce the value of L 1 (making it most costly for P! to “give in”). • Sometimes “weakness can be [bargaining] strength. ” – (b) P 1 brings all his friends (and maybe enemies too) to watch the chicken game. – (c) Given numerous hostages, the hostage holders kill one or a few (but definitely not all) of them, • so that they must expect a worse penalty if they give in and are captured. • [The hostage holders are also “decomposing their threat. ”] • (k) P 1 “burns his bridges behind him, ” so that he (or his soldiers) can’t retreat and must either fight (“stand firm) or be killed or captured.

Strategic Moves: Reducing L 2 (cont. ) • (f) Union leaders arouse expectations among members (“If we don’t get you a 20% wage boost, you should kick us out of office”) • (g) U. S. puts lightly armed 5, 000 troops in Berlin. – Also see below on “trip wires” and “the threat that leaves something to chance. ” • (k) Israel builds settlements on West Bank, so that it becomes more difficult for them to make future territorial concessions • (k) The U. S. President is negotiating a treaty with another country, which makes a demand the President doesn’t want concede to: his bargaining power is enhanced if he can say “I sorry, but my hands are tied; if I make this concession, I’ll never be able to get the treaty we both want ratified by the Senate • “two-level games” and the “Schelling Conjecture”

Strategic Moves: Reputation Effects • One move of this type is especially important: P 1 can invest his long-term reputation in the outcome of the present bargaining situation, • thereby (greatly) reducing the value of L 1, possibly to the point that L 1 is worse than P 1. – “If I give in on the issue, everyone will expect me to give on other issues, so it is clearly in my long-term interests to stand firm now, even if that means getting the worst payoff P 1 in the short-run. ” – Such reputation effects may be powerful even if P 1 does not deliberately enhance them. – Reputation effects make a “this is my last demand” ploy by P 2 less likely to succeed. • (b) If P 1 plays chicken regularly (and his future opponents are watching) while P 2 does not, P 1 cares more about his reputation and has the stronger incentive to stand firm, and P 1 knows this. • (h) JFK’s speech of 10/22/62: Soviet offensive missiles in Cuba “cannot be accepted by this country if our courage and our commitments are ever to be trusted again by either friend or foe. ”

The “Last Clear Chance” to Avoid Mutual Disaster • Consider the game of “Discrete Chicken” displayed below. – It is played sequentially (with perfect information). – The players move in alternating terms. – At each move, a player has two choices: • advance one additional (“discrete”) step toward the other player (i. e. , continue to “drive straight”), or • to stop advancing (or step off the board, in any event to “swerve”). – The payoffs are the same as in standard “ 2 x 2 Chicken. ” • What will happen?

The “Last Clear Chance” (cont. ) • Nothing dramatic will happen -- the game is perfectly safe (unless one of the players is entirely irrational). • The winner of the game is determined not by skill or by nerves of steel but by these two factors: • which player moves first, and • whether the number n of discrete steps (boxes) between the players at the outset is odd or even. – If n is odd (as below), the first moving player wins – If n is even, the second moving player wins.

The “Last Clear Chance” (cont. ) • These two factors determine which player has the “last clear chance” to avoid mutual disaster (see Schelling, Arms and Influence, pp. 44 ff). – Note that “Sequential Chicken” (Topic #6, last slide) has n = 1 = odd, so the first mover has the advantage. • Note also that “real chicken” is a “continuous” game, – i. e. , the cars do not advance towards one another in discrete alternating steps. – Thus it is unclear who has the “last clear chance” to avoid collision, • which is what make the game dangerous and a test of nerves • Note also that the “Classic 2 x 2 Game of Chicken” payoff matrix is discrete, – i. e. , players a single choice to either “drive straight” or “swerve. ” – What makes this dangerous is simultaneous (rather than sequential) choice. • Lesson: in a bargaining situation each player may try to displace onto the other player the “last clear chance” to avoid mutual disaster (by “giving in”).

Strategic Moves: Irrevocable Commitment • A strategic moves may actually and irrevocably commit P 1 to stand firm, by eliminating “giving in” as a feasible option. • See Schelling, Arms and Influence, Chapter 2 [“The Art of Commitment”] and • Dixit and Nalebuff, Chapter Six (“Credible Commitments. ”) – Such an irrevocable commitment displaces clearly onto P 2 the “last clear chance” to avoid mutual punishment by giving in. – It is of course very important for P 1 to make sure that P 2 sees what P 1 has done. (a) P 1 appoints an instructed agent to negotiate with P 2; the agent has no authority to make substantial concessions and cannot communicate with P 1 (b) P 1 locks his steering wheel in the “straight ahead” position and throws key out the window.

Irrevocable Commitment (cont. ) • The Hostage-Holding Game: The bargaining power of the hostage holders derives from the fact that they can kill the hostages. – This fact sustains their deterrent threat against the authorities: • – It may also sustain their compellent threat against the authorities: • – If you move in to capture us and/or free the hostages, we will kill the hostages. If you do not release our comrades from prison (or whatever their demand is), we will kill the hostages. But if and when the hostage holders carry out this threat, they lose all of their bargaining power, and the authorities can move in and capture them • so will they really carry out the threat? (c) The hostage holders can rig up a trip-wire system that is visible to the authorities, such that an attempt by authorities capture them or free the hostages will trigger an automatic killing of the hostages. – This can sustain the hostage holders’ deterrent threat but not their compellent threat.

Post-WWII Germany

Irrevocable Commitment (cont. ) (g) U. S. troops in West Berlin served a “trip-wire” function: – If the Soviets were to attack West Berlin and kill or capture the U. S. soldiers, U. S. decision makers would be politically compelled to dispatch reinforcements to West Berlin and thereby risk general war. – So the Soviets knew that a military move against West Berlin (which would certainly be successful, even with U. S. troops there) would carry a real risk of general war. – On the other hand, if all U. S. troops had been stationed in West Germany (rather than West Berlin), the U. S. would have to make the decision that would risk general war in the event of a Soviet move on West Berlin.

The Ultimate Trip Wire: A “Doomsday Machine” (h) The US (or SU) might install a “Doomsday Machine” that would automatically destroy the world if SU’s (or US’s) missiles ever strike US (or SU) territory. – Herman Kahn proposed such a “Doomsday Machine” as a thought experiment, exemplifying • a perfect “Type I Deterrent” but highly flawed otherwise (and not just morally). – In the Dr. Strangelove movie, the SU installs such machine • but makes the mistake of not immediately announcing what it has done.

Strategic Moves to Avoid the “Last Clear Chance” Dilemma (a) P 1 makes a pre-emptive commitment (to deter P 2 from making his own irrevocable commitment) (a) P 1 “decomposes” the execution of his threat to inflict punishment on P 2 (i. e. , the threat is carried out gradually) (c) To sustain a compellent threat, the hostage holders announce they will kill one hostage a day until authorities give in to their demands. (e) A strike or lockout is really the decomposed execution of a threat, – – because collective bargaining continues as each side inflicts gradually increasing punishment on the other. Remember the Dollar Auction Game (from Topic #2, Playing Games).

Post-WWII Germany

The Berlin Blockade and Airlift, 1948 -49 • The Soviets placed barricades and soldiers across the roads and railway lines leading from West Germany to Berlin, thereby – forcing (they thought) the western Allies to choose between capitulation or shooting their way through the barricades and – they (correctly) anticipated that the Allies would not be willing to start shooting. • The creative (and costly but ultimately successful) western response was the airlift, – which forced the Soviets to acquiesce or to start shooting down Allied planes, and – the Allies (correctly) anticipated that the Soviets would not be willing to start shooting.

A “Threat That Leaves Something Chance” • See Schelling, Arms and Influence, Chapter 3 (“The Manipulation of Risk”). • This means that P 1 says to P 2: – If you don’t give in, I may or may not carry out my threat to inflict mutual punishment on us — but whether it is carried out or not will be determined, not by my own choice (I know that I will always have an incentive to renege on carrying out my threat), but by a chance mechanism that I am now setting in motion. • It is more credible – that P 1 will set such a random mechanism going than – that P 1 would deliberately chose to carry out a mutually punitive threat.

Threat That Leaves Something Chance (cont. ) (c) To sustain a compellent threat, a single hostage holder with a single hostage (for whom a decomposed threat is not feasible) announces the following: – – – he will put one bullet in his gun, spin the bullet chamber, aim the gun at the hostage, and pull the trigger, and repeat this process once a day until the authorities give in to his demands. (g) U. S. troops in West Berlin more realistically served as a trip wire that would generate (in the event of a Soviet move on West Berlin) (g) not the certainty of escalation leading to general (even nuclear) war (an outcome the U. S. would be extraordinarily reluctant to choose deliberately) but rather (h) a substantial risk of escalation leading to general (even nuclear) war (that neither the US nor the SU could confidently control ).

Threat That Leaves Something Chance (cont. ) (j) One (of many) drawbacks of a “doomsday machine” is that it is totally unforgiving in the event of accidental missile firings; – perhaps a doomsday machine should trigger a random mechanism that would destroy the world with some positive probability much less than 1. – Of course, if the doomsday machine were tested in some accidental incident and if it did not destroy the world [to the huge relief of everybody, including the side that installed it], the other side might speculate as to whether the whole thing is a bluff.

Threat That Leaves Something Chance (cont. ) (k) Probably the best simple model of intense international conflict is Discrete Chicken with this added element: – In each move, players can either stay where they are or advance or retreat in discrete steps. – Between the moves of each player, “Nature” uses a random device to decide whether to blow up the world, where the probability that Nature will blow up the world • • • is zero if the players remain at opposite ends of the board, increases as the players get closer to one another, and is at a maximum (but still less than certainty) if the players collide (i. e. , occupy the same position on the board). – Note that neither has the “last clear chance” to avoid blowing up the world.