Training In Smith's Theory of Bargaining

Michael Webster asks:

“Gavin, did you ever post your note about Smith's conditional bargain? on Adam Smith on Bargaining and My Experience Applying His Theory”.  Post yesterday as a comment on my post about Adam Smith’s on Bargaining exchanges, 9 August 2011.

I shall answer it here because readers may not read a comment listed in 2011.

GK: A simple game I included in my negotiation workshops from 1972 to 2005, was the ‘red-blue’ (Prisoner’s Dilemma) game, which opened the Negotiate workshop (see ‘Kennedy on Negotiation’, Gower, 1997 or Kennedy, ‘The New Negotiating Edge’, Nicholas Brierely, 1998).  Red-Blue introduced beginners (and 'old hands') to the consequences of the common behaviour of pure self-interested bargaining by allowing participants to show themselves the folly of their only considering one’s own selfish and short-sighted interests when trying to transact with others. Thousands of plays of Red-Blue over 40 years revealed interesting data about those consequences.

The game is played in pairs, randomly chosen. Each player is given two coloured plastic disks, one red and one blue, or asked to mark two small squares of paper labelled “R” or “B”. They are told the rules (especially about no talking with partners, except when allowed under the rules), and they are given absolutely no advice on how to play or what they will learn, or even the point of the exercise.

The scores for each round were shown on flip charts for the four possible outcomes of each round of play: If both play ‘Blue-Blue’ = +4 points each; both play ‘Red-Red’ = -4 points each; one plays ‘Red’ and the other plays ‘Blue’, then the Red player = +8 points and Blue player = -8 points.  They divide into their pairs and commence playing anywhere in the room, standing or sitting.  The noise level rises during the games.

Each player chooses the colour they intend to play, first held out of sight behind their backs for each round and each then revels their plays simultaneously on a common signal between them. They note their scores for each round on printed score sheets according to what they played. They then play the next round again without talking. After the first four rounds they pause for a 5-minute conversation, perhaps recriminating on the other’s plays or defending their own, and perhaps agreeing on how to play the next four rounds, under the same rules and scores. Again, after round 8, they stop for a 5-minute conversation perhaps again recriminating if one or both defected on their agreement from the previous 5-minute break. The last two rounds (9 and 10) are played with all scores doubling. Paired-blue play = +16 points each; paired red play = -16 each; one plays blue and one plays red = +16 points to the red player = -16 points to the blue player.

They then discussed with tutor the resulting total scores over the 10 rounds from each pair. Over the years the pattern of plays across all levels of management, experience, countries of origin and current domicile, moral (religious) labels, ages (from youngest school children to retired adults), education levels, private and public sector employees, caring professions, hard-nosed financial traders, all nationalities, mixed groups, both sexes, politicians, health staff (from porters to surgeons), and beginners or experienced sales and buying staffs.  The results showed relative stability.

Now the maximum score from total cooperation (no defections) was +48 points each. I found that over the years this score was achieved by only about 8 per cent of the players. Negotiate tutors gave absolutely no pre-game briefing suggestions or hints, other that describing the scoring system. Despite almost always being asked to identify the objects of the exercise, we said nothing other than ‘maximise your individual scores’. Of course, the only way to achieve this was by discovering the blue-blue play, the jointly co-operative strategy, because Red play tended to be punished in retaliation.   Attempts to gain by defecting to other strategies were mostly unsuccessful because defection provoked the other player’s defection in subsequent rounds.

Players could suffer from the other’s early red play and subsequent defections, other than the almost predictable retaliatory Red play defections by former Blue players in some fairly drastic red play from Round 5 onwards to round 10 (and almost certainly from round 9). Counter-defectors from broken promises by red players could reduce the early defector’s scores, even though both also ended with a high minus score. No red player with early counter defections reached +48 (the Blue-Blue score) or better. On two occasions only in 33 years did a Red player reach +96 - because the other player played Blue every round irrespective of the red player’s play every round.  The two  blue players appeared unconcerned at their constant losses of -96.

In a large minority (sometimes a majority) of plays of the game, early defection was followed by unbroken promises to play blue in every round, which though the total positive score was less than +48 (perfect, no-defections), it was at least +32 each and sometimes better.

In brief, players could learn that playing a co-operative blue each round after early defections could result in a better score than defecting to gain at their partner’s expense. Those who defected would often simply provoke retaliation in subsequent rounds. It was not a perfect exchange, but zero-sum bargaining never was better than non-zero bargaining as identified by Smith on bargaining:

“Give me that which I want, and you shall have this which you want, is the meaning of every such offer; and it is in this manner that we obtain from one another the far greater part of those good offices which we stand in need of” (WN I.ii: 25).

The rest of the Negotiate Workshop’ Agenda showed how to achieve non-zero sum bargaining in the real world.

Red-Blue is about the learning process that occurs in the real world and was summed by Adam Smith as “the great school of self-command” where individuals learn in society’s “mirror” as they leave the exclusive boundaries of the family and mix with other children and adults who may not have the same protective emotional relationships as in the smaller world of their family.   Others do not indulge them and they have to learn to cope with and adjust to that new circumstance.  Smith, from his sickly constitution, went to school later than others in Kirkcaldy but he still made some close friends who remained his life-long close companions. 

In short, he graduated from the “great school of self-command along with graduating from the scholarly school intellectually.

Those who attended Negotiate Workshops showed how prevalent is the process through which learn to persuade and develop co-operation so necessary for successful negotiation. Those who learn that bargaining, for instance, is about mediating their self-interest with the self-interests of others to achieve some degree of their own self-interests.

In practise, as the Red-Blue game illustrates, the “propensity to exchange” identified by Smith in Wealth Of Nations is not a well understood process across the population, which Smith clearly identified as the ‘If-Then’ conditional proposition (WN I.ii: 25-6). By recognising Smith’s ‘If-Then’ proposition it is easily understood and practised in the real world.

Once again, neoclassical Max U economics approaches bargaining by wrongly formulating it as confrontational problem (see modern economics on bargaining since the 1930s around themes like Zeuthen’s ‘economic warfare’, Hicks on ‘strikes’, Cross and others on ‘conflict’, even actual warfare, through to the 1980s.

Yet Adam Smith set it out in both Moral Sentiments and Wealth Of Nations in the 18th century in his two great, but mostly unread, books.  Hence, my particular sadness, at people libelling Smith with a self-interest theory that he never held.