Saturday, January 19, 2013

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.


Blogger michael webster said...


1. I like this version of the dilemma because the plays "blue" and "red" are about as neutral as possible. Most versions of this dilemma build a great deal into the choice of labels for the strategies.

2. There are (2) changes to this exercise which I have used, although I used "left" and "right" to denote the strategies.

a) Change the payoff to the red/blue to 0 for red and -8 for blue.

You will still get a significant portion of people playing red together.

b) Change the payoffs as in a), but announce to the world the payoffs for red/blue are 8 for red and -8 for blue.

This is a good model of an arm's race. Each side, wrongly believes, that other side has a dominant strategy and must "protect" themselves against being taken advantage of. We end up with joint reds, and mutual accusations not easily dispensed with.

2:50 pm  
Blogger Gavin Kennedy said...


A most interesting contribution to developing the Red-Blue game. Thank you.
2a. The scores explain the choices. The players prefer 0 to experiencing loss. Loss avoidance is inevitable. Lessons?
2b. Is that not the same as standard?
I would need to have tested the variation in scores over many rounds of play to make a final judgement.
I see the valid point about arms' races. Useful in courses for negotiating diplomats.
Generally the standard Red-Blue game is for general would be negotiators. Those seeking to bully their way to one-sided winning have to change their play if they are going to score positively.
This is Smith's point about mediating our self-interests with others to achieve positive results - specifically the contents of our dinner!
The Butcher, brewer and baker have also to do so if they are going to persuade customers to spend their cash with them rather than other rivals (leading such merchants to "conspire" to collectively raise/ maintain prices).
As I am retired and do not deliver negotiating courses any more, though Negotiate continues under my daughter's management and my course continues at Edinburgh Business School (still popular too!), I am not able to test your suggestions.

7:35 am  
Blogger michael webster said...


I liked the analysis about Karass, red, and Fisher & Ury, blue, in Negotiating Edge.

There are a number of 2 x 2 games that show strategically different problems than the traditional dilemma game - each might very well give rise to a different set of red/blue behavior.

Too bad that you cannot test the intuitions I have for the modified game.

Just to clear up one idea, and it should be really be a full post,

The modification in 2b allows the two players to think that the payoff structure is as announced to the world, the usual set-up.

But, then they are given confidential information - which would be useless to merely disclose- that their real pay-offs are different.

As the US and USSR found it, it is very difficult to disclose and act upon your real preferences in a case like this.

(The theory/evidence which prompted this idea is found in Scott Plous's perceptual dilemma article - easily found online.)

4:15 pm  
Blogger Gavin Kennedy said...

Internal foreign party negotiations pose particular problems; the parties have a history between them with conflicting political perceptions sometimes dominant.
There is also much work done on Tit-fot-Tat sequences. I often used the Gorbechev-Reagan talks to illustrate rival strategies between Red-Blue in the international negotiating strategy seminars to illustrate potential deadlock breaking strategies (US-Soviet Strategic Arms; UK-Northern Ireland; Israel-Egypt).
I agree arms races are a problem not a solution. Understanding their dynamics is helpful background to potential negotiations. The critical point comes in the end game when one or both sides signal as even timid desire for an accommodation of some kind. How might they react, other than in war ceasefires, where one side suddenly feels stronger? Fortunately in South Africa neither side took temporary advantage over the other in this sensitive period.
Northern Irish antagonists likewise (eventually).
Now I am retired - the stress of international negotiating precludes me testing your findings - but I remain interested.

5:16 pm  
Blogger Charlie Irvine said...

Very interesting. I teach mediation (and now negotiation) in Glasgow, Scotland, and stumbled on the Prisoners' Dilemma via a red/blue game. I have found you can tweak the results in other ways:

1. Knowing nothing about it, I first introduced the game as a pure prisoners' dilemma, describing the other prisoner in their cell etc. I found that fewer people defected, and that there was a distinct gender difference, with women being less likely to defect. Arguably this is closer to the 'real world' where by and large we do have contextual information about our counterparts, and factors like empathy come into play.

2. Playing it larger groups. The bigger the group the more likely it is for 'hawks' to predominate. Even though the rationality ought to be the same, and their group performs poorly, the hawks tend to be reinforced in their hawkishness by the responses they engender in their negotiation counterparts.

3. Playing in larger groups where all groups play against each other. in this scenario, a single hawk can doom the remainder of the group (up to 30) to non-cooperative behaviour.

I also think it makes a difference whether or not the exercise is framed as a game. In one instance a woman kept cooperating in the teeth of her male counterpart's defecting. Debriefing afterwards, she said she couldn't bring herself to do the dirty on her fellow prisoner; he said 'its just a game'.

I'll be using it again in a couple of weeks, so this is a helpful discussion. Thanks both.

10:06 am  
Blogger Charlie Irvine said...

Interesting discussion. I teach mediation in Glasgow and stumbled across the red/blue game on a course. Not knowing anything about it I started using it in the original prisoners' dilemma form. Gender and culture come into play in a number of ways:

1) When I first set it using the prisoners' dilemma story, far fewer people defected, and there was a distinct gender bias with more men defecting and women cooperating. While this form seems less 'pure' than red/blue, it is arguably closer to the real world where we do have contextual information about our negotiation counterparts.

2) Playing the game in larger groups. Here the phenomenon of 'hawks' and 'doves' comes into play. By and large the hawks predominate, driving groups to defect. Even though this doesn't maximise scores, those hawks tend to be reinforced in their strategy by the hawkish response that they engender in their counterparts.

3) In groups against all other groups. This variant is even worse. It only needs one hawk in up to 20 people for their strategy to predominate. It illustrates well the 'race to the bottom' once people believe they are under threat.

I also think it makes a difference whether we frame this as game or exercise. On one occasion a women cooperated for all the rounds while he male counterpart consistently defected. Debriefing afterwards, she said she couldn't bring herself to betray her fellow prisoner; he said 'But it's just a game!' Carol Gilligan's research suggested that games may mean something different to males and females.

Thanks both for a fascinating discussion. I will be using it again in a couple of weeks, so this is very helpful

10:20 am  
Blogger michael webster said...


You might find it interesting, given your dissertation, to use models in which there appears to be common information, but which in fact there are completely divergent understandings.

Drop me a line if this is of interest to you.

3:02 am  
Blogger Gavin Kennedy said...

You have a most interesting learning experience in introducing prisoner’s dilemma into your mediation and negotiation programmes. I too used to teach negotiation in Glasgow - at Strathclyde University - from 1972 (after a short spell teaching it at Brunel University in 1971-2).
One of the many books on prisoner’s dilemma that I found useful later on was William Poundstone’s “Prisoner's Dilemma: John Von Neumann, Game Theory and the Puzzle of the Bomb”. It is not very technical, more a narrative account of its history. From memory it reproduced the plays in the over 100 rounds of the very first PD game with two economists ran at Rand, California, which eventually sparked off great interest and useful technical treatments in the literature.
While the original PD game and the dilemma facing each prisoner are useful background, I switched to Red-Blue because its focus is on the real issue of consequences of the behaviour of participants in negotiation (and in deadlocked mediation).
This illustrates in academic economics Adam Smith’s theory of bargaining (Wealth Of Nations, Book 1, chapter 2) that all attempts to serve one’s own self-interests in ‘Red’ plays at the expense of the self-interests of the other party, generally leads to lower ‘scores’, and sometimes wholly negative ‘scores’, whereas mediating one’s self-interests with the self-interests of the other party (the famous trio of ‘butcher, brewer, and baker’) leads to better ‘scores’ for both parties (i.e., the contents of dinner for the buyer and the wherewithal for whatever for the sellers). Negotiation is not a negative sum game, unless made so by the players.
Red-Blue abstracts from the contexts you describe to focus on the outcome. Party A is responsible for her own outcome, as Party B is for his outcome. Once negotiators understand that truth, there is no hiding place in blaming the other party (male chauvinism, authoritarian behaviours, or whatever). Each is totally responsible for him self.
Deadlocked negotiations are heavily influenced by context; the way to undo the negative context is not to ‘give-in’ but to identify what in the other-party’s stance – as seen by them – can be influenced to become tradable, i.e., negotiable. Only looking at context feeds the continuation of the context – a lesson not yet learned by either party in the Israeli-Palestinian deadlock. Context is often the alibi of people who are part of it.
That is what we used the Red-Blue game for. There is no instant ‘conversion’ from playing RB; it’s the start of the course learning process.
I am most interested in the outcomes of your work. Drop me a line (at the heading of Lost Legacy Blog).

12:15 pm  
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