Game of Chess on A Flea Market

Theses and thoughts about game theory, strategic games and conflict of interests (part 3, look into the part 2). By Tomas Shelling, the book “Strategy of Conflict”.

What we struggle for in the course of bargaining in some game? What is the import of game? What is gain in game and what it is made up of?

These questions are important enough, and it’s necessary to sort out the matter here and form a picture in the way to be able to sort out deeper the game practice.

So, the game is manageable conflict where all players struggle for their interests’ realization, playing one against another, and where the game result and resulting gains of each side depend on actions and decisions of all game players.

But games are different. One would determine it as bargaining with trader on a flea market somewhere in Amsterdam aiming to beat down prices for lovely knick-knack, for another one the game means long game of chess where deep analysis of current situation, mentally checking of prospective combinations as well as forecasting for adversary’s potential moves take place, where each move closes one part of canned combinations and opens wide opportunities for new ones, and where the end of a set doesn’t have to be the end of the game.

Why is it so? Just because games are different by different people and everyone has its own unique gain.

Let’s look it in detail what the gain is on some simple situation – trading on the flea market.

While bargaining on the market, it seems to be that the gain for both parties of bargaining is the selling price, and concerning interest: for a customer – it’s in buying price which is as low as possible, for a trader – in selling price as high as possible. By this, the one and the other have their proper understanding about how much a certain article of commerce may cost, and what is the better rate to buy or sell it.

Therefore, all possible variants of this game’s results can be displayed schematically on the following line of various results’ (situations, decisions, actions) set: in our case with the article price – from the lowest till the highest rates.

For the customer, this article costs 20 $, but in his understanding it would be well to buy it for 10 $. And exactly from this starting point he is likely to start bargaining. For the trader, this article really costs 15 $, but it would be well to get 25 $ for it. And exactly this price is likely to be announced in the beginning. For the customer – all possible gains (decisions) are disposed in the AD-range, and correspondingly all what is out of the range represents losses.  For the trader – the gain field is the BE-range appropriately, where he is likely to play in.

The AE-range, that’s exactly the bargaining field with all possible results’ (situations, decisions, actions) range. And both parties are to move up and down this range, by using various arguments, by persuading, by applying different manipulation techniques, and they bid fair to negotiate a price somewhere in the middle of the BD-range.  The C-point represents the game result (outcome). Gain for each of parties is to be what each of them could spare or earn. In our case, the customer gain will be 2$, the trader’s – 3 $.

We have studied an ideal and quite simple situation where the final price was the gain for both parties. But what if for a trader the bargaining process itself would be more valuable? Or what in case he were bored?

Or, he turned to be no trader at all, but was temporarily supervising the selling point, when trader was out for a short while? What would be gain in such case?

Even from this simple example the following findings inevitably comes to mind:

-               the gain for someone is what is valuable in one’s value system, or, in other words, what represents one’s interest. And the question is here: what about interests of our partners and contractors? Do we really understand their interests? Do we understand value system of theirs?  If we don’t, are we sure that our interests are in contradiction?

-               such situation may occur when there is nothing intersected in the gain field of two bargaining parties. If to consider our given example, it may have occurred that the customer’s gain range was disposed within the AB-range, and the traders’ – within the DE-range. In result – we get stalemate, when the parties are never able to come to agreement.

-               game result (outcome) is always gain and loss division. For example, the trader gained 3 $, but lost potential gain in 7 $. Though, the situation could occur there when the trader had to give up some other thing in the way to get his gain.  

-               in practice, there is hardly ever ideal game outcome which would completely suit all the parties, by this, certain part of game results is to be better (worse) for both parties than others. For example, the case when the trader is ready to sell off the article for 15 $, but the customer is eager to get the highest gain, i.e. in his understanding – to buy it for minimal price making 10 $. The evident result here is that their negotiation is to fail, and they will hardly come to mutual agreement. And what’s more in such case is that the both parties will lose more than they gain.

-               the total sum of parties’ gain in result of the game is far of being constant. If to study our example, the section where the parties can come to an agreement represents the BD-range of 5 $. And if to arrange that the price only can be gain, then, particularly – yes, it’s constant. But in real life the gain is much more complicated notion. A trader could be mad for the long and pleasant bargaining process itself, as for a customer – what's important for him is his status and understanding that he could cope with and beat down the price as low as possible. Every decision is to give in total absolutely different amount here. The more complicated an article of commerce and the more parameters we include in our understanding of the gain – the more the parties’ gains and losses will differ.

-               it may turn out that we are bargaining in the same field (play upon adverse interests), but without any contradiction in our gains at the same time, because they lay on different levels. What concerns the conflict of interests, i.e. what the game started through – it implies that actions of one party aiming to attain the gain may depend, anyway, on decisions and actions of the other party. In result it may turn out that, trying to attain one’s own interests, one just prevents the opposite party from attaining its own gain, even though parties’ gains are not controversial in the matter of the fact.

And now let’s bring a little difficulty in the studied case. For example, let me take some contract terms discussion between chief contractor and subcontractor. In the course of bargaining between parties there will be much more suchlike lines reflecting the parties’ interests, as an example – warranty division, terms of main and supplementary equipment delivery, costs and supply a building area with electricity, water etc. Then, the bargaining process itself concerns more dimensions, where each of them is to be bargained separately, as in the given customer-trader example on the flea market, where bargaining results over one question (one line) depend or may depend on other questions (lines) and where coming to agreement in one direction can significantly change the before-arranged articles of the contract etc.

It’s that the gain itself for any party represents the total result of local outcomes due to each direction. However, during one round of talks it’s possible to negotiate successfully contract articles and points, i.e. to finish the game, and come to a final result.

Then, once more again, let’s make the situation a bit more difficult – imagine that it’s necessary to accomplish a complex infrastructure project – be it some plant construction. The whole project here, it’s a great deal of negotiations and meetings on different directions, with different sets of participants, with different mediatory results and situations. Yes, probably, we’ll succeed with its organization, but what concerns the gain-loss volume and proportion, it’s formed in result of such negotiations, one by one. Consequently, what we hold is some kind of immense game framed from a multitude of little and separate gamelets which form a plenty of complicated interconnections, where it’s often too difficult to foresee the power of some mediatory result’s impact on the following operating stage.

Not easy. But the project consists of negotiations and meetings series. Each round of talks is the set of questions (lines) we bargaining upon here. And each question we bargain upon, it’s like situation on the flea market – we know how much it can cost, and what cost it would be well to buy or sell it for.

Each local game can be replayed. There are no final results. The win is calculated totally from little gains. That’s why there is nothing fearful in big games. Everything is composed from little wins gained and mediatory results. And, finally, these tiny bricks will bring us to a big victory with maximal gain and minimal loss.

To be continued…