The Link between the Mathematical Game Theory and the Transactional Analysis. A New Kind of Psychological Game Comes into Being in New Interpersonal Relations.

VANDRA ATTILA
Trainer of the Romanian Association of Debates, Oratory and Rhetoric (ARDOR) and Transsylvanian Debate Association (EDE)

Abstract
MGT studies human games to find the best strategies for gaining a concrete advantage. TA studies human games to get the answer to the question why people make efforts in order to suffer, (to win negative payoffs), and how these people can be helped to give up these daily repeated games. These cause sufferings for all participants, and are the causes of many psychological diseases. However both describe the human conflicts, suffering having a sense of lost in MGT, apparently MGT games and TA games are in contrast with each other. Studying the evolution (the degeneration) of MGT games, we can observe that the majority of human conflicts start off with a “Prisoners Dilemma”, goes on with the “Chicken! Game” and degenerates into a “Dollar Auction Game”. The last one is a trap, and its main characteristic is that all participants, even those who wins the “dollar” (the target of the game), loose, having invested more than they could earn back. The psychological games result for the need for self-justification, for psychological pay-offs of the participants. The more you play the game the earlier the suffering as a target appears in the MGT game, transforming it into a „Fireman game”, than in a „Double target game”. At the end the concrete target transforms into gimmick, a pretext for winning the psychological pay-off of negative strokes. At this point we can speak about a real psychological game. In the author’s opinion the negative stroke is not a real target, it is only a way, a means of winning the real one, the self-justification, which is a positive pay-off in comparison to loosing without having any justification.
Keywords: Mathematical Game Theory, Transactional Analysis, Human conflicts, Game degeneration, to win and to triumph, psychological game, pay-off



1. Introduction
The term “Game” has two meanings: one is related to children’s activity and time spending, the other is a concept related to human conflicts. Other languages, like Romanian and Hungarian, use two different terms for these concepts („joacă” and „joc”, respectively „játék” and „ játszma”) The literally, wrong translation of the word „game” is the source of many confusions and the incorrect use of these terms.
Mathematical game theory is a branch of applied mathematics that studies strategic situations where players choose different actions (moves) in an attempt to maximize their returns. The target of the game is to win the reward, a concrete advantage (like in chess). First developed as a tool for understanding economic behaviour, game theory is now used in many diverse academic fields, ranging from biology, psychology, philosophy, political science, military strategy etc. (Mérő László, 1996, Wikipedia, 2006) In the MGT the game has participants, rules, rewards (pay-offs), moves, an optimal strategy and an unpredictable outcome. In MGT games participants can not be characterized as being „positive” or „negative”; every participant acts according to his interest. If one of the participants can make an unpunished move which breaks the rules, the game degenerates into another game, in which the named move is allowed (for example a card game degenerates into a card-sharp game ). MGT studies games in order to find the most rational and optimal strategies (series of moves), which lead to the most probable or highest reward.
‘Game’ is also a key-concept in transactional analysis (Towards TA – Berne, E., 1964). TA (or psychological) games are a repetitive, stereotyped human behaviours with a predictable end, following predetermined patterns and rules, and have a pay-off of racket feelings (Parr, J., 2002, p39). They are psychological games (towards PG), because:
- They have strict rules
- Have a lot of tactical moves. PG-s can not be continued if one of the participants quits the game, or introduces new rules (F. Várkonyi Zsuzsa, 2001)
- At the end of the game every participant earns a pay-off of racket feelings (Berne, E., 1964).
From the point of view of MGT, PG-s are irrational behaviours. TA tries to get the answer to the question why people play repetitively such absurd games if they suffer because of them, and how they can be helped to quit these games.
Conflict situations are TA games only if:
- The game goes through a set of sequences as follows: Con+Gimmick (accepted provocation) = Response + Switch + Cross up + Pay-off (Parr, J., 2002). These are repetitive and have a predictable end.
- The switch is an obligatory step. In one of the moments of the game one of the participants changes his behaviour which surprises the other (crossup). From this moment participants concentrate on making each other suffer (Berne E., 1964). These negative pay-offs give them psychological advantages. Earning these advantages is the real target of the TA games. While in MGT games participants can win and lose, loss is an unknown notion in TA. (Lassus, René de, 1991)
- If anybody tries to deprive them of the sufferings, they make desperate efforts to earn these irrational pay-offs. (Berne, E. 1964)
- In TA games there are three typical roles: the Persecutor, the Victim and the Rescuer, which form Stephen Karpman’s Drama Triangle (Parr, J., 2002). In TA games participants can change their roles. There are no “positive” or “negative” roles, each participant (even the Victim) has its own interest to continue the TA game. (Berne, E. 1964)
If one of these conditions is missing then the described phenomenon is not a TA game. (Stewart, I. – Joines, V. 1987, English, F. 1987).
Transactional game analysis was considered fundamentally different from rational or mathematical game analysis in the following senses:
- The players do not always behave rationally in transactional analysis, but behave more like real people
- Their motives are often ulterior (Wikipedia, 2006)
This study tries to give the answer to the question if there is a link between a pragmatic, rational MGT game, which tries to give the answer to the questions “Who, and how much will win?” and “Which is the optimal strategy to win more?”, and an irrational TA game with a predictable end (whose main question is: “Why do we continue this absurd game?”). The example of the poker-player is thought-provoking. When the poker-player plays for the first time, he wants to win. For an ingrained poker-player the game itself is a necessity, he has to play even if he wins or not, even if he loses everything. When and why should he change his attitude? In order to get the answer we shall study a conflict of a young couple from the point of view of the game theories.

2. The Prisoner's Dilema
In most cases human conflicts begin when participants realise that their interests come into conflict.
We shall study the conflict of a young couple, Maria and John. Each of them likes to drink coffee served in bed. But who will prepare the coffee? Which of them will give up the joy of serving it?
On the first day John woke up first. He thought he would surprise his young wife…
Next day it was Maria’s turn to surprise his lovely husband…
On the third day they woke up at the same moment. After having good fun, because they tried to get up at the same moment, they drank the coffee in the dining room after preparing it together. But not in bed…
Next day both of them concluded: „I will wait to be served in bed…”
Both of them had to choose between two behaviours (moves, strategies).
1) Adaptive move: „I give up to be served, but I do what my partner expects from me.” (MGT uses the term “cooperative” instead of “adaptive” In my opinion it is not a correct terminology, because cooperation needs the participation of both participants, and a move is chosen by one of them. Cooperation appears in case of mutual adaptive behaviour).
2) Defecting (Non-adaptive) move: „I wait till I am served, even if I do not what my companion expects from me.”
Both have a dilemma. They have to choose between adaptive behaviour and the defecting (non-adaptive) one, which maintains the possibility of earning the maximum advantage. The game has 2*2=4 solutions:
1. John prepares the coffee and loses, Maria triumphs over him.
2. Maria prepares the coffee and loses, John triumphs over her.
3. They get up and prepare the coffee together, but both give up the maximum advantage: to be served in bed.
4. Both wait to be served by the other in bed, so the conflict continues: Who will get up and will prepare the coffee? This is not a real solution. The possibilities are shown in Table 1:

table1.JPG
Table 1. The solutions of the „who serves the coffee” game. Free Roman numbers show how beneficial the solutions are from the point of view of John, the Roman numbers in parenthesis show the order from the point of view of Maria. (I. most beneficial … IV. less beneficial).

This will be a repetitive game in this family. The question is which is the best strategy to win the maximum advantage in this situation (to be served as frequently as possible with coffee). In MGT, this game is known as „The prisoner’s dilemma”. The game has got its name from Merril Flood and Merlin Drescher’s idea and since 1950 has probably become the most studied game in MGT. (Mérő László, 1996, In: Wikipedia, 2004). This game is beyond formal logic’s limits. (The classical Prisoner’s dilemma: Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and having separated both prisoners, visit each of them and offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, the police can only give both prisoners 6 months for a minor charge. If both betray each other, they receive a 2-year sentence each. Each prisoner must make a choice – to betray the other, or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. What will happen? (In: Wikipedia, 2004)
For John seemingly, it would be advantageous to stay in bed (defecting strategy). If Maria got up (adaptive strategy), it would be better for him to be served than to drink the coffee together with His wife in the living-room. If Maria didn’t get up (defecting strategy), it would still be advantageous for John to stay in bed, because in the case of a “stay in bed contest”, which has got a 50% chance of winning, he would still get his coffee in bed in at least half of the cases. But the rules of logics are valid for Maria as well. According to formal logics, each day will start with a “stay in bed contest”. Wouldn’t it be more advantageous to have the coffee in the living-room? Or to reach an agreement according to which one of them will prepare the coffee one day and the other the next day without a fight? Cooperation, mutual adaptive behavior, would be more effective on a long term.
MGT researches have shown that the one who can get more out of the prisoner’s dilemma-situation is the one who can persuade the other to apply the adaptive strategy. For this he needs a strategy that the opponent can only fight back advantageously by applying the adaptable strategy. The most effective in repetitive Prisoner’s Dilemma was invented by Anatole Rapoport and he called it “Tit for Tat” (TFT). (Rapoport, A. – Chammach, A. 1965, Axelrod, R. 1984). The main point is that during the first round he applies an adaptable strategy, and then during the next rounds he applies the strategies used by his opponent during the first rounds. In this way, if the opponent wants to be adaptable, he has to adapt as well. A long-term cooperation is the result of this. Wanting to triumph is a trap and it implies a non-adaptive strategy.
Two concepts need to be clarified:
1. To win, that is to earn more advantages and does not suppose triumphing
2. To triumph, is to overcome the opponent in a direct confrontation mo matter what.
One can check theoretically and practically as well that one can not triumph applying a TFT strategy. However, it ensures the biggest win on a long term if the game is symmetrical. (if the chances of the competitors are equal). Some observations:
- The most significant element of the game is trusting the other (mutual trust). If you can trust your opponent that he will be adaptive, then it is worth to be adaptive, if not, it is more advantageous to defect in order to avoid loss. (Axelrod, R., 1984).
- In an asymetrical game, when the chances of the players are not the same, one of the players gains more or easier than the other and the tendency for cooperation (for adaptive behaviour) will decrease. (Kelley, H. H. – Thibaut, J. W., 1978). The player who starts off with a higher chance of winning hopes to win more and the one who is in disadvantage counts on the fact that his opponent will try to take advantage of his own situation and will not trust his opponent.
- During the asynchronous game, when the players do not take decisions together but separately, the will to cooperate decreases. (Kelley, H. H. – Thibaut, J. W., 1978).
- The defecting strategy might have two motivations: the will to triumph and distrust.
Three out of the four situations of the game (when at least one of them is adaptive) gives an immediate solution to the conflict. But if both of them apply a defecting strategy there will be a rivalry, but this is a completely different game situation. Some of the prisoner’s dilemma situations regularly turn into a “Chicken” game.
As a trainer, I have often used “The prisoner’s dilemma” as a starting point for debates. The students had to play the repetitive “Prisoner’s dilemma” using a scoring which has been modified by me (winning = 5 points, cooperation – mutual adaptive move = 2 points, mutual defecting = 2 points, loss = 5 points). The playing conditions were as follow: after 5-6 rounds the two players that got the least points were disqualified, but the game moved on by swapping partners and zeroing their points, until only two players remained. This is the final. If there were pairs in the first two rounds who were disqualified together because they used mutual defecting strategies, the ones who got to the final and was adaptive, would lose. But usually this was not the case. In 90% of the cases the game was a draw. It seemed as if they had played a completely different game in the final, but, apparently, nothing has changed. “All” that happened was that there were only the two of them left; staying in the game did not depend on what happens in the other games. Winning was not the point in the final, but triumphing… But let’s see what is going on here in fact.

3. THE "Chicken!" Game
Let’s return to our story.
None of them had spoken. However, each of them knew that there was a competition. But it was more and more uncomfortable to stay in bed. Each of them hoped that the other would eventually give up… John gave up, Maria triumphed over him. But next day John woke up with the thought of not giving up and he succeeded: 1:1 was the score! It was a sport. When the honeymoon ended, they had to go to work, and Maria needed more time to prepare. The game became asymmetric; Maria prepared the coffee all week.
The „The one who gives up, loses” type of game in MGT is known as the „Chicken!” game. The adolescent dare game of chicken came to public attention in the 1955 movie Rebel Without a Cause. In the movie, spoiled Los Angeles teenagers drive stolen cars to a cliff and play a game they call a “chickie run.” The game consists of two boys simultaneously driving their cars off the edge of the cliff, jumping out at the last possible moment. The boy who jumps out first is jeered “chicken” and loses. (W. Poundstone, 1992, Mérő László 1996)
Is the merit of Bertrand Russel, who saw in „Chicken” a metaphor for the nuclear stalemate. MGT studies as model the “Highway chicken game” in which players drive their cars towards the other’s car with high speed and the one who swerves sooner is the „Chicken!”
At the beginning, the game seems to be a Prisoner’s Dilemma. Players can decide, in each moment of the game, on using adaptive or defecting behaviour. As time passes, going on with the game becomes more and more dangerous. At a certain moment, it becomes more rational to swerve giving the game up and lose than risk frontal collision. But this is also valid for the opponent. He may give up… The one who triumphs in this game can remain in the game. It seems to be a sport.
Studying the model-game, we should think that normal people do not play such a crazy game. In real life, most human conflicts pass over this phase of the game. People with rational behaviour have no chance of triumphing in this game, because giving up the game would be the rational behaviour! (Mérő László, 1996).
Cooperation has no chance, because nobody trusts the opponent. There are only two solutions in this game: to lose or to triumph. A new motivation is coming into being: the desire to triumph, which can be more powerful than to earn the original reward. Triumph is a psychological reward, which has concrete advantages, so it is a typical reward in MGT games. The risk of collision is another parameter of the game: what can players lose by “making a collision”. (In real life chicken games game is not about life or death, players often risk collisions). It is not the same risk as being in a tank or in a Trabant. The one who has more to worry about is in a disadvantage. But how can anybody triumph in this game?
The most efficient strategy is to convince the opponent that you will not quit the irrational game in any circumstances. The most significant elements of the game are self-confidence and fear. It is not the one who has more to lose that loses, but the one who is more afraid of “collision.” (Children, who are dependent of their parents’ nurturing, are the artists of this game. Usually they triumph in most “Chicken!” games played against their parents).
Causes of asymmetry in “Chicken!” games are related partially to the material world, and only partially have psychological sources (can be found in their scripts).
If the game is asymmetric, it will always have the same end. The player which always loses becomes frustrated, because he can not satisfy his necessities. Being desperate, he will tend to break the rules of the game (Aronson E., Mettee, D., 1968): he will probably apply to emotional blackmail. Blackmail is not a permitted move in the “Chicken!” game, because it degenerates into another game. Sport transforms into war.

4. The Dollar Auction Game
On Saturday the “competition” continued. Maria, who had lost all week, broke the rules of the game. “Please serve the coffee”,said John. The emotional blackmail stated as a request was efficient. How could John say no, if he was asked? Power relations changed. But next day John wasn’t so compliant. He realised that this is part of the game. “I served it yesterday” – he answered to the request. “But I have done it all week” – was her answer. He began to tickle her. She answered by pounding him playfully. “Don’t be a bad girl!” – said John. “If you don’t prepare it today, you’ll get no coffee all week!” threatened Maria, offended. This was not a sport any more, it was war. It was like in an auction: one of them tried to put pressure on the other and the other raised the ante… John gave in again, but he served the coffee less kindly than before. He lost again.
This type of game is known in MGT as the Dollar Auction Game. (Shubik, M., 1971). In the model game, a 1$ bill is auctioned, but the rules are not conventional. The upset price is 10 cents, the ante can be raised only by 10 cents, (not more, not less), and the most important rule is the trap of the game: at the end of the auction not only that pays who made the highest bid and won the dollar, but also the one who made the last bid, whose bid was lower by 10 cents than that of the winner.
The one who bids 90 cents (0.9$), while his opponent bids 1$, will be caught in a trap. Either he loses 90 cents or makes a bid of 1.1$ for the 1$ bill. Continuing the game seems to be a rational move, because it is better to lose only 10 cents than 90 cents. But his opponent’s logic will be the same and he will bid 1.2$… According to Shubik (1971), the average price paid for the dollar bill is 3,5$, but Baga Tibor, my student, organized an auction, where the final bid was 12.4$! The slogan of the game is “Too much invested to quit.” (Mérő László, 1996). Every move (bid) seems to be rational, but the whole behaviour is completely irrational because the winner pays more for the dollar than it is actually worth. But the one who gives up easily, decreases his chance to triumph in the next game. He will lose more and more games.
In the Dollar Auctions of life, “bids” are emotional blackmails or threats. Players send each other the following message: “I can hurt you more than you can!” This is real war, not a sport.
Threats, emotional blackmails, as bids in the model game, can not be retracted. Each player feels himself a Victim, identifies his opponent as a Persecutor. If one of the players began the “auction”, the opponent would only keep his chance to win overbidding him. Some real-life auctions end up in law courts, in hospitals, at the police or even in the cemetery. Let us return to our story.
The atmosphere cooled down by next morning. “We had a fight over nothing!” They made a deal: on weekdays Maria serves the coffee, during the weekends it is John’s turn. The conflict seemed to be solved.
Because the ones who triumph can also lose, the consequences of this are motivation for finding a joint solution. H. H. Kelley and J. W. Thibaut’s (1978) researches have shown that a long term mutual adaptive behaviour (real cooperation) is possible after a mutual defecting one and they quit the game all at once. But this is only a chance. It is very important how the players assimilate the events after the game. The self-respect of the players is manhandled in this game because they have lost (even if they have triumphed) and because they were forced by the trap of the game to have an antisocial behaviour. A new necessity of the players comes into being: to save their self-respect whatever the costs. Without positive self-respect, man would lose self-confidence, their safety-feeling. (Várkonyi F. Zsuzsa, 2003) Self-respect can be saved by transferring all responsibility to the opponent (to the enemy), using a double ethic (Allport, G. W., 1999) and rationalisation (Festinger, L. 1957). The lawful consequence of the Dollar Auction Game is the desperate desire for self-excuse. This necessity becomes more and more imperative as auction degenerates, because he commits more and more blameworthy acts (Glass, D., 1964).
John escapes his remorse by transferring responsibility to his wife. It is a relief for him that her wife is the guilty. Maria is also relieved, because she can accuse her husband. No one could prevent them to do so. It was a game without a real opponent, in which they could triumph without an effort.
The attempt to save self-respect is a new MGT game, but it is the lawful consequence of the first game. The motivation for playing this second game came into being while playing the first game. Losing the first game generates a situation, in which it became easy to accuse, to transfer the whole responsibility. How could they accuse each other before the coffee-conflict? To do so, they needed to suffer first.
There are some advantages of being a Victim. There are diverse forms of emotional blackmail. The punitive (Persecutor) is not the only one. The suffering (Victim) can also be an emotional blackmailer (Forward, S. – Frazier, D. 1997). Suffering is also blackmailing others by attacking their self-respect: “You have made me suffer!” But you have to suffer first, you have to make a “queen-sacrifice.” You have to provoke the opponent to produce you suffering, and after that you can switch to accusing him for it. The more the Persecutor punishes, the more efficient the blackmailing by suffering of the Victim can be. Moreover, you can punish yourself in order to blackmail, like the child, who blackmails his parents by refusing to eat. This type of emotional blackmailers are named by Forward, S. and Frazier, D., (1997) as self-punishers. Such a manoeuvre is a typical tactical move in MGT games (like the queen-sacrifice in chess), but in these pragmatic games the target of the sacrifice is to earn a concrete advantage. Sacrifice is only worth if the reward of the second game is bigger than the negative consequences of losing the first game.

5. Different Grades Of Psychological Games
The Fireman-game (Fireman psychology)

Studying PG-s, we can observe that PG-s can be divided into two MGT games. The first one, with a pay-off of a concrete advantage, is only a gimmick (a queen-sacrifice). It is easy to triumph in the second game, earning psychological pay-offs of negative strokes by losing the first one. In my opinion, it is a wrong interpretation that the target of psychological games is suffering; the real target is to save positive self-respect. Suffering is only an instrument, a manoeuvre, a “queen-sacrifice” for winning the real target.
In PG-s, the switch is a compulsory move. But, suddenly behaviour-changings (switches) have different forms:
1. After the end of the game, the player begins a different activity (a new, different MGT game).
2. After loosing the game, the player looks for compensation, playing another, different game. (For e.g. John after losing the game began to growl alone, being angry with her).
3. Giving up an unreachable target switches to running after a more reachable (winnable) one, finding compensation in it.
4. Switching is a calculated manoeuvre; the real target is to win the second game.
Only the last two are real switches, because behaviour change occurred while playing, not after the end of the game. The difference between the last two examples is that in the third case the intention to make a switch “to compensate losses” did not exist at the beginning. If he won the first game, he would not try to make efforts to triumph in the second game. In the fourth case, winning the first game would make him feel a loser, because he had lost a chance of winning the real target. In this situation, the player would make more effort to reach his real target. The third case isn’t a manoeuvre even if it looks like it, the fourth is, however.
A degenerated Dollar Auction Game isn’t a real PG, even if it seems like it. Without a real switch, it can be classified as racketeering. (English, F., 1987). The main difference is that, for the player, who accepts to take part in a Dollar Auction-like game, the concrete target is more important than psychological compensation, thus saving his wounded self-respect. For John and Maria, to be served with coffee in bed and the symbolic meanings of being served were important. The other difference was that the game did not have a predictable end. But degeneration of the game has given birth to a new necessity: saving self-respect. Let us return to our story.
They complied with the agreement until Christmas Holidays came, but during the holidays, they did not have to go to work on Monday. Maria tried a gimmick: “Do you love me?” “Yes.” “Then you should prepare the coffee!” John did not let himself be fooled. “It is a weekday today” “Holidays are like weekends, we do not go to work” she answered. “You are being selfish” she added. “And you?” replied John. Maria got angry: “You are insolent!” This remark opened Pandora’s Box. They began to accuse each other, overbidding each other. Neither of them prepared the coffee, they did not drink coffee that morning. Their only consolation was that the other was the guilty one. Neither of them felt responsible for the happenings. Or was it only appearance? If Maria’s mother-in-law had not come to visit, they would probably have never made up again. John “accidentally” broached the coffee story. His mother immediately took his son’s part. “I prepare the coffee for my husband every morning. That is a woman’s duty”. The game became asymmetric once more.
This fight was different from the previous one. In the first fight each tried to put pressure on the other one to convince him/her to prepare the coffee. They even used labels (For example: “Don’t be a bad girl!”) to convince the other to give the game up. In today’s fight, the same thing happened at the beginning, but only up to a point. “You are insolent”, was an unmistakable insult. An insulted person would do what you expect him to do. This action did not bring the target nearer, it made it more improbable to reach. After the switch, they made efforts not to reach the original target; they tried to save their self-respect. The easiest way seemed to provoke the other to antisocial behaviour, to have enough reason to accuse him/her, to make revenge possible. Coffee served in bed? It was not important any more. Why?
We have seen that degeneration of the conflict gives birth to a new necessity: to save self-respect. When the game repeated itself, they saluted the well-known feeling which appeared, in previous cases, only after finishing the game. This necessity brought up a dilemma: to triumph in the “Who prepares the coffee?” Game, they had to continue overbidding the opponent, leading to further decreasing self-respect. To save self-respect, they had to transfer responsibility to the opponent, but for this they had to give up the “Who prepares the coffee?” Game. I named this “Skylla or Charybdis”-type of dilemma the “Fireman psychology”. If your house is burning, you can do two things: either you are fighting with the fire, risking losing everything in the fire, or you give up the fight and try to save what you can. First you are thinking about having chances to rake out the fire, but you gradually lose faith to carry it out and you will make a switch and will begin to save what can be saved. After the house has burnt down, you will tell your neighbours how happy you are, because you have rescued the TV and they will be surprised how happy you can be when your house has burnt down… Rescuing the TV is a gain if we make a comparison to the situation before the fire, with the possibility of losing everything, even the TV. Is it worth to get series of insults only to have the opportunity to accuse the other? For a rationally thinking man, the answer is a categorical NO. But for those who fell in the trap of the Dollar Auction Game and have lost all hope to triumph, things appear different. A gain is a relative notion. “I have more after the game, than before, so I have won”. But what is the sense of “before?” Before what? Rescuing self-respect is a real gain, if we think like this: I have lost the game anyway, but I am not responsible”. For those who have lost all hope to triumph, rescuing the remaining of self-respect is a real gain.
Theoretically, the conflict can be solved in such a situation, if both players accept the responsibility for their own mistakes. But there is a risk. If one of them accepts and the other does not, the fist one not only loses, but the whole responsibility for the happenings will be his/hers. (Is a Prisoner’s Dilemma-like decision). For such a risk neither has enough self trust, but in a degenerated game it is easy to accuse the other…
In our story, the switch appeared when Maria concluded that she has no chance to triumph. Switch is related to losing self-confidence and the desperate try to rescue self-respect.
This can be considered a PG; however, it is not a typical one. The game follows the typical steps of a PG, includes a switch and each player gains a pay-off of racket feelings. But we can not sustain that the target of provoking the game was to have justification to accuse the other, the outcome was not predictable at the beginning of game. The game is a hybrid between MGT games and PG-s. The more you play the game, the earlier the switch appears in the MGT game. A factor, which introduces asymmetry in the game (for example the appearance of a “Rescuer” who interferes with one of the players), will be the catalyst of transforming into a PG. The player in disadvantage, when he concludes that he will lose, will make a switch to rescue his self-respect, posing himself as a Victim, and his opponent and his unconditioned Rescuer as a Persecutor.
If the game is asymmetric, its outcome will always be the same and the roles become steady. It is easy to imagine that if the mother-in-law had lived with them, Maria would have lost every day. Maria would try to win, but… she would lose every time. (“As you see, I tried everything, but…” game – Berne, E., 1964) In asymmetric games, the scenario is the same and has a predictable outcome. The one who loses every time, has no alternatives: he has to compensate the permanently lost game or triumph in other games (reciprocity = a type of cooperation), or console himself with something like a child with a dummy: “the other is the guilty one”
The Double-Target Game
Next morning Maria asked John: “Will you prepare the coffee or not?” John became upset by the tone, hesitated a moment, but was ready to get up to serve the coffee. Maria gave him no opportunity to do so, seeing that he doesn’t get up immediately and feeling herself a loser after losing the game a day before. So she played her last card: “If you don’t make it hearty, I do not need it!” John fell in the trap, he had two bad choices: either he prepares the coffee to prove his wife that he makes it hearty (and loses) or he will be the (only) guilty in his wife’s opinion (and he will feel as he has lost too). John got up angrily, but he did not prepare the coffee. He’d rather give up to drink coffee. His consolation was the feeling of revenge.
The experience of S. Berglas and E. E. Jones (1978) is the proof that those who don’t have self-confidence have the tendency to increase their self-handicap in order to have justification for losing. Their experience subjects, students, who had to give a test, had to choose between two pills which they had to swallow before the test. They were told that one of the pills increases, the other decreases efficiency at the test. Those who had low self-confidence about passing the test chose the pill that decreases efficiency, in order to have further justification for not passing. If they did not succeed in taking out the fire, they would try to have justification.
The tone used by Maria and then her “pride”, deprived her from beginning to obtain what she desired. Despite this behaviour, she wished to be served with coffee in bed. Her low self-confidence motivated her to have insurance against loss. For her, the game had two targets: “Either I’ll be served coffee or John will be guilty of everything.” If she loses, at least she’ll have justification. She could be sure that one of the targets will be obtained. It was impossible to loose both games. But desire to be served with coffee still existed.
Maria still wanted to get John ask her for forgiveness and she let him serve the coffee. But because John did not ask for forgiveness, it was clear, that morning, that she has lost the chance to be served. The game transformed into a PG, in which both have gained a pay-off: “You are the guilty one! Everything is all on you!”
From this moment, the psychological advantage gained from suffering became a real target. It is not easy to separate a Double Target Game from a typical PG. Theoretically, the separation limit is where the original target (to be served coffee in our story) becomes negligible compared to the psychological pay-off. When you lose an MGT game, it is only a manoeuvre to gain the real target, the psychological pay-off, a good occasion to play your favourite PG.
A Double Target Game is also a transition between MGT games and PG-s, but in comparison to the Dollar Auction Game (or the Fireman Game), this game contains only tracks of the main characteristics of an MGT game, that is the purposefulness.
The Typical Psychological Game
Next morning they had another quarrel, but this time it did not count if the other serves the coffee or not. Only who is the guilty was important. They quarrelled over unimportant things all that day and each time the issue was brought back onto the coffee story. Every scene had a similar scenery: Maria asked for something, using an imperative, impolite tone, and if his husband didn’t react immediately, she said offended: “I don’t need your help, if I have to implore you!” John tried to make her to change her mind about it, but because his wife didn’t change her proud attitude immediately, he gave up relieved his attempt to persuade her to change her attitude. “As you see, I tried everything, but…” They agreed on a single thing: the other is the guilty one. They tried to persuade each other in a way that did not succeed, as if they wanted to suffer.
The fact that Maria did not let John to persuade her to give up on the self-punisher behaviour, shows that, in this game, the debate was not about the coffee. Coffee was only a gimmick, a trap, and John did not learn from the happenings (as he did not want to). After John fell in the trap, Maria began to play the Victim’s role and could prove that she had justification for channelling her rage on John. John, after the first uncourageous attempt, suffered relieved because of her wife’s rage and named her “hysterical” because she escaped responsibility. (As you see, I tried everything, but…” game – Berne, E., 1964) The “Who is served coffee in bed?” Game was a lost game for both of them from the start point. If one is guilty, the other can justify any behaviour. The other deserved it… Didn’t he?
When all participants of a game find their own psychological pay-off, we have a typical PG. In PG-s, players have double motivation. On the one hand they are suffering from the game, they would like to avoid it, and on the other hand they desire to relieve transferring whole responsibility to the other, being ready to sacrifice the reward of MGT game as well. There is a competition between these contrary motivations (fireman psychology). While the first motivation and the desire to earn the reward of the MGT game seams to be more important and reachable, players make efforts to win the MGT game and to avoid PG. But as the game advances and because of the trap of the Dollar Auction Game, the self-respect becomes lower and lower, the second motivation becomes more and more important and at a certain moment it lawfully takes initiative. This is the moment when the switch happens. From this moment, the player makes desperate efforts to gain the psychological pay-off (transfer of responsibility).
Switch upsets efforts to avoid PG. This is the key moment of transforming the MGT game into a PG. But a PG can not be continued only by the participation of all players. If one of the players makes a rule-breaker move and tries to quit the game, then a new MGT game bears. The target of this game is whether players would play the PG or not. The player, who wants to quit, tries to persuade his opponent to give the game up, the other will provoke him to continue it. Game has finished when all players give up making efforts to gain the psychological pay-off. One can be dependent on saving self-respect as on alcohol or drugs. As somebody becomes more and more dependent on psychological pay-off-s, he will provoke more and more desperately, he is not obligated by social rules any more or to have rational behaviour, so in most cases he will triumph in this game. The player, who tries to quit without succeeding, has a psychological pay-off too.
As the reward of MGT games is more important, players could more easily be persuaded to avoid PG-s. There are only quantitative differences among the Fireman-game, the Double Target Game and a typical PG. The main quantitative difference is the relative importance of the concrete and psychological target in the starting moment of the game, in the Prisoner’s Dilemma situation. In the Fireman Game, the target of the MGT game is more important, the psychological pay-off is only an alternative for losing. In the Double Target Game the motivations are similar. In typical PG-s the target of the MGT game is only a queen-sacrifice for gaining the real target, the psychological pay-off. In the Fireman Game the player is happy to earn the reward of the MGT game, giving up the psychological pay-off. In the Double Target Game, he can be persuaded to give up psychological pay-off if he earns the reward of the MGT game, but in a typical PG, gaining the reward of an MGT game instead of psychological pay-off would make the player feel like a loser, so he will make other desperate efforts to win the psychological pay-off, provoking other games. But how can players quit such a game?
The antithesis
That night they slept back-to-back. However, neither could sleep nor said a word, although night was a good adviser. In the morning, John got up, prepared the coffee, and served it to Maria, and then he said: “I know that you like coffee served in bed. Me too. I realized how much my mother’s words offended you. Yesterday, I wanted to serve the coffee, but you did not give me a chance. I do not want to begin another quarrel on this subject, but I have to say, that it makes me nervous when somebody speaks to me on such an imperative tone. If somebody speaks to me like that, I say no, even if normally I should say yes.” After he finished, he left the bedroom. Maria was so surprised, that, for a moment, she had no answer. Then she had nobody to quarrel with. Her first reaction was: “If he did not bring it to me with pleasure, I do not need it!” She did not drink the coffee, but she did not get up either. She only tried to channel her rage on John. But as time passed, she realized that she can’t persuade herself. But how would she confess? Both were very quiet all day. At night, in the bed, Maria wreath her arms around John, and said: “I do not want to quarrel with you. I love you.” – Then burst into tears. John strained her in his arms and said: “Neither do I.” then added: “I wanted to say me too” They began to laugh… In the morning, Maria told John, who was about to get up: “Let me do it. It’s my turn!” That day the mother-in-law came again to visit. She brought up the coffee story again. They responded in the same moment: “Mother, we can work out our problems alone!” In that moment, they looked at each other and screamed with laughter. The game was over. Or was it? The mother-in law felt that the youngsters made her feel like an idiot… She has lost the occasion to “rescue” his son…
This message of John’s was different. He did not implore his wife; he did not let her feel dominant, provoking her to be a Persecutor. In the same time, he did not accuse her, provoking her to be a Victim. He told her his own feelings and thoughts. Thomas Gordon (1974) names this type of messages I-messages, because, in the message, the subject is “I”; the person who is communicating has a problem. For example: “I should like to” “Disturbs me”. Characteristic of these games is that these messages are changed by messages which communicate about “you”, the person who you are speaking to. These types of messages are named by Th. Gordon “you-messages”. For example: “(You) serve the coffee!” “It’s your obligation” I-messages contain no crawl and no accuse, so they make it more difficult to transfer responsibility, to gain the psychological pay-off. If a message contains an alternative as well, another reward instead the lost psychological pay-off and also gives time to assimilate the happenings, then, it increases the probability of quitting the game. The behavior, which makes it more difficult to obtain the psychological pay-off, makes the game meaningless, and is named antithesis. Using antithesis, deprives partners of psychological pay-offs, so they will provoke the game-breaker desperately to continue the game (Berne, E., 1964). A new MGT game appears when using antitheses: “Do we play PG or not?” This MGT game can be won by both parts.
The consequence of the unsuccessful use of antithesis is that next time it will be more difficult to use it. Partners learn how the game-breaker can be provoked back in the game. His provocation will be more vehement and the player will apply to more desperate moves.
If antithesis is applied with success, it puts the basis of a real, long-term cooperation, like in our story. In real cooperation, in the thinking of participants (not players!), “I (my)” is changed by “we (ours)”. (Our common interest is to renounce to some advantages because I trust that you will do the same).
Using antitheses deprive the Rescuer as well to earn the psychological pay-off, so he will provoke the others to continue the game. In our story the loser of the cooperation of the young family is the mother-in-law, who can not gain psychological pay-offs rescuing his son. She will probably try to provoke other games to get the pay-off from other games.

6. Conclusions
The metamorphosis of motivations

Human conflicts work on the pattern of Prisoner’s Dilemma "Chicken! – Game", "The Dollar Auction Game", "A type of PG (Fireman Game, Double Target Game or Typical PG)" sequence. Motivations are not constant; they change while the game advances and time passes. The following is a wrong question: “Which is the motivation of the game?” For a wrong question there are only wrong answers. The way games generate the motivation of players changes too. The way the outcome of MGT games (Prisoner’s Dilemma, Chicken! Game and Dollar Auction Game) is decided by reciprocal trust, self-confidence and self-respect, motivations change in the same way. In the Prisoner’s dilemma the main motivation is “I want to hit my target”. Next to this motivation, in the Chicken! Game, the desire to triumph appears and also the fear of the consequences of continuing the game. In the Dollar Auction Game, the desire to rescue self-respect, lawfully appears, which becomes more and more important than motivations to hit the original target. Switch is the consequence of lawfully changes in values. The intention to make a switch and transform the MGT game into a PG is not compulsory in the starting point of the game (the moment of provocation). In the case of repetitive conflicts, achieving psychological triumph as a motivation appears in more and more earlier stages of the game. From this point we can speak about double motivation, which accompanies it all through the game.
Reasons why people play PGs
According to TA, the main reason why people play PGs is the necessity of stimuli, of strokes. But this necessity can not explain exclusively all phenomenology of PGs. The necessity of strokes can not explain why a peaceful activity, by reason of a mutual rigid standpoint (both want to triumph), transforms suddenly into a power play, which degenerates into racketeering and, after a switch, ends as a PG, which does not solve anything. It is not easy to explain what the source of stroke necessity is, because it was not present in the peaceful activity.
The internal pressure to be fit to script messages achieved during childhood has an important influence on the general self-image and decisions taken in PGs. But these scripts also can not be considered as exclusive reasons why people play PG. Scripts can decide inclination for games, which will be the preferred games, but do not give any explanation for changes in intensity of PGs. Why does the dictator-director play the role of the Victim at home, when, in his office, he plays the role of a Persecutor? Why does the intensity of PGs increase in the elderly period? Why does the intensity of PGs increase during the teenager period and decrease (without the help of the TA specialist) spontaneously at the end of this period? Scripts do not change.
Prank campaigns carried on with the classroom’s scapegoat within a children’s group are also PGs.
Why do all members of the group participate independently regardless of their scripts? Why is the tendency of finding a scapegoat more intensive in the case of discipline-centered (punitive) education? If the scapegoat leaves the group, there is a high probability of another scapegoat to appear in the game-deprived group. If we transfer the scapegoat, the class, which was deprived of it, will most probably look for another one. (Allport, G. 2000). The series of questions can be continued. Neither necessity of strokes nor scripts give a satisfying answer.
In all PGs it is common that the target of the game is to save self-respect no matter what.
The key-move of the PG is the switch. Players switch exactly when, in their vision, saving self-respect becomes more important than making efforts to hit an unreachable target. Saving self-respect as a necessity can exist at the beginning of the game (at the moment of provocation – MGT game is only a gimmick), but can come into being while playing the MGT game too, as a lawfully consequence of the degeneration of the MGT game. The laws of MGT games give enough explanation how PGs come into being. Using Occam’s razor (one should not increase, beyond what is necessary, the number of entities required to explain anything. – F. Heylighen, 1995), we can conclude that PG can come into being without the influence of scripts.
Negative experiences of PGs give enough motivation for quitting repetitive PGs. If players do not quit, it is hard to give a satisfying explanation to the phenomenon without referring to scripts.
Beyond scripts, other influences can increase probability of playing PGs:
1. Non-scriptic origin relationship asymmetry.
2. Frustration because of losing other games.
3. Physiologic or healthy bodily causes: hunger, tiredness, illness.
4. Rule-systems and expectations of the environment (in such situation the correct behaviour is…) or examples can have an influence (conformism – Aronson, E., 1999).
A part of the factors that have influence on playing PG-s are found in the present (here and now) or in recent past. These factors, together with the scripts, lead to PGs.
Degrees of PGs
According to Eric Berne, Games vary in intensity or degree from the relatively harmless first degree to the hard third degree game which leads to personal injury, involves tissue destruction and end in the law court, in the hospital, at psychiatry or in the cemetery. (Berne, E., 1964).
The link between MGT and TA give us another criteria of classification the degrees (intensity) of games. As I have shown, the PG can be divided in two MGT games. The target of the first is a concrete advantage; the second one’s saving self respect by sacrificing the reward of the first game. The relative importance of the two targets in the vision of the player (in the moment of provocation in the first MGT game) defines three degrees of a PG in the start point of the game.
- First degree game: In the start point the concrete target is more important, but as game evolves, the psychological pay-off becomes more and more important. In the Fireman-game player is happy to hit the reward of the first MGT game, the concrete advantage, renouncing to get the psychological pay-off.
- Second degree game: The importance of the targets is appreciatively equal. (Double target game). The player assures himself that he is going to have a consolation in case of losing the first game. The player can be convinced to give the psychological pay-off up by getting the reward of the first game, the concrete advantage.
- Third degree game: The MGT game is only a gimmick, a pretext. There is only a single real target and that is to hit the psychological pay-off. If somebody deprives him of this pay-off, he will desperately provoke another game.
One can be dependent of games as of alcohol. (Berne, E., 1964). The degrees of dependency are also measures of the degrees of games. Dependency has four degrees as shown in the analogy with degrees of alcohol dependency. Every degree of dependency can be considered another degree of the PG.
Degree 0: Testing (first time tastes alcohol) – game degree 0 –it is not a game.
Degree 1: Enjoying (drinks occasionally with friends) – first degree game
Degree 2: Falling into a habit (is drinking regularly, but he can give up making an effort) – second degree game
Degree 3: Dependency (alcohol becomes a vital necessity, he sacrifices anything for a drink) – third degree game.
Table 2 shows the correspondence between dependency, Berne’s game degrees and degrees given by the relative importance of the concrete and psychological target. There is no equivalence between different types of degrees, only similarity.

table2.JPG
Table 2 Similarity between different expressions of psychological game degrees

7. After Word
There are two different methods for solving human conflicts: cooperation and games. The condition of cooperation is mutual adaptation, but adaptive behaviour is risky, you can lose. The consequence of mutual defecting behaviour is a competition, which lawfully transforms into a “Dollar Auction” if none give up. In “Dollar Auction Games”, it lawfully decreases self-respect of participants and the low self-respect creates ideal conditions for transforming into a PG. By switching, conflict situation it transforms into a PG.
All PGs can be divided into two MGT games. Both games studied separately seem to be rational, but together they are an irrational behaviour.
In my opinion, the statement, according to which the target of PGs is suffering, is false. Suffering is only an instrument in rescuing the remaining of self-respect. Sufferings can justify any unsocial behaviour.
It is an exaggeration to say that stroke necessity and forwarding scripts are exclusive causes of PGs. Both lead to PGs only together with MGT games (here and now phenomena). Variation in PGs’ intensities can be explained by the help of here and now phenomenon.
Adequate treatment of MGT games can prevent one from having inclination to play PGs here and now. For prevention, it is worth being attentive to laws of MGT games, because in different phases of the game the efficient strategy is different. But the efficient treatment of a concrete MGT game does not solve the script-based tendency for playing PGs and the dependency on PGs.
In new relations, two different mechanism lead to PGs:
1. A person who has script-given tendency to play PGs, looks for partners to play favourite games.
2. The lawfully decreasing self-respect in generated by MGT games make ideal conditions to a runaway into PGs. If the conflict does not have a real solution, the game will repeat itself on a higher degree. The Fireman-Game, in the course of time, transforms into a Double Target Game and then into a typical PG.
In my opinion, the statement according to which PGs are unambiguously prejudicial for players is false. Low degrees PGs (Fireman games) have their positive role, for example, rescuing self-respect. (Contrary, according to natural selection, people who have the tendency to play PGs would be eliminated, forming a non-player human race).
When appealing to antithesis, it is not sufficient to deprive players of psychological pay-offs, it is necessary to give them a consolation and the reward of the MGT game is one of the best options.
Those who want to deprive the partner of an absurd psychological pay-off, have to know the laws of MGT games too. Quitting a PG is an MGT game… (Do we play or not a PG?)
Patients go to TA specialists when they reach higher degrees of PGs, when scripts have the most important role in guiding PGs. Without scripts, MGT games would not generate chronic PGs. Even so, MGT conclusions can help TA specialists.
MGT game conclusions have an important role in prevention. Educators (parents or pedagogues) have the opportunity to block games coming into being in time. Most of the time the educators do not realise that by punishing or “rescuing”, they are, in fact, the ones who drive children to PG-s.

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9. Biographical Note
Vandra Attila, Trainer of the Romanian Association of Debates, Oratory and Rhetoric (ARDOR www.ardor-deb.ro) and Transylvanian Debate Association (EDE – www.ede.ngo.ro), member of International Debate Education Association (IDEA – www.idebate.org)
Adress: Vandra Attila, str. Berzei 2B ap. 20, 500276 Brasov, Romania
E-mail: vandraattila@rdslink.ro
Tel: 0040 368 402 523
Mobile: 0040 722 264 666