The games we play
http://gospelfutures.org/2013/04/04/the-games-we-play/
by Neil Williams
April 4, 2013
When the mathematical genius John von Neumann (1903 – 1957) sat down to figure out how he could use mathematics to improve his poker playing, little did he realize the repercussions of his inquiry, not only in mathematics but also in almost every other field of inquiry. Considered the father of game theory, Neumann, with the economist Oskar Morgenstern, produced the founding textbook Theory of games and economic behavior that revolutionized economics.
When playing a game such as poker, you have limited information (you cannot see all the cards), other players will deceive you, and they intend to win. Game theory is about what decisions and strategies you should take to achieve a favorable outcome.
Games consist of three main areas: players, strategies, and outcomes. A basic form of a game is a two-person game where a win for one player means a loss for the other. Known as a zero-sum game, the outcome of this type of game adds up to zero—a win (+1) is offset by the other player’s loss (-1). These games are one hundred percent competitive with no co-operation between players.
In a positive-sum game, your win does not mean a total loss for your opponent and involves some co-operation as well as competition. In such games, all players benefit, the outcome being positive. The cliché “win-win situation” refers to a positive sum game where all players benefit from the outcome. Trade between two nations is a classic example of a positive-sum game.
Game theory started in mathematics, but expanded to other disciplines including psychology, economics, politics, evolutionary biology, warfare, and theology. We can conceive of most, if not all, interactions in terms of a game: people bidding on an ebay auction, the Cuban missile crisis, a couple arguing with each other, a job applicant negotiating a salary, airlines overbooking flights on the assumption that some passengers will not turn up, a criminal taking a plea agreement instead of a jury trial, a person sacrificing their life for the sake of another.
The ways games are structured have implications for relationships and transformation. A married couple may frame an argument as a zero-sum game where each maneuvers, like game pieces on a board, to achieve a winning position—a position that means a defeat for their partner. Seminaries, religions, churches, and para-churches may frame their institutional identity as zero-sum games. Rules and beliefs establish and dictate how and why the game is played and who may play it. If you play, you play to win. If you play, you may only play as long as you stick to the parochial system; otherwise you are out. Blogs—from religious to atheist—will make little progress in relational transformation if a zero-sum mentality demands winners and losers.
In these zero-sum games, a community builds a petty game with rules and beliefs that exclude a multitude of other realities, creating a system of thought that is placed above people and transforming relationships.
The most famous example in game theory is the Prisoner’s Dilemma devised by Merrill Flood and Melvin Dresher. The basic idea of the Prisoner’s Dilemma is this: The police have arrested you and your partner-in-crime on suspicion of robbing a bank. Lucky for you, the prosecutor lacks sufficient evidence to convict. You and your friend, however, are locked in separate, isolated cells and the prosecutor comes to you with a few options:
• Confess and we will let you go free and put your friend behind bars for 15 years.
• Don’t confess and if your partner confesses we will put you in jail for 15 years.
• If you both confess, we will drop the penalty to 3 years.
• If neither of you talk, well, we have enough to convict you on a lesser charge and put you both away for 6 months.
What do you do? The dilemma is this: the rational choice is to confess, no matter what your friend does. If they do not confess, you go free. If they confess, you only get three years instead of fifteen. But here is the catch: if you both keep silent the jail time is even less—only six months instead of three years. Do you confess or stay silent, or in the language of game theory, do you defect or cooperate? In the Prisoner’s Dilemma, the rational choice is to defect, but the best possible outcome for both of you is to cooperate and keep silent.
Cooperation needs a relational connection. To achieve the best possible outcome we need trust, but trust is vulnerable to exploitation. Do you trust your friend enough, because if you co-operate and they deflect, then you are behind bars for fifteen years? In this case, game theory underscores that trust and cooperation achieves the best outcome for everyone. The rational choice is not always the best. The relational choice is the best.
Game theorists have studied many variations of the Prisoner’s Dilemma including iterative cases. Most interactions in life are not once off. Instead of a one-off game, what happens when we have the opportunity to repeat the game a hundred times? What strategy should we now adopt? The answer was discovered in two experiments organized by the political scientist Robert Axelrod, author of the highly influential The Evolution of Cooperation, a book that opened with the question: “Under what conditions will cooperation emerge in a world of egoists without central authority?” Axelrod invited game theorists in economics, psychology, sociology, evolutionary biology, political science, mathematics, physics, and computer science to submit computer programs that would compete against each other in an iterative Prisoner’s Dilemma scenario. What program would receive the highest score? One that was more willing to cooperate? One that defected all the time?
Axelrod describes some of the programs:
Massive retaliatory strike: cooperate at first, but after a defection, retaliate for the rest of the game.
Tester: this program tries to find out what you are like, so it attacks in the first move. If met with retaliation, it will cooperate for a while. Then it will defect again, just to see how much it can get away with.
Jesus: always cooperate
Lucifer: always defect
If Tester plays Massive retaliatory strike, they both do poorly. Tester defects on the first move and Massive retaliatory strike defects from them on.
If Lucifer plays Jesus, Lucifer wins.
Axelrod thought that the winning program would contain thousands or tens of thousands of lines of code. The mathematical psychologist Anatol Rapoport submitted the highest scoring program, and it was also one of the simplest, five lines of code, a tit-for-tat program, where co-operation was met with co-operation, and defection met with defection. Overall, the top ranking programs were all nice, and on average, the defector programs scored significantly lower.
Axelrod described the tit-for-tat program as nice, retaliatory, forgiving, and clear. It is nice so it starts with co-operation. It retaliates to discourage the other player from continued defection. It forgives and quickly restores cooperation. It is clear in that it is not duplicitous; its actions are straight forward and easily interpreted, thus providing a basis for long-term cooperation. The one distinguishing feature of programs that did well versus those that did poorly, was being nice. In other words, start with trust and co-operation, and avoid unnecessary conflict. A nice player is never the first to defect and co-operates whenever the other player co-operates. Surprising, nice people finish first.
Tit-for-tat is the most successful strategy when the Prisoner’s Dilemma is played numerous times. You start with co-operation and basic trust. If the other player cooperates, you continue to cooperate. If they defect, then you respond with defection. The strategy punishes those who take advantage of other players’ trust and generosity. The strategy, however, also allows for a change of mind. After deflecting, your opponent may once again decide to co-operate with you. In tit-for-tat, you respond with cooperation.
To express these ideas in theological language, for an iterative game that achieves the best outcomes for all players, we need trust, forgiveness, and repentance. Trust is necessary for cooperation and as we cooperate we repeatedly send the message that we are trustworthy. In a repeated game, however, there will be failures by all players. Forgiveness is necessary, for it allows us to continue to play the game when a defector decides to cooperate. Repentance is necessary, for it allows us to change from defecting to cooperating. It turns out that forgiveness and repentance are even more important than first realized by game theorists. In the complicated world of relationships, signals can be misinterpreted. Perhaps a player intended to cooperate but her actions are misconstrued as a defection. A player can make a mistake or perhaps they just need a second chance. Does the game now have to continue with repeated retaliation? Here is where a small tweak optimizes the tit-for-tat program; named “generous tit-for-tat,” it will randomly throw in a forgiveness about ten percent of the time. Call it grace—an undeserved mercy that breaks a cycle of repeated defection.
Playing games that benefit all players depends on healthy relationships. If we are in relationship with other players, we are more likely to cooperate than defect. Relationships encourage a willingness to forgive and repent. Relationships temper our fear that we will be tricked. And relationships temper our greed that seeks outcomes advantageous to us while at the expense of other players.
The tit-for-tat strategy illustrates that a relational approach is far from being a sugary pushover. Unconditional pacifism is a losing strategy because psychopaths and con-artists are always scouting to exploit some unwary soul, softie, or sucker. A relational approach that includes trust, forgiveness, and repentance, also includes a credible threat of repercussion for defection. “If another person sins, rebuke that person; if there is repentance, forgive” (Luke 17:3). A relational approach will retaliate, for example, against the zero-sum games of patriarchy, racism, and other forms of bigotry. It starts with trust and co-operation, is quick to forgive, but will also punish defectors.
There is, however, a problem with a game repeated a finite amount of times. If you know the game is finite and is going to end after a hundred moves, then even after repeated cooperation, the rational strategy is to defect in the final move. Take the money and run—there is no retaliation because the game has ended. This suggests the importance of infinite games, games that continue indefinitely, where there is no end and therefore no temptation to defect at the end.
The religious scholar James Carse has developed this idea in Finite and infinite games: a vision of life as play and possibility. Carse distinguishes between two types of games: finite and infinite. There are substantial differences between the characteristics and goals of finite and infinite games. Carse writes, “A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.” A finite game ends when somebody wins, thus finite games need fixed boundaries and unchanging rules to decide who wins. Because of the boundaries of finite games, it is impossible to play an infinite game within a finite game. In contrast, infinite games are ongoing and have no fixed boundaries or rules. Thus for Carse, “Every move of an infinite player makes is toward the horizon. Every move made by a finite player is within a boundary. Every moment of an infinite game therefore presents a new vision, a new range of possibilities.”
For Carse, the goal of players of finite games are to become powerful, entitled, Master Players, supremely competent in every detail of the game that they essentially play as if the game is already completed. And because a finite game always ends, finite players have to repeatedly play to prove they are winners. In a finite game, the last thing you want is surprise, whereas in an infinite game, surprise is a reason for continuing to play. An infinite game is fluid and open ended, and the reasons for playing an infinite game are not to become powerful or to win. The concern of infinite players is “not with power but with vision.”
Finite games are defined by their boundaries, whereas infinite games are defined by their horizon. Boundaries are fixed and clear, and one cannot move beyond a boundary. But in an infinite game the horizon is open-ended—it is a direction toward we move, a place we never reach, a journey always open to newness and surprise.
Is Christianity a finite or an infinite game? What should it be? We would be naïve to assume that there is one message of Christianity. In the church’s two thousand year history, people have expressed a multitude of different ideas about Jesus and different versions of Christianity.
It is possible to conceive of Christianity as a finite or an infinite game.
1. Christianity formulated as a finite zero-sum game: we win; everyone else loses. We are master players, essential to this grand game, a game that has a definitive conclusion resulting in a win for us, and a loss for everyone else. The game is one of good versus evil, us versus them. Our particular beliefs and rules establish fixed boundaries of the game, and distinguish us from other Christians and their games. You may join our game and play, but only if you accept the rules that structure and direct our game. The benefits include power, titles, solid explanations, fixed boundaries, solidarity with us, and a winning hand.
As a finite game, Christianity has had little difficulty aligning itself with patriarchy, slavery, racism, hate crimes, torture and death of infidels, and colluding with empires—Roman, Spanish, English, American. In each case, there are clear winners and losers.
If Christianity is setup as a megalomaniacal finite game, it is impossible to play an infinite game. By its nature, it excludes the possibility of the gospel story as an infinite game.
2. A vision of Christianity as infinite play: Jesus creates a new playground that plays fast and loose with the rules, dissolves boundaries and fixed beliefs, and opens new horizons of possibility. In an infinite game, the central themes of the gospel story—incarnation, life, death, resurrection—are articulated in ways that place people and relationships above the system. In Christ, there are no winners or losers—there is neither Jew nor Gentile, slave nor free, male nor female (Gal 3:28). Jesus is not a master player but an infinite player who invites all to an infinite game by including the excluded and rebuking the excluders. Anyone can play, no titles are awarded, no winners are announced, and boundaries are replaced by a gospel horizon.
This infinite game is characterized by vision and openness, where beliefs and rules are continually rewritten in order to keep the game going. To put boundaries on an infinite game, destroys it and stops the game. There is no end of play, and if need be, infinite players will choose death over life in order for the game to continue.
The gospel story as an infinite game contrasts with the beliefs and rules of finite games. Beliefs are certain and bounded. Stories have development, surprises, twists, paradoxes, uncertainties, even contradictions. Beliefs often end the conversation. An infinite story invites further discovery, directs us to the horizon, continues the game, and reformulates the conversation.
If the story is a great pyramid of inspiration and awe, beliefs are limestone rocks dug out from the structure. Beliefs are not necessarily bad, we just need to recognize them for what they are—abstractions from the story, attempts to collate our understanding, pieces of rock dismantled from the magnificent structure. Sometimes these rocks are useful for constructing smaller buildings, but often people just throw them at others. Beliefs are ready tools to create finite or zero-sum games that leverage power over others, but if all we have is rocks, we have reduced the grand story to rubble and can no longer resonate with its openness, poetry, surprises, and vision.
There is an infinite game, an infinite story, which starts: in the beginning was the game maker, and the one who plays, and the one who invites others to join the game and continue the play....
• Don’t confess and if your partner confesses we will put you in jail for 15 years.
• If you both confess, we will drop the penalty to 3 years.
• If neither of you talk, well, we have enough to convict you on a lesser charge and put you both away for 6 months.
What do you do? The dilemma is this: the rational choice is to confess, no matter what your friend does. If they do not confess, you go free. If they confess, you only get three years instead of fifteen. But here is the catch: if you both keep silent the jail time is even less—only six months instead of three years. Do you confess or stay silent, or in the language of game theory, do you defect or cooperate? In the Prisoner’s Dilemma, the rational choice is to defect, but the best possible outcome for both of you is to cooperate and keep silent.
Cooperation needs a relational connection. To achieve the best possible outcome we need trust, but trust is vulnerable to exploitation. Do you trust your friend enough, because if you co-operate and they deflect, then you are behind bars for fifteen years? In this case, game theory underscores that trust and cooperation achieves the best outcome for everyone. The rational choice is not always the best. The relational choice is the best.
Game theorists have studied many variations of the Prisoner’s Dilemma including iterative cases. Most interactions in life are not once off. Instead of a one-off game, what happens when we have the opportunity to repeat the game a hundred times? What strategy should we now adopt? The answer was discovered in two experiments organized by the political scientist Robert Axelrod, author of the highly influential The Evolution of Cooperation, a book that opened with the question: “Under what conditions will cooperation emerge in a world of egoists without central authority?” Axelrod invited game theorists in economics, psychology, sociology, evolutionary biology, political science, mathematics, physics, and computer science to submit computer programs that would compete against each other in an iterative Prisoner’s Dilemma scenario. What program would receive the highest score? One that was more willing to cooperate? One that defected all the time?
Axelrod describes some of the programs:
Massive retaliatory strike: cooperate at first, but after a defection, retaliate for the rest of the game.
Tester: this program tries to find out what you are like, so it attacks in the first move. If met with retaliation, it will cooperate for a while. Then it will defect again, just to see how much it can get away with.
Jesus: always cooperate
Lucifer: always defect
If Tester plays Massive retaliatory strike, they both do poorly. Tester defects on the first move and Massive retaliatory strike defects from them on.
If Lucifer plays Jesus, Lucifer wins.
Axelrod thought that the winning program would contain thousands or tens of thousands of lines of code. The mathematical psychologist Anatol Rapoport submitted the highest scoring program, and it was also one of the simplest, five lines of code, a tit-for-tat program, where co-operation was met with co-operation, and defection met with defection. Overall, the top ranking programs were all nice, and on average, the defector programs scored significantly lower.
Axelrod described the tit-for-tat program as nice, retaliatory, forgiving, and clear. It is nice so it starts with co-operation. It retaliates to discourage the other player from continued defection. It forgives and quickly restores cooperation. It is clear in that it is not duplicitous; its actions are straight forward and easily interpreted, thus providing a basis for long-term cooperation. The one distinguishing feature of programs that did well versus those that did poorly, was being nice. In other words, start with trust and co-operation, and avoid unnecessary conflict. A nice player is never the first to defect and co-operates whenever the other player co-operates. Surprising, nice people finish first.
Tit-for-tat is the most successful strategy when the Prisoner’s Dilemma is played numerous times. You start with co-operation and basic trust. If the other player cooperates, you continue to cooperate. If they defect, then you respond with defection. The strategy punishes those who take advantage of other players’ trust and generosity. The strategy, however, also allows for a change of mind. After deflecting, your opponent may once again decide to co-operate with you. In tit-for-tat, you respond with cooperation.
To express these ideas in theological language, for an iterative game that achieves the best outcomes for all players, we need trust, forgiveness, and repentance. Trust is necessary for cooperation and as we cooperate we repeatedly send the message that we are trustworthy. In a repeated game, however, there will be failures by all players. Forgiveness is necessary, for it allows us to continue to play the game when a defector decides to cooperate. Repentance is necessary, for it allows us to change from defecting to cooperating. It turns out that forgiveness and repentance are even more important than first realized by game theorists. In the complicated world of relationships, signals can be misinterpreted. Perhaps a player intended to cooperate but her actions are misconstrued as a defection. A player can make a mistake or perhaps they just need a second chance. Does the game now have to continue with repeated retaliation? Here is where a small tweak optimizes the tit-for-tat program; named “generous tit-for-tat,” it will randomly throw in a forgiveness about ten percent of the time. Call it grace—an undeserved mercy that breaks a cycle of repeated defection.
Playing games that benefit all players depends on healthy relationships. If we are in relationship with other players, we are more likely to cooperate than defect. Relationships encourage a willingness to forgive and repent. Relationships temper our fear that we will be tricked. And relationships temper our greed that seeks outcomes advantageous to us while at the expense of other players.
The tit-for-tat strategy illustrates that a relational approach is far from being a sugary pushover. Unconditional pacifism is a losing strategy because psychopaths and con-artists are always scouting to exploit some unwary soul, softie, or sucker. A relational approach that includes trust, forgiveness, and repentance, also includes a credible threat of repercussion for defection. “If another person sins, rebuke that person; if there is repentance, forgive” (Luke 17:3). A relational approach will retaliate, for example, against the zero-sum games of patriarchy, racism, and other forms of bigotry. It starts with trust and co-operation, is quick to forgive, but will also punish defectors.
There is, however, a problem with a game repeated a finite amount of times. If you know the game is finite and is going to end after a hundred moves, then even after repeated cooperation, the rational strategy is to defect in the final move. Take the money and run—there is no retaliation because the game has ended. This suggests the importance of infinite games, games that continue indefinitely, where there is no end and therefore no temptation to defect at the end.
The religious scholar James Carse has developed this idea in Finite and infinite games: a vision of life as play and possibility. Carse distinguishes between two types of games: finite and infinite. There are substantial differences between the characteristics and goals of finite and infinite games. Carse writes, “A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.” A finite game ends when somebody wins, thus finite games need fixed boundaries and unchanging rules to decide who wins. Because of the boundaries of finite games, it is impossible to play an infinite game within a finite game. In contrast, infinite games are ongoing and have no fixed boundaries or rules. Thus for Carse, “Every move of an infinite player makes is toward the horizon. Every move made by a finite player is within a boundary. Every moment of an infinite game therefore presents a new vision, a new range of possibilities.”
For Carse, the goal of players of finite games are to become powerful, entitled, Master Players, supremely competent in every detail of the game that they essentially play as if the game is already completed. And because a finite game always ends, finite players have to repeatedly play to prove they are winners. In a finite game, the last thing you want is surprise, whereas in an infinite game, surprise is a reason for continuing to play. An infinite game is fluid and open ended, and the reasons for playing an infinite game are not to become powerful or to win. The concern of infinite players is “not with power but with vision.”
Finite games are defined by their boundaries, whereas infinite games are defined by their horizon. Boundaries are fixed and clear, and one cannot move beyond a boundary. But in an infinite game the horizon is open-ended—it is a direction toward we move, a place we never reach, a journey always open to newness and surprise.
Is Christianity a finite or an infinite game? What should it be? We would be naïve to assume that there is one message of Christianity. In the church’s two thousand year history, people have expressed a multitude of different ideas about Jesus and different versions of Christianity.
It is possible to conceive of Christianity as a finite or an infinite game.
1. Christianity formulated as a finite zero-sum game: we win; everyone else loses. We are master players, essential to this grand game, a game that has a definitive conclusion resulting in a win for us, and a loss for everyone else. The game is one of good versus evil, us versus them. Our particular beliefs and rules establish fixed boundaries of the game, and distinguish us from other Christians and their games. You may join our game and play, but only if you accept the rules that structure and direct our game. The benefits include power, titles, solid explanations, fixed boundaries, solidarity with us, and a winning hand.
As a finite game, Christianity has had little difficulty aligning itself with patriarchy, slavery, racism, hate crimes, torture and death of infidels, and colluding with empires—Roman, Spanish, English, American. In each case, there are clear winners and losers.
If Christianity is setup as a megalomaniacal finite game, it is impossible to play an infinite game. By its nature, it excludes the possibility of the gospel story as an infinite game.
2. A vision of Christianity as infinite play: Jesus creates a new playground that plays fast and loose with the rules, dissolves boundaries and fixed beliefs, and opens new horizons of possibility. In an infinite game, the central themes of the gospel story—incarnation, life, death, resurrection—are articulated in ways that place people and relationships above the system. In Christ, there are no winners or losers—there is neither Jew nor Gentile, slave nor free, male nor female (Gal 3:28). Jesus is not a master player but an infinite player who invites all to an infinite game by including the excluded and rebuking the excluders. Anyone can play, no titles are awarded, no winners are announced, and boundaries are replaced by a gospel horizon.
This infinite game is characterized by vision and openness, where beliefs and rules are continually rewritten in order to keep the game going. To put boundaries on an infinite game, destroys it and stops the game. There is no end of play, and if need be, infinite players will choose death over life in order for the game to continue.
The gospel story as an infinite game contrasts with the beliefs and rules of finite games. Beliefs are certain and bounded. Stories have development, surprises, twists, paradoxes, uncertainties, even contradictions. Beliefs often end the conversation. An infinite story invites further discovery, directs us to the horizon, continues the game, and reformulates the conversation.
If the story is a great pyramid of inspiration and awe, beliefs are limestone rocks dug out from the structure. Beliefs are not necessarily bad, we just need to recognize them for what they are—abstractions from the story, attempts to collate our understanding, pieces of rock dismantled from the magnificent structure. Sometimes these rocks are useful for constructing smaller buildings, but often people just throw them at others. Beliefs are ready tools to create finite or zero-sum games that leverage power over others, but if all we have is rocks, we have reduced the grand story to rubble and can no longer resonate with its openness, poetry, surprises, and vision.
There is an infinite game, an infinite story, which starts: in the beginning was the game maker, and the one who plays, and the one who invites others to join the game and continue the play....
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