The cooperative edge: new versions of Scrabble, bridge and basketball help teach us the advantages of cooperation in play and real life – includes related article

Gerald Rabow


WE ARE A PLAYFUL SPECIES. We start playing games in early childhood and keep playing them for most of our lives. They give us pleasure and, we are told, help prepare us for real life. Football is said to ready its players for the rough and tumble of business, and chess is encouraged in war colleges to sharpen strategy skills useful in battle. The games we play, however, ignore one fact of life–that there are many situations in which both sides can gain by cooperating.

What’s good for the Soviet Union, for example, such as arms reduction, is not necessarily bad for the United States. Playing as if we lose whenever the Soviets gain is both a poor way of conducting international relations and a good example of the zero-sum (ZS) thinking behind most familiar games: What one side wins, the other side losses. Any positive score by one side is in effect a negative score by the other; hence the name, zero sum. Such zero-sum thinking is also a poor approach to negotiations in business and in resolving personal disputes. Learning to play some cooperative non-zero-sum (NZS) games as children and as adults might help us reach better solutions to personal, national and international problems.

One rudimentary NZS game (see “The Prisoner’s Dilemma,” this article) has been studied extensively by psychologists and game theorists of all kinds. But more complex ZS games as diverse as Scrabble, bridge and basketball can be converted into challenging, enjoyable NZS games in which cooperation, as well as competition, is rewarded.

NZS SCRABBLE. In regular Scrabble, two to four players take turns placing lettr tiles on a special board to form words. Their score depends on, among other things, the letters of the new words formed by the play (each letter of the alphabet has a specific point value) and the position of the letters on the board. For ease of discussion, I’ll describe a two-player game, but the NZS adaptation also works well with more players.

Scrabble’s important characteristics, for our purpose, are that it requires skill in forming high-scoring words and that a particular play not only determines the player’s immediate score but can heavily influence what happense on the following play. Since the idea of conventional Scrabble is to obtain a higher score than the other player, strategy consists of limiting the opportunities for the other player as well as scoring high yourself.

Scrabble can be converted into an NZS game by changing each player’s objective to that of obtaining as high a score as possible, regardless of the other player’s score. The task offorming high-scoring words remains, but the strategy of limiting opportunities for the other player is changed. Now each player wants to induce cooperation from the other to produce a mutually high-scoring game. There is also opportunity for competition. If one player grabs a choice spot on the board, it becomes unavailable to the other player.

The strategy for NZS Scrabble is more complicated than the “nice” Tit-for-Tat strategy described in “The Prisoner’s Dilemma.” Instead of having only two choices, to cooperate or not, a player can cooperate to a greater or lesser degree and can retaliate to various degrees when the other player doesn’t seem to cooperate. In addition, the amount of cooperation or retaliation intended by player A may not be clear to player B and vice versa. For example, B sometimes can’t evaluate A’s situation accurately because B doesn’t know precisely which letter tiles A has available to play.

Further, failure to make the most cooperative move may be due to failure to find that move, rather than a deliberate attempt to take advantage of the other player. The players have differing abilities and a superior player, even when being scrupulously nice, can achieve a consistently higher score in a match with a lesser player.

Strategy near the end of the game, when retaliation in that game is no longer effective, poses another interesting question: Will players continue to play nice through the end of the match with another player, hoping to achieve a reputation that might help them in future games?

NZS BRIDGE. In conventional ZS bridge, as in team games generally, partners cooperate completely with each other while competing against their opponents. In bidding preceding the play of cards, one of the two-player partnerships becomes declarer with a contract to win at least a specific number of the 13 tricks available. If the contract is made, the declarer side scores; if not, the defenders score. The size of the score depends on the contract, the number of tricks made and the results of the previous deals.

You convert conventional bridge into NZS bridge by dividing the normal partnership score at the end of each deal between the partners in proportion to the number of tricks each has won. This converts the identical goals of partners in conventional bridge into an NZS relationship. The members of each partnership must still cooperate in the contest with their opponents, but they now also compete with each other to receive the largest possible fraction of the partnership score.

Good strategy requires that the partners not allow competition between them to diminish their joint score. There will be many borderline cases, however, in which it is not clear whether something a player does to increase his or her fraction of the partnership score will work out well or disastrously. A competitive move that inadvertently results in a partnership winning only 9 tricks rather than the contracted 10 in a particular hand, for example, may make a player lose a hundred points on the deal rather than winning several hundred by making the contract.

NZS BASKETBALL. This version retains the task and most of the rules of conventional basketball but changes each player’s objective from concern for the team scor to concern with individual points. This creates a tension between cooperating and competing with members of your own team. Cooperation is necessary to overcome the other side’s defense, but you are competing for the opportunity to score yourself rather than pass the ball to a teammate for a score.

Each player’s socre is the conventional point value of one to three points, depending on the situation, each time that player shoots the ball through the hoop, minus one-fifth of the number of points scored by the other team while the player is in the game. The reason for the subtraction is to make the combined score of the teams zero while maintaining an incentive to play defense. Otherwise, it would be to the advantage of all 10 players to just run up the score, thereby losing the balance between offense and defense that makes the game challenging.

The NZS component is the interaction among the players on each team. They cooperate to increase their score, just as partners do in NZS bridge, but they compete for individual opportunities to score. Players who do not cooperate will fare poorly, for example, because it takes coordinated play to score well against a good team.

The NZS variant of basketball has some advantages for the players. In conventional basketball, the coaches’ overwhelming interest in having their team win sometimes conflicts with acting in the best interest of each player. In NZS basketball, since there are no team victories, coaches can concentrate on teaching and developing the players. For the same reason, the coaching and refereeing functions can be combined and all players can get roughly equal playing time. Players rather than coaches can make strategic decisions, with coaches available to resolve any disputes that arise among the players.

These three NZS games appear to be the ones most readily adaptable from common games, but some entirely novel ones can surely be devised. The fact that NZS games call for new kinds of cooperation and competition with other players can make them more interesting to play. And the new skills that they stimulate can be useful in the real, NZS world. The strategies that successful players evolve may even provide some useful insights into solving real-world problems.

COPYRIGHT 1988 Sussex Publishers, Inc.

COPYRIGHT 2004 Gale Group

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