The Paradox of Spontaneous Formation of Private Legal Systems

ion is made by determining a ‘payoff’ to each player (i.e., benefit conferred on the player) based on both what that player did, and what others interacting with that player do. The payoff is measured in “utils”, a generic scale measuring benefits of any kind conferred on a player (e.g., money, other material benefits, spiritual elation, a sense of being loved, etc.). There might be a different payoff to the player for each combination of her and others’ actions; mirroring real life, the choice a player makes affects her welfare, but so do the choices others make. To reduce complication, several abstractions will be made in the games examined in this paper. First, it is assumed there are two players—a network member and the other network members (or a network member and the network governance institution). Second, each player is limited a choice between two actions. These actions will change from game to game depending on the illustrative story of the game, but generally they will be called ‘Cooperate’ ({C}) and ‘Default’ ({D}). To clarify the concept of a game type, consider the ‘function’ of providing a venue for scorn: Statler and Waldorf, the grumpy old men sitting on the balcony in “The Muppets’ Show”, love to express derision at anything and everything. When the Muppets Show is not on and they find no targets for their venom on stage, they must verbally attack each other. The best that can possibly happen from Statler’s point of view is when he says something nasty to Waldorf, and Waldorf does not reply. Second to this “oneupsmanship” is a situation in which they exchange gibes. Much less satisfying is a 69 To make the illustrative examples more intuitive, this paper will sometimes call the more socially beneficial of the two actions “cooperating”, while the other, less virtuous action will be called “defaulting”. But this is not always the case. There does not have to be anything morally or socially better in an action called “cooperating” over an action called “defaulting”. In some games, the two options would be equivalent morally and from a welfare-maximizing perspective. For example, in the Battle of the Sexes game, described supra, in Section III.3, the “cooperating” action is going to see a baseball game, while the “defaulting” action is going to see a movie. The tags of cooperation and default are used merely to make this game comparable to other games discussed in this section, and not to denote a positive or negative connotation to either action. The Paradox of Spontaneous Formation of Private Legal Systems/Amitai Aviram 29 situation in which both Statler and Waldorf are nice to each other, and their venom fails to find an outlet. Bad as that sounds, it can get worse—Statler might act nicely to Waldorf, who in return will mock Statler with a nasty jeer; suffering an unanswered jab is even worse than having everyone play nice. Waldorf has the same preferences as Statler (reversing the roles, of course). Abstracting these preferences into a table, the payoff structure will look like this: Waldorf acts nicely Waldorf mocks Statler acts nicely 1,1 0,3 Statler mocks 3,0 2,2 Placing the payoff information in a table helps us identify the likely outcome. Let’s put ourselves in Statler’s shoes. If he expects Waldorf to act nicely, Statler is better off mocking him (he will then get 3 “utils” (southwest box) instead of one util (northwest box)). And if Statler expects Waldorf to mock him, Statler will—once again, mock Waldorf (he will get 2 utils (southeast box) rather than zero utils (northeast box)). So Statler will mock Waldorf regardless of what he expects Waldorf to do. Since Waldorf has the same preferences, he will reach the same conclusion, and the two will end up teasing and insulting each other. That’s good news—this happens to be the welfaremaximizing solution, since they get two utils each, or 4 total—a larger total than in any of the other boxes. This game is known as the “Deadlock” game, because if acting nicely were considered to be “cooperating”, the parties would be deadlocked in refusal to cooperate. The Deadlock game is among the most costly to enforce mutual cooperation—not only do the parties tend to not cooperate, but the welfare maximizing situation for them is 70 To summarize, the set of preferences for each player of the Deadlock game is: {D,C}>{D,D}>{C,C}>{C,D}. 71 For the payoff set in each box, Statler’s payoff is noted first, then Waldorf’s payoff. 72 A commonly cited real world example of this game would be arms control negotiations between two countries who do not want to disarm (i.e., would prefer that both they and their enemy be armed than both they and their enemy be unarmed). The likely result is a failure of the arms control negotiations. See, e.g., Janet Chen, Su-I Lu & Dan Vekhter, Game Theory—Non Zero Sum Games—Other Games, available at: http://cse.stanford.edu/classes/sophomore-college/projects-98/game-theory/dilemma.html. The Paradox of Spontaneous Formation of Private Legal Systems/Amitai Aviram 30 mutual default, so if they could coordinate, they’d attempt to enforce mutual default rather than mutual cooperation. Imagine, for example, Statler & Waldorf’s response if Kermit tried to force them to act kindly to each other... The following subsections will examine other games, their illustrative stories, their payoff structure, the likely behavior of the players and the relative ease of enforcing cooperation in them. A. Harmony The Harmony game can be seen to be an inverse of the Deadlock game. It is the easiest game in which to enforce mutual cooperation. In fact, no enforcement at all is necessary. Alice and Bill, two very good friends, face a choice between the same two actions that Statler and Waldorf chose from in the Deadlock game: they can act nicely to the other or they could mock him/her. Unlike Statler and Waldorf, each of them prefers to be nice to the other, even if he himself is slighted by the other (after all, the other’s slight may have been merely a misperception, and at any rate, they care for each other so much that hurting the other would indirectly hurt them). Next worst possibility is that they themselves somehow failed and mocked the other. In that case, each hopes that the other would show restraint and not mock back (this would be worse than being mocked while acting nicely, since the shame of being rude to one’s friend in the former case outweighs the anger at being mocked in the latter case). The worst for these two would be slipping into mutual taunting. Putting these preferences into a payoff table yields this: Bill acts nicely Bill mocks Alice acts nicely 3,3 2,1