Rules of the Game

Wojtek Sokolowski sokol at
Thu Jun 18 14:42:59 PDT 1998


I'll certainly try to find my notes with the rules, but I do not think that the actual rules how to win matter that much, as long as they meet certain formal properties I describe below.

What was important about the game (BTW, popular among a number of TAs at that time) could be summarized as follows:

1. It is a team effort; it is teams that lose or win; team assignment is random and cannot be changed throught the game; 2. It is a competitive game played in rounds; only one team can win each round 3. The rules are set in such a way that winning one round improves a team's chances of winning the next round (I do not remember what was the specific catch, though); and the more rounds you win the greater your chances of winning subsequent rounds. 4. Any rules of the game can be changed if the majority of players agree; therefore, the advantage of the winning team can be counterbalanced by the consesus of the losers.

Of course the object of the game was to demonstrate the benefits of consensus and collective action (the prisoner's dilemma); and people petitoning to be admitted to a winning team was not an anticipated outcome - this was an essentially individualist response that not only had no chance of passing, but also derailed the attempts of the losing players to win a consensus required to change the unfair rules. As long as the petitioners hoped to be admitted to the winning team, they had no incentive to change the rules that would wipe the advantage they hoped to get.

Just like in the US - even the lowest schmuck thinks he will strike it rich one day, and will resist any collective effort aimed at wealth redistribution. That, BTW, explains why the captains of industry in this country like to organize lotteries and sweepstakes so much. As in my old country they used to say: Hope is the mother of fools.

Please note that the actual rules of competition mentioned in item 3 above are not as important, as long as they meet one formal requirement: - the probablity of winning or losing subsequent rounds is a function of the outcomes of the previous rounds.

Think of it as a game of poker with unlimited bids, or the capitalist market - all players may start with more or less equal amount of money, but if you win one round, that gives you more money to play in subsequent rounds, and you can simply out-bid your competitors.

You can express that as the joint probability p=r*q where p is the probablity of your loosing a round; r is the probability of your opponents having a winning hand (a chance event), and q is the probability of your opponents being able to challenge you.

Please note that at the beginning of the game that probability is equal to 1 (every player must be able to challenge other players to be eligible to play), but it decreases as the opponents' resources shrink; and when their resources are depleted, q=0 meaning it is ceratin they will not challenge you; hence your probability of losing also equals zero (p=r*0=0), even if you have otherwise losing hand - you win by deafult.



At 04:01 PM 6/18/98 -0400, you wrote:
>if you do find the detailed rules to your game, i'd be quite
>interested. i go both ways on your conclusion, but maybe i'd be swayed
>one way or t'other if i saw what you actually pulled off.
>____ Les Schaffer godzilla at ___| ------->> Engineering R&D
>Theoretical & Applied Mechanics | Designspring, Inc. Westport,
>Center for Radiophysics & Space Research | les at
>Cornell Univ. schaffer at |

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