Sunday, May 01, 2005

Notes On Games And Life - Unabridged

i. “Will my number come up eventually? Like Love is some kind of lottery, where you can scratch and see what is underneath. It’s ‘Sorry’, just one cherry, ‘Play Again’. Get lucky.” (Bright Eyes. ‘Waste Of Paint’ on Lifted or The Story is in the Soil, Keep You Ear to the Ground (2002))

ii. “I have known what the Greeks do not know, incertitude.” (Jorge Luis Borges. ‘The Lottery in Babylon’ in Labyrinths (London: Penguin, 2000), p. 55)

iii. Game – “Contest played according to rules & decided by skill, strength, or luck” (The Concise Oxford Dictionary of Current English, Fifth Edition, p. 502)

iv. Game (Philosophic) – “this term includes but is not limited to contests and sports. To play a game is to attempt to achieve a certain state of affairs using only those means permitted by the rules” (Robert M. Martin. The Philosopher’s Dictionary, Third Edition (Peterborough, Ontario: Broadview Press, 2002), p. 133)

The toss of a coin
v. “they are betting on the toss of a coin, in the following manner: GUILDENSTERN … takes a coin out of his bag, spins it, letting it fall. ROSENCRANTZ … studies it, announces it as “heads” (as it happens) and puts it into his own bag. Then they repeat the process. They have apparently been doing this for some time.

The run of “heads” is impossible, yet [Rosencrantz] betrays no surprise at all – he feels none.” (Tom Stoppard. Rosencrantz and Guildenstern are Dead (London: Faber and Faber, 1974), p. 7)

vi. “The law of averages, if I have got this right, means that if six monkeys were thrown up in the air for long enough they would land on their tails about as often as they would land on their – ” (Stoppard. Rosencrantz and Guildenstern are Dead, p. 8)

Game Theory and The Prisoner’s Dilemma
vii. “a game is a choice situation where more than one individual is choosing and where the choices made by the participating individuals determine how well the other individuals’ choice turns out.” (Martin. The Philosopher’s Dictionary, p. 133)

viii. Áthamas and Báttus are being interrogated in separate cells by the Inquisition. They are accused of collaborating in a crime, but the Inquisition lacks the evidence necessary to convict them. The Inquisitors offer Áthamas and Báttus, individually, the same deal: if one of them confesses their guilt, and agrees to testify against their co-accused, he will be banished. If they stay silent, while their co-accused accepts the deal, it will be their partner who is banished while they are imprisoned for ten years. If both the co-accused confess, they are told, then both will be imprisoned for five years. While if neither confesses, the Inquisitors admit, the Inquisition will be unable to secure a conviction and both Áthamas and Báttus will be freed, though their property will be seized. Áthamas and Báttus are left with the choice to either ‘cooperate’ – that is remain silent – or to defect and confess their guilt to the Inquisitor.

ix. Payoff matrix for Áthamas and Báttus

Cooperate Defect
Cooperate Property seizure, Property seizure (2,2) 10 years, Banishment (4,1)
Defect Banishment, 10 years (1,4) 5 years, 5 years (3,3)

The numbers in brackets represent each player’s ranking of the options from most preferable (1) to least preferred (4)

x. Perhaps the solution is for Áthamas to confess and accept either being banished or imprisoned for five years …

xi. “Such a scenario postulates a lack of enforced co-operation; and to avoid the undesirable outcome, the actors in the drama need to be forced into co-operation by a system of rules. So it has been argued that we can find in this dilemma a basis for the generation of the institutions of morality – or, at least, of prudent co-operation. But that conclusion is challenged by others who point out that the same choice-theoretic problems also arise with ends that immoral or prudentially harmful.” (Ted Honderich [Ed.]. The Oxford Companion To Philosophy (Oxford: Oxford University Press, 1995), p. 719)

xii. “One way to express the paradoxical implications of prisoner’s dilemma-type situations is to say that when its conditions apply, rational agents do less well than irrational.” (Neil Levy. What Makes Us Moral? Crossing the Boundaries of Biology (Oxford: Oneworld Press, 2004), p. 63)

xiii. In each bout a player must adopt one of three strategies, choosing to play either ‘rock’, ‘scissors’, or ‘paper’. Rock blunts scissors, scissors cut paper, and paper wraps rock; in each case the dominate neutralises the subordinate.

xiv. Payoff matrix for rock-scissors-paper

Rock Scissors Paper
0,0 +1,-1 -1,+1
Scissors -1,+1 0,0 +1, -1
Paper +1,-1 -1,+1 0,0
(‘x,y’: ‘x’ equals player on the left, ‘y’ equals player above)

xv. “a player adopting the pure strategy ‘Rock’ will lost in the long run, because his opponent will catch on and play ‘Paper’. A player adopting the mixed strategy ‘1/3 Rock, 1/3 Scissors, 1/3 Paper’ will break even.” (John Maynard Smith. Did Darwin Get It Right? (Harmondsworth: Penguin), p. 206)

xvi. How often does the future course of events rest on the strategy employed to win a game of rock-scissors-paper?

xvii. “These things always happen …” (Jon Brion. ‘Strangest Times’ on i (heart) huckabees (2004))

xviii. So, heads-or-tails or rock-paper-scissors?

[This post is the unabridged text from which Martin's contribution to Opus 3, 2005 (p. 11) was drawn – Editor.]

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